USF Libraries
USF Digital Collections

Stress analysis and mechanical characterization of thin films for microelectronics and MEMS applications

MISSING IMAGE

Material Information

Title:
Stress analysis and mechanical characterization of thin films for microelectronics and MEMS applications
Physical Description:
Book
Language:
English
Creator:
Waters, Patrick
Publisher:
University of South Florida
Place of Publication:
Tampa, Fla
Publication Date:

Subjects

Subjects / Keywords:
Residual stress
Sputtering
X-ray diffraction
Nanoindentation
Wafer curvature
Dissertations, Academic -- Mechanical Engineering -- Doctoral -- USF   ( lcsh )
Genre:
non-fiction   ( marcgt )

Notes

Summary:
ABSTRACT: Thin films are used for a variety of applications, which can include electronic devices, optical coatings and decorative parts. They are used for their physical, electrical, magnetic, optical and mechanical properties, and many times these properties are required simultaneously. Obtaining these desired properties starts with the deposition process and they are verified by a number of analysis techniques after deposition. A DC magnetron sputter system was used here to deposit tungsten films, with film thickness and residual stress uniformity being of primary interest. The film thickness was measured to vary by up to 45 % from the center to outer edge of a 4" wafer. Ar pressure was found to influence the thin film residual stress with lower Ar pressures leading to compressive residual stress (-1.5 GPa) and higher Ar pressures leading to tensile residual stress (1 GPa).Residual stress measurements of the tungsten films were made using a wafer curvature technique and X-ray diffraction. The results of the two techniques were compared and found to be within 20 %. Nanoindentation was used to analyze the mechanical properties of several types of thin films that are commonly used in microelectronic devices. Thin film reduced modulus, hardness, interfacial toughness and fracture toughness were some of the mechanical properties measured. Difficulties with performing shallow indents (less than 100 nm) were addressed, with proper calibration procedures for the indentation equipment and tip area function detailed. Pile-up during the indentation of soft films will lead to errors in the indentation contact depth and area, leading to an overestimation of the films' reduced modulus and hardness.A method was developed to account for pile-up in determining the indentation contact depth and calculating a new contact area for improving the analysis of reduced modulus and hardness. Residual stresses in thin films are normally undesired because in extreme cases they may result in thru-film cracking or interfacial film delamination. With the use of lithography techniques to pattern wafers with areas of an adhesion reducing layer, thin film delamination was controlled. The patterned delamination microchannels may be used as an alternative method of creating microchannels for fluid transport in MEMS devices. Delamination morphology was influenced by the amount of residual stress in the film and the critical buckling stress, which was primarily controlled by the width of the adhesion reducing layers.
Thesis:
Dissertation (Ph.D.)--University of South Florida, 2008.
Bibliography:
Includes bibliographical references.
System Details:
Mode of access: World Wide Web.
System Details:
System requirements: World Wide Web browser and PDF reader.
Statement of Responsibility:
by Patrick Waters.
General Note:
Title from PDF of title page.
General Note:
Document formatted into pages; contains 196 pages.
General Note:
Includes vita.

Record Information

Source Institution:
University of South Florida Library
Holding Location:
University of South Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
aleph - 002000964
oclc - 319169370
usfldc doi - E14-SFE0002523
usfldc handle - e14.2523
System ID:
SFS0026840:00001


This item is only available as the following downloads:


Full Text
xml version 1.0 encoding UTF-8 standalone no
record xmlns http:www.loc.govMARC21slim xmlns:xsi http:www.w3.org2001XMLSchema-instance xsi:schemaLocation http:www.loc.govstandardsmarcxmlschemaMARC21slim.xsd
leader nam Ka
controlfield tag 001 002000964
003 fts
005 20090424141058.0
006 m||||e|||d||||||||
007 cr mnu|||uuuuu
008 090424s2008 flu s 000 0 eng d
datafield ind1 8 ind2 024
subfield code a E14-SFE0002523
035
(OCoLC)319169370
040
FHM
c FHM
049
FHMM
090
TJ145 (Online)
1 100
Waters, Patrick.
0 245
Stress analysis and mechanical characterization of thin films for microelectronics and MEMS applications
h [electronic resource] /
by Patrick Waters.
260
[Tampa, Fla] :
b University of South Florida,
2008.
500
Title from PDF of title page.
Document formatted into pages; contains 196 pages.
Includes vita.
502
Dissertation (Ph.D.)--University of South Florida, 2008.
504
Includes bibliographical references.
516
Text (Electronic dissertation) in PDF format.
520
ABSTRACT: Thin films are used for a variety of applications, which can include electronic devices, optical coatings and decorative parts. They are used for their physical, electrical, magnetic, optical and mechanical properties, and many times these properties are required simultaneously. Obtaining these desired properties starts with the deposition process and they are verified by a number of analysis techniques after deposition. A DC magnetron sputter system was used here to deposit tungsten films, with film thickness and residual stress uniformity being of primary interest. The film thickness was measured to vary by up to 45 % from the center to outer edge of a 4" wafer. Ar pressure was found to influence the thin film residual stress with lower Ar pressures leading to compressive residual stress (-1.5 GPa) and higher Ar pressures leading to tensile residual stress (1 GPa).Residual stress measurements of the tungsten films were made using a wafer curvature technique and X-ray diffraction. The results of the two techniques were compared and found to be within 20 %. Nanoindentation was used to analyze the mechanical properties of several types of thin films that are commonly used in microelectronic devices. Thin film reduced modulus, hardness, interfacial toughness and fracture toughness were some of the mechanical properties measured. Difficulties with performing shallow indents (less than 100 nm) were addressed, with proper calibration procedures for the indentation equipment and tip area function detailed. Pile-up during the indentation of soft films will lead to errors in the indentation contact depth and area, leading to an overestimation of the films' reduced modulus and hardness.A method was developed to account for pile-up in determining the indentation contact depth and calculating a new contact area for improving the analysis of reduced modulus and hardness. Residual stresses in thin films are normally undesired because in extreme cases they may result in thru-film cracking or interfacial film delamination. With the use of lithography techniques to pattern wafers with areas of an adhesion reducing layer, thin film delamination was controlled. The patterned delamination microchannels may be used as an alternative method of creating microchannels for fluid transport in MEMS devices. Delamination morphology was influenced by the amount of residual stress in the film and the critical buckling stress, which was primarily controlled by the width of the adhesion reducing layers.
538
Mode of access: World Wide Web.
System requirements: World Wide Web browser and PDF reader.
590
Advisor: Alex Volinsky, Ph.D.
653
Residual stress
Sputtering
X-ray diffraction
Nanoindentation
Wafer curvature
690
Dissertations, Academic
z USF
x Mechanical Engineering
Doctoral.
773
t USF Electronic Theses and Dissertations.
4 856
u http://digital.lib.usf.edu/?e14.2523



PAGE 1

Stress Analysis and Mechanical Characterization of Thin Films for Microe lectronics and MEMS Applications by Patrick Waters A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Mechanical Engineering College of Engineering University of South Florida Major Professor: Alex Volinsky, Ph.D. Craig Lusk, Ph.D. Frank Pyrtle, Ph.D. Ralph Fehr, Ph.D. George Nolas, Ph.D. Date of Approval: April 22, 2008 Keywords: residual stress, sputtering, X-ray diffraction, nanoindentation, wafer curvature Copyright 2008 Patrick Waters

PAGE 2

Dedication I would like to dedicate this manuscript to my parents. This would not have been possible without the support and guidance they have provided me throughout the years.

PAGE 3

Acknowledgements I would like to thank my advisor Alex Volinsky for guiding me through this process. He has always made himself available for any questions and problems t hat I’ve had. I would also like to thank the staff of the Mechanical Engineering Departme nt for all the help they’ve given me throughout my entire stay at USF, specifically S ue Britten, Wes Frusher and Shirley Tevort. Most importantly, I would like to thank my wife Heather for her incredible patience in dealing with me while I’ve been in gra duate school.

PAGE 4

Note to Reader The original of this document contains color that is necessary for understanding the data. The original dissertation is on file with the USF library in Tampa, Fl orida.

PAGE 5

i Table of Contents List of Tables.....................................................................................................................iii List of Figures....................................................................................................................iv List of Nomenclature..........................................................................................................x ABSTRACT......................................................................................................................xii Chapter 1 Introduction........................................................................................................1 1.1 Motivation for Thin Film and MEMS Research.......................................................1 1.2 Thin Films.................................................................................................................6 1.3 Thin Film Characterization.......................................................................................8 1.4 Chapter Objectives....................................................................................................9 Chapter 2 Sputter Deposition............................................................................................11 2.1 Introduction.............................................................................................................11 2.1.1 Sputtering Yield...............................................................................................12 2.2 DC Magnetron Sputter Deposition.........................................................................19 2.2.1 Glow Discharge Plasma...................................................................................21 2.2.2 Magnetic Field in Sputtering...........................................................................25 2.3 Gas Pressure Effects...............................................................................................34 2.4 Film Structure.........................................................................................................42 2.5 Summary of Sputtering Results..............................................................................49 Chapter 3 Residual Stresses in Thin Films.......................................................................51 3.1 Thin Film Residual Stress.......................................................................................51 3.2 Measuring Residual Stress......................................................................................53 3.2.1 Curvature Method............................................................................................54 3.2.2 Stress Calculation Assuming Uniform Curvature and Film Thickness...........59 3.2.3 Accounting for Non-uniformities....................................................................62 3.2.4 X-ray Diffraction.............................................................................................78 3.3 Summary of Stress Measurements..........................................................................96 Chapter 4 Thin Film Mechanical Testing.......................................................................101 4.1 Nanoindentation....................................................................................................101 4.2 Indentation Calibration and Analysis....................................................................105 4.2.1 Indentation Stiffness......................................................................................108 4.2.2 Tip Area Function..........................................................................................110 4.2.3 Finding the Tip Radius...................................................................................113 4.2.4 Machine Compliance of the Indenter.............................................................119

PAGE 6

ii 4.3 Material Effects.....................................................................................................123 4.3.1 Pile-up During Indentation............................................................................124 4.4 Dynamic Testing...................................................................................................130 4.5 Non-traditional Tests............................................................................................135 4.5.1 Adhesion Measurements................................................................................136 4.5.2 Fracture Toughness Measurements................................................................151 Chapter 5 Delaminated Film Buckling Microchannels..................................................160 5.1 Introduction...........................................................................................................160 5.2 Creating Patterns...................................................................................................161 5.3 Delamination Morphology....................................................................................168 5.4 Delamination Microchannel Conclusions.............................................................172 Chapter 6 Summary and Future Work............................................................................173 6.1 Summary...............................................................................................................173 6.1.1 Sputter Deposition.........................................................................................173 6.1.2 Residual Stress Measurement........................................................................175 6.1.3 Thin Film Characterization using Nanoindentation.......................................175 6.1.4 Creating Microchannels from Controlled Film Delaminations.....................177 6.2 Future Work..........................................................................................................177 6.2.1 Pop-in Phenomenon.......................................................................................177 6.2.2 Microfluidic Devices.....................................................................................181 References.......................................................................................................................184 Appendices......................................................................................................................194 Appendix A. Excel Spreadsheet for Theoretical Film Thickness...............................195 Appendix B. Sample of Mathcad Calculation for Film Stress....................................196 About the Author...................................................................................................End Page

PAGE 7

iii List of Tables Table 1. XRD data from tungsten target...........................................................................16 Table 2. Effects of argon pressure on the deposition rate of tungsten films.....................34 Table 3. Effects of argon gas pressure on tungsten residual stress...................................37 Table 4. Small-deflection assumptions C = 1...................................................................57 Table 5. Stress measurement results.................................................................................97 Table 6. Strain energy release rates results for copper and OSG low-k films ................151

PAGE 8

iv List of Figures Figure 1. Damascene metallization starting with the second step: a) etch tr ench in oxide, b) deposit metal and c) planarization........................................................4 Figure 2. SEM view of IBM's six-level copper interconnect technology in an integrated circuit chip..........................................................................................4 Figure 3. Physical sputtering process................................................................................13 Figure 4. Tungsten target 2 q peaks...................................................................................16 Figure 5. Comparison of Mahon model with Stuart and Wehner experimental results [19, 20]...................................................................................................18 Figure 6. DC magnetron sputtering system layout...........................................................20 Figure 7. Ionization and current flow in a plasma sustained between electrode s.............22 Figure 8. Structure of DC glow discharge [11].................................................................24 Figure 9. Effect of electric and magnetic fields on electron motion.................................25 Figure 10. Helical orbit caused by the magnetic and electric fields.................................26 Figure 11. Planar magnetron setup with circular magnets................................................27 Figure 12. Profile of tungsten target erosion....................................................................28 Figure 13. Setup for measuring the film thickness profile................................................29 Figure 14. Film thickness measured across the diameter of the wafer.............................30 Figure 15. Film thickness measured in two radial directions...........................................31 Figure 16. Predicted film thickness profile.......................................................................32 Figure 17. Residual stress dependence on argon pressure................................................38

PAGE 9

v Figure 18. Hoffman and Thornton findings: a) Residual stress of Cr films b) Transition points for various targets (Graphs reproduced from [36, 37])...........................................................................................................39 Figure 19. Microstructure zones from sputter deposition (Schematic reproduced from Thornton [47])........................................................................................43 Figure 20. Surface scan of sputter deposited tungsten films; a) Argon pressure of 4 millitorr b) Argon pressure of 10 millitorr...................................................44 Figure 21. Comparison of the load-displacements curves for tungsten films deposited with different argon pressures........................................................45 Figure 22. Hardness of tungsten films deposited at different argon pressures. ................46 Figure 23. Stiffness of tungsten films deposited at different argon pressure s..................48 Figure 24. Reduced modulus of tungsten films deposited at different argon pressures..........................................................................................................48 Figure 25. a) Low-k dielectric film in tension [54] and b) tungsten film in compression....................................................................................................52 Figure 26. Schematic of film/substrate bending due to compressive residual str ess in the film........................................................................................................55 Figure 27. Free body diagrams of the film and substrate with indicated forces and moments..........................................................................................................56 Figure 28. Elastic bending of a beam under an applied moment......................................57 Figure 29. Geometry of the Flexus 2-300 curvature calculation......................................60 Figure 30. Flexus 2-300 stage rotation.............................................................................61 Figure 31. Profilometer stage layout for 4” wafers...........................................................64 Figure 32. Profiles of a wafer before and after film deposition........................................65 Figure 33. Finding the curvature of 3 mm segments........................................................66 Figure 34. Change in wafer curvature after film deposition at 4 millitorr Ar pressure...........................................................................................................67 Figure 35. Change in wafer curvature after film deposition at 10 millitorr Ar pressure...........................................................................................................68

PAGE 10

vi Figure 36. Fourth order polynomial used to fit the thickness profile...............................69 Figure 37. Residual stress in a tungsten film deposited at 4 millitorr Ar press ure...........71 Figure 38. Residual stress in tungsten film deposited at 10 millitorr Ar pressure ............71 Figure 39. Change in wafer curvature after film deposition at 6 millitorr Ar pressure...........................................................................................................73 Figure 40. Residual stress in tungsten film deposited at 6 millitorr Ar pressure ..............74 Figure 41. Delamination of a tungsten film deposited at 2 millitorr Ar pressure............. 75 Figure 42. Effects of using different segment sizes on the stress results.......................... 76 Figure 43. Deviations of fourth order polynomial curve fit from experimental data..................................................................................................................77 Figure 44. Schematic of the diffractometer setup.............................................................79 Figure 45. Sin 2 technique..............................................................................................80 Figure 46. Types of d versus sin 2 plots observed in residual stress analysis from polycrystalline materials: a) equi-biaxial stress, b) shear strains are non-zero and c) anisotropic elastic constants..................................................82 Figure 47. 2 Theta scan of tungsten film..........................................................................84 Figure 48. (110) plane and [110] direction of the new compliance value........................85 Figure 49. Peak shift with changing angle for the 6 millitorr tungsten film.................87 Figure 50. Change in d-spacing with a change in .........................................................88 Figure 51. Sin 2 technique performed in the positive and negative directions............91 Figure 52. Peak determination by fitting a parabola.........................................................92 Figure 53. Sin 2 plot for tungsten film deposited at 4 millitorr Ar pressure....................94 Figure 54. Sin 2 plot for tungsten film deposited at 6 millitorr Ar pressure....................94 Figure 55. Sin 2 plot for tungsten film deposited at 10 millitorr Ar pressure..................95 Figure 56. Comparing the curvature found with the Flexus and Tencor tools for the tungsten film deposited at 4 millitorr Ar pressure....................................98

PAGE 11

vii Figure 57. A diffraction peak made up of many peaks.....................................................99 Figure 58. Load-displacement data for an indent into tungsten......................................102 Figure 59. Load-displacement plots for different types of films....................................104 Figure 60. Schematic of the TriboIndenter transducer...................................................106 Figure 61. Oliver-Pharr power law fit for the top 65 % of an unloading curve from fused quartz..........................................................................................109 Figure 62. Schematic of indentation geometries.............................................................110 Figure 63. Ideal and experimentally measured Berkovich tip contact areas. .................113 Figure 64. Hertzian contact fit for a cube corner tip.......................................................115 Figure 65. Hertzian contact fit for a Berkovich tip.........................................................115 Figure 66. Comparison of Thurn and experimentally measured area function at shallow depths...............................................................................................117 Figure 67. Increase in hardness for a 200 nm gold film as a function of contact depth..............................................................................................................118 Figure 68. Effect of machine compliance on high modulus material.............................119 Figure 69. The effect of machine compliance on the reduced modulus of quartz..........120 Figure 70. The effect of machine compliance on the hardness of fused quartz..............121 Figure 71. Machine compliance check...........................................................................122 Figure 72. Topographic scan showing pile-up from a 1600 N indent in gold..............125 Figure 73. Pile-up measurement from a 1600 N indent in gold: a) topographic image and b) line profile taken across the indent.........................................125 Figure 74. Load-displacement plot of a 1600 N indent in 200 nm thick gold film......126 Figure 75. The ratio of h f to h max versus the maximum indentation load for a 200 nm thick gold film.........................................................................................127 Figure 76. Pile-up as a function of the contact depth for a 200 nm thick gold film.......128 Figure 77. Corrected gold film hardness compensating for pile-up...............................129

PAGE 12

viii Figure 78. Corrected gold film reduced modulus compensating for pile-up..................129 Figure 79. Modeling the dynamic test method...............................................................132 Figure 80. Comparison of dynamic and quasi-static indentation results of Er for a 140 nm thick low-k film...............................................................................133 Figure 81. Comparison of dynamic and quasi-static indentation results of Er for a 200 nm thick gold film..................................................................................134 Figure 82. Contact angle technique................................................................................137 Figure 83. Static crack system for defining the mechanical energy rele ase rate............140 Figure 84. Modes of fracture: a) Mode I b) Mode II c) Mode III...................................142 Figure 85. Strain energy release rate as a function of ................................................143 Figure 86. Hypothetical operations used to calculate the strain energy asso ciated with an indentation-induced delamination in a stressed film........................145 Figure 87. Delamination blister from the superlayer indentation test............................149 Figure 88. Strain energy release rate for 97 nm thick Cu film.......................................150 Figure 89. Half-penny fracture morphology...................................................................153 Figure 90. Reduced modulus of sapphire.......................................................................154 Figure 91. Hardness of sapphire.....................................................................................155 Figure 92. Berkovich indent into sapphire: a) load-displacement curve and b) corresponding optical micrograph................................................................156 Figure 93. Load-displacement curve for a 1000 N indent with a Berkovich and cube corner tips.............................................................................................157 Figure 94. Topographic scan of 2000 N indent in low-k film using a) Berkovich and b) cube corner tip...................................................................................158 Figure 95. Maximum indentation load as a function of c 3/2 ............................................159 Figure 96. Process of creating microchannels................................................................162 Figure 97. Photoresist thickness as a function of spin speed for Shipley 1813..............164

PAGE 13

ix Figure 98. Photoresist profiles after different exposure times........................................166 Figure 99. Effect of exposure time on the final photoresist thickness: a) 10 sec, b) 8 sec, c) 6 sec, and d) 4 sec...........................................................................167 Figure 100. Straight-sided delaminations of a W/DLC film on Si.................................168 Figure 101. Tungsten delamination a) Optical image of delamination morphology, and b) Profile of delaminations..................................................................170 Figure 102. Delamination morphology with different photoresist widths: a) telephone cord delamination and b) straight-sided delamination..............171 Figure 103. Pop-ins observed at the same load for a sapphire sample using a Berkovich indenter.....................................................................................179 Figure 104. Perfectly elastic indent prior to pop-in loads...............................................180 Figure 105. Hertzian fit prior to pop-in event modeling elastic loading........................180 Figure 106. Different delamination channels profiles....................................................182 Figure 107. Delamination propagation induced by the introduction of water................183 Figure 108. Excel spreadsheet for predicting film thickness..........................................195 Figure 109. Sample of Mathcad program used for calculating residual stress ...............196

PAGE 14

x List of Nomenclature a lattice constant, interfacial crack length A fracture surface area A c indentation contact area c plastic zone size d lattice plane spacing D grain size E Young’s modulus E r reduced modulus F E electrostatic force constant G strain energy release rate h indentation depth H thin film hardness I number of incident ions j current density k curvature K stress intensity at a crack tip (K I,II,III are used for mode I, II and III) K C fracture toughness M atomic mass n e electron concentration N s number of sputtered atoms P load q electronic charge R radius of curvature s n ’ reduced nuclear stopping cross section S indentation unloading stiffness S n nuclear stopping power S y sputtering yield T temperature t film thickness U energy V I indentation volume W A thermodynamic work of adhesion W A,P practical work of adhesion Z atomic number thermal expansion coefficient, Dundar’s parameter Dundar’s parameter g surface energy, indentation correction factor Gi interface fracture toughness d displacement

PAGE 15

xi e strain wavelength sputtering constant dependent on target material shear modulus n Poisson’s ratio s stress y mode mixity (phase) angle

PAGE 16

xii Stress Analysis and Mechanical Characterization of Thin Films for Microe lectronics and MEMS Applications Patrick Waters ABSTRACT Thin films are used for a variety of applications, which can include electronic devices, optical coatings and decorative parts. They are used for their physic al, electrical, magnetic, optical and mechanical properties, and many times these properti es are required simultaneously. Obtaining these desired properties starts with the deposition process and they are verified by a number of analysis techniques after depos ition. A DC magnetron sputter system was used here to deposit tungsten films, with film thi ckness and residual stress uniformity being of primary interest. The film thickne ss was measured to vary by up to 45 % from the center to outer edge of a 4” wafer. Ar pressur e was found to influence the thin film residual stress with lower Ar pressures lea ding to compressive residual stress (-1.5 GPa) and higher Ar pressures leading to te nsile residual stress (1 GPa). Residual stress measurements of the tungsten films wer e made using a wafer curvature technique and X-ray diffraction. The results of the two technique s were compared and found to be within 20 %. Nanoindentation was used to analyze the mechanical properties of several types of thin films that are commonly used in microelectronic devices. Thin film reduced modulus, hardness, interfacial toughness and fracture toughness were some of the mechanical properties measured. Difficulties with performing shallow ind ents (less than

PAGE 17

xiii 100 nm) were addressed, with proper calibration procedures for the indentation equipment and tip area function detailed. Pile-up during the indentation of soft films wi ll lead to errors in the indentation contact depth and area, leading to an overestimation of the films’ reduced modulus and hardness. A method was developed to account for pile-up in determining the indentation contact depth and calculating a new contact area for improving the analysis of reduced modulus and hardness. Residual stresses in thin films are normally undesired because in extreme cases they may result in thru-film cracking or interfacial film delamination. W ith the use of lithography techniques to pattern wafers with areas of an adhesion reducing layer thin film delamination was controlled. The patterned delamination microchannels m ay be used as an alternative method of creating microchannels for fluid transport in ME MS devices. Delamination morphology was influenced by the amount of residual stress i n the film and the critical buckling stress, which was primarily controlled by the width of the adhesion reducing layers.

PAGE 18

1 Chapter 1 Introduction 1.1 Motivation for Thin Film and MEMS Research The current trend in technology is to make everything smaller and faster. A fe w decades ago a person was lucky to have access to a computer at work. Now it is not only standard to have a personal computer at both work and home, but computers can even be found in our vehicles and in the form of cell phones and personal digital assistants (PDAs). This is possible because of a number of improvements in the semiconductor industry such as: improved integration level, compactness, functionality, storage and us e of power, reduced cost and increased speed. These improvements allowed for smaller devices to be contrived and have made computers available to the mass population. The development of microfabrication in the semiconductor industry was sparked by the invention of the transistor in 1947. Before transistors, large vacuum tubes were used in electronic equipment and computers that were the size of rooms. Now, hundreds of millions of transistors are placed on semiconductor chips, with the size of transis tors being reduced down to the sub-micrometer range. The increase in device density has been following a trend known as Moore’s law. In 1965, Gordon Moore a co-founder of Intel, made a prediction on the development of semiconductor technology that the number of transistors on a chip will approximately double every eighteen months [1]. This prediction has been accurate for the last four

PAGE 19

2 decades. The primary reason for this exponential growth in integrated circuit ( IC) technology is the reduction in manufacturable feature size, which is defined as the minimum element size on a chip. Gate widths in transistors were around 30 m in the early 1960s, then reduced to around 10 m in the 1970s, to less than 0.2 m in the year 2000 and they continue to decrease. At one point physicists predicted that the lower bound of gate width would be around 50 nm for the current form of metal-oxide-semiconductor field-effect transistors (MOSFET)[2]. This prediction was challenged by the end of 2007 when Intel released its 45 nm process technology and the International Technology Roadmap for Semiconductors has recently predicted that devices will ha ve a physical gate width of 13 nm by the year 2013 [1]. Unfortunately, for many of the materials used in these devices only the elect ronic, magnetic and optical properties are of focus. Chemical and mechanical properti es are often overlooked because these materials are generally not thought to be meant for load bearing applications. Integrated circuits, microelectromechanical sys tems (MEMS), and magnetic disks are perfect examples of where materials are needed not onl y for their electric, magnetic and optical properties, but for their chemical and mecha nical properties as well [3]. The manufacturing of integrated circuits is a perfect exampl e where high levels of stress may be introduced during processing. In order to avoid device fa ilure, they must be able to withstand the stresses introduced in film deposition and processin g. The types of stress may depend on the deposition and processing methods involved, such as residual stresses introduced by sputter deposition and thermal stresses int roduced because of deposition at elevated temperatures and subsequent cooling to room temperature.

PAGE 20

3 Elevated temperatures are often required during the processing of ICs and this will lead to thermal stresses when there are materials with different t hermal expansion coefficients. The expansion and contraction of a material is normally proporti onal to the temperature change it experiences and can be seen in the following equation T D = a e (1), where is the strain, is the thermal expansion coefficient and T is the change in temperature. For the case of a film/substrate combination, the strain of the fil m will be constrained by the substrate due to mismatched thermal expansion coefficients a nd the thermal stress of the film can be expressed as: ( ) f f f s f E T Tn a a s D = 1 ) ( (2), where E and v are the modulus and Poisson’s ratio, respectively, and the subscripts s and f stand for the substrate and film, respectively. In addition to thermal stresses, integrated circuit s may also be exposed to external forces that are applied during chemical mechanical planarization (CMP). The CMP process uses an abrasive/corrosive chemical slurry to remove material and irregularities from the sample surface. CMP is the final step in the damascene process, which is broken down into four basic steps: 1) oxide deposit ion, 2) oxide etching, 3) metal deposition and 4) metal planarization and polishing The damascene process is commonly used for metals that cannot by plasma etch ed. Copper is an example of a metal that cannot be patterned using standard photo lithography and plasma etching techniques. Therefore, damascene is used for coppe r metallization of ICs (Figure 1).

PAGE 21

4 Figure 1. Damascene metallization starting with the second step: a) etch trench in oxide, b) deposit metal and c) planarization. Figure 1 starts with the second step in the damasce ne process which is etching a desired pattern of trenches into a silicon dioxide layer. This is followed by the deposition of a metal film, which overfills the trenches. CMP is then used to polish the excess metal to the point where it is level with the top of the trenches. Ideally, the only metal that is left is in the trenches and this process can be rep eated several times to develop multiple layers of contacts and interconnects (Figure 2). Figure 2. SEM view of IBM's six-level copper interc onnect technology in an integrated circuit chip. The last two causes for stress are common examples of what can be expected when producing ICs. One example of large stresses experienced after production is in the use of magnetic disks. Magnetic disks are often us ed in information storage for products a) b) c)

PAGE 22

5 such as the hard drives in computers. During norma l usage, large stresses will be experienced as a result of high rotational speeds a nd frequent collisions between the read/write heads and the disk surface. The collisi ons will occur each time the disk is turned on and off reducing the layer of air between the disk and read/write head. This layer of air between the disk and read/write head a cts as a fluid dynamic bearing created by the rotation of the disk. Currently, carbon coa tings in the thickness range of 5-10 nm are used to protect the magnetic layers underneath from the externally applied forces. To achieve the expected storage densities within the n ext few years (Gbit/in2), it will be necessary to reduce the head to disk fly height and the protective coating thickness [4]. This ultra thin film is what stands between normal operation and failure of the hard drive. That is why a thorough understanding and control ov er the mechanical properties is so important. Whatever the cause of stress, it must be accepted t hat stresses are commonly present and may result in deformation, fracture and delamination of films. To ensure device reliability, the mechanisms that control the mechanical properties of these materials must be understood. To understand these mechanisms, analysis and characterization of the materials and devices must be performed after processing. From there, the manufacturing parameters may be adjusted to improve the final product. The focus of the work presented here will be on add ressing issues with film deposition using DC magnetron sputtering and charac terizing the film’s mechanical properties using nanoindentation. It was observed that factors such as inert gas pressure used during sputter deposition will have significan t effects on the residual stresses present in the deposited film. Film non-uniformities produ ced from sputtering were measured

PAGE 23

6 and the factors leading to these non-uniformities w ill be discussed. Typically, residual stresses and film non-uniformities are not desired, but the possible use of these in creating microchannels will be examined. A close e xamination of using nanoindentation for measuring thin film mechanical properties was d one and some potential challenges will be addressed. 1.2 Thin Films Thin films are a perfect example of how much techno logy has advanced in the last two centuries. Many of the advances in the IC indu stry have been the result of advances in thin film technology. Thin films are now widely used for making electronic devices, optical coatings and decorative parts. They are us ed for their physical, electrical, magnetic, optical and mechanical properties and man y times these desired properties are obtained simultaneously. By variations in the depo sition process, as well as modifications of the film properties during deposit ion, a range of unusual properties can be obtained which are not possible with bulk materi als. Additional functionality in thin films can be achieved by depositing multiple layers of different materials. Multiples film layers have found use in applications such as optic al interference filters, where tens or even hundreds of layers are deposited. The layers are alternated between high and low indexes of refraction to achieve the desired filter ing effects. There are many different methods available for film deposition, but all could be broken down into three basic sequential steps: 1) A source of film material is provided, 2) the material is transported to the substrate and 3) deposition takes place. If the deposition process is relatively new, the film will be analyze d to evaluate the success of the process. The results of the analysis can then be used to adj ust the deposition conditions if the film

PAGE 24

7 properties need to be modified. Additional process control and understanding are obtained by monitoring the first three steps during film deposition. The source of the film material may be a solid, liquid, vapor or gas. For solid materials, vaporization is needed to transport the material to the substrate. This can be accomplished by heat or by an energetic beam of electrons, photons and ions. These methods are categorized as physical vapor deposition (PVD) processes. Thin fi lm deposition processes where the source materials are brought in as gas phases are c ategorized as chemical vapor deposition (CVD) processes. Film uniformity will primarily be affected by the t ransport and deposition steps. The transport medium plays a significant role in af fecting film uniformity and may consist of a high vacuum or a fluid medium dependin g on the deposition method. The transport medium will directly affect the source ma terial’s arrival rate, direction and energy. The deposition behavior is determined by t he source and transport factors and by conditions at the substrate surface. The principal factors are the substrate surface condition, reactivity of the arriving material and energy input. Substrate surface conditions include roughness, level of contaminatio n, degree of chemical bonding with the arriving material and crystallographic paramete rs in the case of epitaxy. Epitaxial deposition is a special case of thin film depositio n where film growth will be single crystal and dependent on the crystal orientation of the substrate. In order to grow properly the crystal lattices of the film and subst rate must be closely matching. Analysis of the film after deposition can be though t of as the final stage of the process monitoring. This stage consists of directl y measuring those properties that are important for the application at hand. For example properties such as the hardness for a

PAGE 25

8 tool coating, the breakdown voltage of an insulator or the index of refraction of an optical film are all important. Many film depositi on processes are optimized by measuring the key film properties as a function of the process variables. The process variables are then adjusted in the three steps of t he deposition sequence to achieve the desired product. 1.3 Thin Film Characterization Just as the technology used for manufacturing small er devices and new materials is evolving, so is the equipment available to test and analyze it. The reduction in material size means that there must be a change in testing e quipment and methods used. It must be kept in mind that thin film material properties do not always resemble those measured at the bulk level. The application of thin films i s becoming increasingly interdisciplinary in nature, leading to new demands for film characte rization and properties measurements for both individual films and multilayer films. At first, single films on thick substrates were studied. Now, thin films are able to be depos ited one atomic layer at a time, which creates the need for testing instrumentation that h as control and sensitivity at that scale. Atomic layer deposition (ALD) is a method that is s imilar to CVD, but it allows for conformal atomic level control over the deposit ion process. This control is achieved by introducing the reactants individually, separati ng the purge steps in a sequential manner and carrying out self-limiting surface react ions that occur during each step on the substrate surface. The result from using ALD is th e ability to deposit films with accurate thickness control, excellent conformability and uni formity over large areas that are not achievable in CVD [5, 6]. Measurements and charact erization of the film thickness, microstructure and composition can be carried out u sing various techniques. They

PAGE 26

9 include ellipsometry, X-ray diffraction (XRD), tran smission electron microscopy (TEM) and X-ray photoemission spectroscopy (XPS). The previously mentioned techniques have been aroun d for quite some time and have proven their effectiveness in analyzing ultrathin films. So far, experimental techniques for measuring film thickness, structure, composition and surface morphology have been proven reliable. However, thin films mus t be characterized with respect to all the various properties equally and to the same ease and precision that we associate with testing bulk materials. Mechanical testing is lack ing when material size is decreased to the extreme that we see in ALD. Questionable resul ts are presented using nanoindentation to measure thin film elastic modulu s and hardness, at contact depths below 50 nm. This is due to a measurement process that is complicated by effects such as unknown geometry of the indenter tip, surface an d substrate effects and limitations in the testing equipment [7-10]. Nevertheless, resear chers will continue to push the limits of the existing equipment used for these measuremen ts and strive to find a way over the mentioned hurdles. Until then, the proper consider ation should be taken when reviewing results for ultra thin films and shallow indentatio n depths. 1.4 Chapter Objectives This manuscript has been broken-down into 6 differ ent chapters. Chapter 1 was to get the reader familiar with thin films, and som e of the uses and issues associated with them. Chapter 2 starts off with an introduction in to DC magnetron sputtering and it then goes into the testing of a CRC-100 sputtering syste m. Experiments were conducted to measure the deposition and etch rates, film thickne ss profile and the relation between Ar pressure and residual stress in tungsten films. Tw o different residual stress measuring

PAGE 27

10 techniques were the focus of Chapter 3. The object ives of the chapter were to be able to compensate for non-uniformities in film thickness a nd residual stress and to then compare the results of the Stoney’s equation using the wafe r curvature method and the sin2 technique using X-ray diffraction. The objectives of Chapter 4 were to introduce the reader to nanoindentation and the different mechani cal properties it is capable of testing. Some of its challenges were addressed, specifically calibration procedures and difficulties with testing in the sub 50 nm region. Indentation pile-up effects on soft films were also compensated for when calculating the film ’s reduced modulus and hardness. The objective of Chapter 5 was to propose an altern ative method for manufacturing microchannels by controlling thin film delamination s. This was accomplished by using photolithography to create patterned areas of an ad hesion reducing material and then the microchannels were created by depositing a compress ively stressed film on top of the patterned area. A summary of the chapters is provi ded in Chapter 6, along with the authors intended future work.

PAGE 28

11 Chapter 2 Sputter Deposition 2.1 Introduction In the past, thermally evaporated and sputtered alu minum films were primarily used for the contacts and interconnects of integrat ed circuits. Due to problems with electromigration and RC delays, aluminum-copper int erconnects became more widely used [11]. The introduction of copper alloys resul ted in larger current densities and reduced resistivity, thereby reducing RC delays and electromigration problems. Unfortunately, this alloy could not be easily evapo rated and it was found that film stoichiometry was maintained by glow-discharge sput tering. Another advantage of using sputtering over evaporation becomes apparent when w orking with refractory materials such as tungsten. Thermal evaporation is not appro priate for high melting temperature materials because it is difficult to find a suitabl e crucible that will not contaminate the target at high temperatures [12]. With the progres sion from aluminum to aluminumcopper as the alloy of choice in IC technology, spu tter deposition became an integral part of the metallization processing in the early 1970s. The earliest published observation of sputtering wa s in 1852 by Grove who was investigating discharge tubes. During his investig ation, Grove noticed the formation of a dull coating on the surface of a highly polished si lver coated copper sample. The coating was only observed when the silver sample was the an ode and the steel wire was the

PAGE 29

12 cathode of the electrical circuit. By reversing th e polarity he was able to remove the deposited material from the silver surface [13]. He did not make any studies of the deposited films’ properties because he was more int erested in the effects of the voltage reversal on the discharge. It wasn’t until years l ater that scientists took note of Grove’s discovery and coined the phrase “sputtering”. Earlier uses of sputtering were for creating mirror s [14], decorative ornaments and chrome coatings on the plastic grilles of cars. No w, sputter deposition is used for various applications across a number of industries. Sputte ring is not limited by the electrical conductivity or melting temperature of the deposite d material. It can be used for depositing materials over a wide range of thickness es. Film thicknesses from a few nanometers up to a few microns are normally classif ied as a thin film and thicknesses above a few microns are normally considered a coati ng. 2.1.1 Sputtering Yield Early theories to explain sputtering were based on the idea that bombarding ions created areas of high local temperatures on the tar get, leading to an evaporation of the target. These early theories also predicted that t he sputtering rate depended on the heat of sublimation of the target and the energy of the bom barding ions. Currently, the accepted cause of sputtering is that sputtering is a momentu m transfer process, where surface atoms are physically ejected from a solid surface b y the momentum transfer from bombarding energetic particles. The energetic par ticles are usually gaseous ions that are accelerated from a plasma. When a solid surface is bombarded with energetic particles, some of the target surface atoms of the solids are scattered backward as shown in Figure 3.

PAGE 30

13 Figure 3. Physical sputtering process. Sputtering is typically a multiple collision proce ss involving a cascade of moving target atoms. This cascade may extend over a consi derable region inside the target, but the sputtered atoms originate only in a layer near the surface. The thickness of this layer will depend on the ion mass, the ion energy and the ion-target geometry. Only atoms that gain enough energy to overcome the target binging e nergy will be ejected from the target, while others are displaced from normal lattice site s. A measure of the efficiency of sputtering is the sputtering yield and is defined a s I N S s y = (3), where Ns is the number of atoms sputtered and I is the number of incident ions. The result of sputtering is like a game of billiards. If the incident ion was represented by the cue ball, the number of sputtered atoms would be th e number of pool balls scattered back towards the player. The sputtering yield will be a ffected by many things, including the ion energy, the angle of incidence, the binding ene rgy of the target material, the type of Sputtered atom Incident ion Target surface Ion implantation Reflected ion

PAGE 31

14 collision cascade that occurs between the ion and t arget atoms, the target surface morphology and the target crystal structure [15-18] Sigmund was the first to describe the sputtering pr ocess as a linear collision cascade and his theoretical modeling of sputtering was been widely accepted by others [15-19]. Sigmund’s work, along with the contributi on of others has pointed out four major concepts in the collisional description of sp uttering: 1) the stopping of the projectile via nuclear energy loss to target atoms, 2) the occurrence of a linear collision cascade, 3) the escape of certain recoils through t he surface potential energy barrier and 4) the introduction of anisotropy into yield distri butions by lattice correlated effects within single crystal regions of the target. The S igmund theory suggests a specific dependence of the sputtering yield on the ion energ y, E for both low and high energies [15]. Sigmund’s general sputtering yield expressio n is a product of two terms: ) ( E F S D y L = (4), where the first term, is a material constant that includes the range of a displaced target atom and the probability of ejection of an atom at the surface. The second term, FD(E) accounts for the energy deposited at the surface an d depends on type, energy and incident angle of the ion, as well as on target parameters. The sputtering yield at low energies ( E < 1 keV) is predicted to be () s yU M M E M M S2 2 1 2 2 13 + =p a (5), where M1 and M2 are the ion and target atomic masses, Us is the target atom’s binding energy, E is the ion energy and is a constant that depends on the mass ratio and a ngle of impact, but often assumes a value between 0.2 and 0 .4. The low energy yield expression

PAGE 32

15 is linear in E and does not predict a threshold. For energies ab ove 1 keV, Sy is predicted to be s n y U E S S ) ( 042 .0 =a (6), where S n (E) is defined as the nuclear stopping power or nuclea r energy loss cross section, and is approximated as 2 1 1 2 2 1) ( 4 M M E s M q Z Z a Sn n+ =p (7), where Z 1 and Z 2 are the atomic numbers of the projectile and target atoms, a is the effective radius (0.1 to 0.2 ) over which the nucl ear charge is screened by electrons during the collision, q is the electronic charge and s n ’(E) is a reduced nuclear stopping cross section. His theory was based on the assumption that there w ill be a random slowing down of the incident ions, with much of his work focused on amorphous targets. For polycrystalline materials there may be a contributi on of focused collision chains to the sputtering yield that may not average out. If this contribution were substantial, the sputtering yield of polycrystalline materials would be greater than that of an amorphous target. With this effect to sputtering yield in mi nd, X-ray diffractometry was used to analyze the 99.95 % pure tungsten target used here. The X-ray diffraction tests were done with a Philips X’pert and the 2 peaks are displayed in Figure 4. The correspondin g dspacing and plane orientation can be found in Table 1. Results clearly show that the target is polycrystalline.

PAGE 33

16 0 50 100 150 200 406080100120Counts2 Theta Figure 4. Tungsten target 2 q peaks. Table 1. XRD data from tungsten target. Pos. [2Th.] d-spacing [] Rel. Int. [%] hkl 40.3672 2.23441 100.00 110 58.3203 1.58221 15.65 200 73.1687 1.29351 16.20 112 reflection 86.9512 1.12047 7.30 220 100.5662 1.00224 9.38 310 115.4510 0.91332 6.22 222 131.0195 0.84645 8.43 321 It has been observed that Sigmund’s theory overesti mates the experimentally measured yields by a factor of 2. More recent attem pts to model sputtering in the linear collision cascade regime have been made by Mahon and Vantomme. It is called the

PAGE 34

17 “simplified collision model of sputtering in the li near cascade regime” and their sputtering yield expression is as follows [19]: 4 1 pp pr avg y R R E E S = (8). The first term gives the number of recoils at the p ractical endpoint of the cascade, where E is the ion energy and E avg is the average energy of the recoils at terminatio n. The second term gives the fraction of recoils which are close enough to the surface to reach it and have enough energy to escape, where R pr is the projected range of recoils and R pp is the projected range of projectiles. The third term gives the fraction of those particles which are traveling in the right directio n. By using Mahon and Vantomme’s newer, simplified expression for sputtering yield, the predicted sputtering yield of tungsten with argon as the working gas was tabulate d and the results are compared with Stuart’s and Wehner’s experimental results (Figure 5). It can also be observed in Figure 5 that there will be a theoretical maximum sputteri ng yield that is asymptotically approached with an increasing ion energy. This cor responds to Sigmund’s predictions that the nuclear stopping power is dependent on the ion energy, thus resulting in a maximum yield. For a tungsten target with argon as the plasma, a maximum yield around 1.5 is calculated using Mahon and Vantomme’s simplified collision model.

PAGE 35

18 0.01 0.1 1 6080100300 Experimental ModelSputtering yieldEnergy (eV) Figure 5. Comparison of Mahon model with Stuart and Wehner experimental results [19, 20]. Along with predicting the sputtering rate, it is al so important to understand the dispersion of sputtered atoms from the target. The profile of dispersion will affect transport of sputtered atoms through the ambient ga s and their finally resting location of the substrate and chamber walls. Sticking with the billiards analogy, just as the pool balls scatter in many directions after the break, the tar get atoms are sputtered from the target in a range of directions about the target normal. The number atoms ejected in a given direction is proportional to the cosine of the angl e from the normal [21]. An atom ejected with a given energy has a greater chance of escapin g from the surface binding energy if it is ejected along the normal. Along with the sputter ed atoms, a percentage of the incident ions will be reflected from the target with a signi ficant amount of energy, while a small

PAGE 36

19 percent will remain in the target and are sputtered later. The fraction of energy reflected depends on mass of the incident and target atoms al ong with the angle of incidence. A great deal of literature has been published attem pting to further explain and simulate the interactions during the sputtering pro cess. Many papers deal with the interactions between incident ions and the target a toms as previously summarized and others concentrate on the transport of sputtered pa rticles through the gas phase [22-28]. The latter of the two bodies of work will be briefl y discussed in the following sections and how they pertain to planar DC magnetron sputter ing. 2.2 DC Magnetron Sputter Deposition Sputtering is generally divided into four major cat egories: DC, AC (mostly RF), reactive and magnetron sputtering. There are clear distinctions between each of the sputtering categories and even hybrids between cate gories. Some of the obvious variants between categories are the power source used, wheth er reactive gases are present in the chamber and if there is an addition of magnetic fie lds. In the current research, a planar DC magnetron sputtering system was used and is cons idered the dominant method of physical vapor deposition using plasma. The two main advantages of a magnetron sputtering s ystem over a diode system are higher deposition rates and lower substrate tem peratures. In magnetron sputtering systems a magnetic field is used to help prevent el ectrons from escaping the target region, which creates a dense plasma near the cathode surfa ce at lower pressures. The lower pressure allow ions to be accelerated from the plas ma to the cathode without loss of energy due to physical and charge exchange collisio ns. This produces a higher current for the same applied voltage as in simple DC discha rges, which results in a higher

PAGE 37

20 sputtering rate. Furthermore, by containing the el ectrons near the target surface, fewer electrons will be striking the substrate keeping su bstrate temperatures close to room temperature. A general system layout for a DC magn etron sputtering system can be seen in Figure 6. Figure 6. DC magnetron sputtering system layout. A CRC-100 sputtering system was used here and can b e operated either in DC or RF modes. The cathode/magnetron assembly is water cooled to help reduce the high target temperatures. Since tungsten was the only t arget used in this research, operation in DC mode was sufficient. If high resistance targets were needed, then RF mode would have been required. Insulating targets would requi re very high voltages because of their large resistivities. This can be overcome by using a RF source since target impedance will drop with increasing frequency. Therefore, hi gh frequency plasmas can pass current through insulating targets the same way DC plasmas do through metal targets. This particular system is contained by a cylindrica l glass container that is 6” in diameter, and it requires targets that are 2” in di ameter and about 0.125” in thickness. Substrate Anode (Ground) Cathode (-0.5 KV) Target Dark Space Ar Magnetic Field Plasma

PAGE 38

21 The unit can also be operated in etch mode to pre-c lean the substrate by reversing the bias on the electrodes. The pedestal, which holds the s ubstrates to be coated, is located 5 cm from the target. Argon was used as the working gas and its flow inside the chamber is manually controlled with a leak valve. Due to the analog nature of the controls and the age of the equipment, some difficulties in attainin g repeatability with gas flow and pressures were encountered. Discussions of some of the essential components that make up a planar DC magnetron sputtering system are in t he following sections. 2.2.1 Glow Discharge Plasma Energy input by non-thermal means is a powerful and widely used process in thin film deposition. The energy may be delivered by el ectrons, photons or ions, with ions being used in sputtering. Sputtering is a ballisti c type process that will work on any material type, which eliminates the issue of high m elting temperature materials. Since sputtering is a momentum transfer process, the bomb arding ions must have energies exceeding chemical bond strengths, which are a few eV. Most energy enhanced techniques such as sputtering, involve the generati on of a plasma, which is a partially ionized gas consisting of nearly equal concentratio ns of positive ions and negative particles (electrons and negative ions). Plasma can be thought of as the fourth state in a p rogression of increasingly energetic states of matter, starting with solids ha ving fixed atom positions. Adding energy to this first state allows the atoms to move around each other as a liquid and then to separate completely as a gas. Adding even more energy causes gas atoms to separate into the ions and free electrons of a plasma. Some familiar examples of plasma include stars, lightning, solar winds, neon signs and fluor escent tubes.

PAGE 39

22 To begin the sputtering process, a discharge is ini tiated by the application of a sufficiently high DC voltage between metal electrod es immersed in a low pressure gas. The discharge represents a gaseous breakdown that m ay be viewed as the analog of dielectric breakdown in insulating solids. The pro cess begins in gases when a stray electron near the cathode carrying an initial curre nt is accelerated towards the anode by an applied electric field. The electron then colli des with a neutral gas atom converting it into a positively charged ion. During this impact, ionization takes place and conservation of charge is maintained by releasing a second elect ron. The process continues by generating more ions and electrons and is represent ed in Figure 7. Figure 7. Ionization and current flow in a plasma s ustained between electrodes. The positive ions are attracted to the cathode wher e they collide with the target ejecting target atoms and secondary electrons. Thi s effect snowballs until a sufficiently large current causes the gas to breakdown, creating a discharge that is self sustaining and the gas begins to glow. To operative in the domain for sputtering and other discharge processes such as plasma etching, the current is in creased further after discharge and this Cathode (-V) Anode (+V) E + – – – plasma

PAGE 40

23 is called the abnormal discharge regime. For magne tron sputtering systems the plasma is able to be self sustaining at much lower pressures. The magnetic field creates a high concentration glow discharge near the cathode which allows for the working gas pressure to be as low as 10 -5 torr. For a DC discharge, it can be observed that there i s a progression of alternating dark and luminous regions between the cathode and a node as shown in Figure 8. The general structure of the discharge has been known f or some time now, but the microscopic details of charge distributions, behavi or and interactions within these regions are not yet understood. The progression of regions starts with the Aston dark space. This first dark space is very thin and contains both low energy electrons and high energy positive ions with each moving in opposite directio ns. The cathode glow is just beyond it and appears as a luminous layer that envelops the c athode. De-excitation of positive ions through neutralization is the probable mechanism of light emission here. Next to the cathode dark space is a region of little ionization The cathode dark space is also referred to as the cathode sheath and most of the discharge voltage is dropped across this region. The resulting electric field accelerates ions towar ds the cathode. Then, next to the cathode dark space is the negative glow region whic h is apparent due to interactions between assorted secondary electrons and neutrals w ith attendant excitation and deexcitation. Finally, the Faraday dark space, the p ositive column and anode then follow, but during sputtering the substrate is typically pl aced inside the negative glow region so the Faraday dark space and positive column normally are not apparent.

PAGE 41

24 Figure 8. Structure of DC glow discharge [11]. Distance Cathode (-) Anode (+) Cathode glow Cathode dark space Faraday dark space Anode dark space Aston dark space Negative glow Positive column j j e j i Current Charge density Field Potential n e n i

PAGE 42

25 2.2.2 Magnetic Field in Sputtering The benefits of a magnetron sputtering system over a basic DC sputtering system are the result of combining magnetic and electric f ields. This combination leads to higher sputtering rates and reduced substrate temperature. By superimposing a magnetic field perpendicular to the electric field, greater electr on confinement is achieved. The ideal electric and magnetic field directions to confine e lectrons near the cathode surface are shown in Figure 9. The combination of an electric a nd magnetic field results in increased ionization close to the cathode which leads to high er levels of current drawn in a magnetron system compared to a DC system at the sam e applied voltage. With a larger current being drawn, higher sputtering yields are a chievable. In addition to producing higher currents, by confining electrons around the cathode surface with the magnetic field, fewer electrons and ions are accelerated tow ards the substrate which reduces substrate temperature and thermal stresses. Figure 9. Effect of electric and magnetic fields on electron motion. Another important advantage of a magnetron system i s the capability of reduced operating pressures. The lower limit of operating pressure is based on the need for ejected electrons from the cathode to undergo enoug h ionizing collisions with the ambient gas to sustain a plasma. If the electrons escape the magnetic field they will more Cathode (-) Anode (+) E B e

PAGE 43

26 than likely reach the anode and be removed before m aking any collisions with the ambient gas. With a magnetron system, the electron s have a longer path length before they can escape to the anode due to their orbital m otion. The increased electron path length will increase the chances of electrons colli ding with the working gas to produce ions. The effects of the magnetic and electric fie lds on electron motion can be observed in Figure 10. For simplification the magnetic and electric fields were drawn parallel to each other to show the helical orbits of escaping e lectrons. The ideal situation in a magnetron system would be to have the magnetic fiel d perpendicular to the electric field everywhere across the cathode. But due to the circ ular magnets used in the system here, the magnetic field is not exactly like the ideal si tuation and some electrons will escape the magnetic field and reach the anode. Figure 10. Helical orbit caused by the magnetic and electric fields. The magnetron configuration used in the current res earch was a planar configuration. A planar configuration means that t he cathode and anode surfaces are aligned parallel to each other. To create the magn etic field, small circular ring permanent magnets are placed on the back of the target. A sc hematic of the planar magnetron system is depicted in Figure 11. The figure is a c ross section view of the real system, so the figure must be revolved 180 to represent the t rue system layout. E B Anode (+) Cathode (+)

PAGE 44

27 Figure 11. Planar magnetron setup with circular mag nets. Because of the magnetic and electric fields not bei ng perpendicular everywhere across the cathode’s surface, electrons will hop ar ound the target plane, which induces a local current of electrons. This creates a region of high density plasma leading to higher sputtering rates in these areas and non-uniform ero sion of the target. The non-uniform erosion observed in a circular planar magnetron is often described as a racetrack pattern in the target [22, 23]. The etch rate in the regio n of the racetrack is so high that the etch rate caused only by the electric field in the surro unding areas is usually ignored. Because film thickness uniformity is important, the surface of the target was scanned to better understand any effects that might be observed in fi lm thickness profiles taken later. The erosion track of the tungsten target was measured u sing a Tencor P-20h profilometer. The profile of the surface was started at the cente r of the target, moving to the outer edge. Results from this scan can be observed in Figure 12 The erosion track on the target was measured to have a maximum depth of 230 m at 1.6 cm from the target center. It is clearly seen in Figure 12 that nearly all of the sp uttered material is from erosion track, which will limit the life of the target. S S S N N N magnets Cu backing plate target Erosion track B B

PAGE 45

28 -200 -150 -100 -50 0 00.40.81.21.622.4Profile ( m m)x-pos (cm) Figure 12. Profile of tungsten target erosion. Turner et al. have observed that the sputtering rat e and erosion profile may vary by a factor of 10 across the radius of the target d ue to the magnetic field profile used in a circular magnetron system [29]. They determined th at the radial sputtering profile is primarily determined by the sheath thickness and th at the uniformity of the sputtering profile increased as sheath thickness was decreased It was also observed that the width of the radial sputtering profile decreased with an increasing magnetic field strength. Caution must be used when depositing films with a s ystem configuration similar to the one shown in Figure 11, because the non-uniform spu ttering of the target will lead to poor utilization of the target and non-uniform film thickness [29-33]. Film thickness uniformity over a large area is a ba sic demand in thin film technology. Therefore, profiling the sputter depos ited tungsten film thickness was a

PAGE 46

29 necessity. To accomplish this task, a 4” silicon w afer was centered in the middle of the substrate holder and was sputtered with tungsten fo r 60 min. Two different runs were performed to obtain the film thickness uniformity i n the radial and circumferential directions. For both runs the current was set at 1 00 mA, the voltage was at 500 V and the gas pressure was approximately 4 millitorr. Glass slides were placed on top of the wafers in two different orientations covering the wafer fr om the center to outer edge (Figure 13). After film deposition the glass slides were removed and a profilometer was used to measure the film thickness. Step height measuremen ts were taken in 2 cm increments. Figure 13. Setup for measuring the film thickness p rofile. The results of the thickness profile taken across t he diameter of a 4” wafer in 2 cm increments are plotted in Figure 14. The discontin uity in film thickness on the left hand side about 12 cm out from the center is probably no t an effect of the sputtering system, but of the measurement process. The likely explana tion for the discontinuity is that a shift must have been made with the wafer while taki ng the thickness measurements with the profilometer. There is a significant change in film thickness from the center of the wafer to almost the outer edge. In Figure 14 there was a maximum film thickness of 2 cm Glass slides 4” wafer 4” wafer

PAGE 47

30 8580 at the wafer center and a minimum film thick ness of 4580 at the outer left edge. That is approximately a 47 % difference in f ilm thickness from the center of the wafer to the outer edge. In addition, there is app roximately a 24 % difference in film thickness between the opposite edges of the wafers. The difference in edge thickness could be caused by the location of working gas in t he chamber. The argon is introduced on one side of the chamber just above the height of the pedestal. This could produce a non-uniform flux in that location having an effect on sputtering rate and gas collisions. 4500 5400 6300 7200 8100 9000 -40-2002040Thickness (10-10m)Position (mm) Figure 14. Film thickness measured across the diame ter of the wafer. The results of the film thickness measurements take n across the radius of a 4” wafer at a 90 orientation to each other are plotte d in Figure 15. For this run there were no major discontinuities noticed like those in Figu re 14, however there was still a significant change in film thickness from the cente r of the wafer to the outer edge. A maximum film thickness of 8260 was measured at th e wafer center and a minimum

PAGE 48

31 film thickness of 4550 at the outer edge. The pe rcent difference in film thickness between the center and outer edge of the wafer was calculated to be 45 % in this case. 4500 5000 5500 6000 6500 7000 7500 8000 8500 -40-2002040Thickness (10 -10 m)x-pos (mm) Figure 15. Film thickness measured in two radial di rections. The second run is a more likely indicator of the ex pected thickness profile because no discontinuities in film thickness were n oticed. There is a consistent trend noticed from both of the runs which shows a signifi cant change in film thickness across the wafer diameter. With the maximum film thicknes s located in the center and the minimum located at the wafers’ outer edge. The 45 % difference in film thickness between the center and outer edges of the wafer was larger than what was expected. A theoretical thickness profile was calculated from o bservations made from the erosion track profile in Figure 12, the sputtering system g eometry and assuming a cosine distribution [21, 34] for the direction of the sput tered atoms. Figure 16 is a plot comparing the expected and experimentally measured thickness profile across a 4” wafer.

PAGE 49

32 The film thickness has been normalized to be able t o compare the two sets of data. The theoretical film profile resulted in a 33 % differe nce in film thickness from the center to the outer edge of a 4” wafer as opposed to the 45 % difference measured experimentally. 0.5 0.6 0.7 0.8 0.9 1 1.1-4-2024 Theoretical ExperimentalNormalized thicknessRadial position (cm) Figure 16. Predicted film thickness profile. To calculate the theoretical profile, 100 % of the maximum value for the sputtering yield was applied to the radial position of the target between 1.1 and 1.8 cm. The sputtering yield was reduced as the radial posi tion on the target decreased to match up the experimental profile measured from the used tungsten target. A more detailed explanation of the theoretical calculation can be f ound in Appendix A. The difference in the predicted thickness profile in Figure 16 and th e experimentally observed profiles in Figure 14 and Figure 15 is probably the result of t he assumptions made for the theoretical calculation. In order to simplify the calculation, it was assumed that target surface was perfectly flat, no collisions between the sputtered atoms and the ambient gas were taking place and there was no mobility of the sputtered at oms on arrival at the film surface. The

PAGE 50

33 target surface will definitely affect the film thic kness profile by obstructing the path of sputtered atoms. It can be expected that the erosi on track will continually change over time. As the track gets deeper, the walls of the t rench will block even more atoms sputtering out at larger emission angles. The film thickness and target profiles were taken after approximately 1 month of target use. I t is unclear what the film thickness profile was for a flat target and how the depositio n profile depends on target geometry. Hong et al. have reported similar results using a p lanar circular type magnetron sputtering system in their experiments [31] as comp ared to the experimentally measured results here. In their experiments they sputtered a 2” target of chromium using a system of similar dimensions. When their substrate to tar get distance was 5 cm, they noticed a 25 % difference in film thickness between the cente r of the wafer and 3 cm out. Their results confirm what was plotted in Figure 14 and F igure 15. Furthermore, as they increased the distance between the substrate and th e target they were able to get a more uniform film thickness across the diameter of the w afer. Fancey’s findings are also in agreement with Hong, where an increase in the distance between the target and the substrate will increase the film thickness uniformity [32]. An increase in target to substrate distance will increase the significance of gas scattering effects, therefore improving uniformity. However, it should be noted that by increasing the target to substrate distance, deposi tion rates may decrease and there may be some unwanted effects on film properties and mic rostructure. An alternative method for improving film thickness uniformity have been a ccomplished by Hong et al. by inserting a mesh into the chamber to enhance the sc attering of gaseous atoms [33]. However, the most common method for achieving film thickness uniformity is by wafer

PAGE 51

34 rotation. This is a frequent industry practice whe n a high level of film thickness uniformity is required. 2.3 Gas Pressure Effects The working gas pressure is one of the most influen tial parameters in sputter deposition. Deposition rate, film uniformity, part icle energy and residual stress are all dependent on the working gas pressure. This is due to the fact that gas pressure has a direct effect on the transport behavior of the sput tered atoms and back-reflected particles through the ambient gas. Predicting this transport process is very complex and has been attempted by many through the use of Monte Carlo mod els. These models have been used to simulate the transport of sputtered atoms a nd predict the effects on sputtered atom’s energy, angular distribution and deposition uniformity [22, 24, 29, 30]. The first parameter tested here was the effect of a rgon gas pressure on the tungsten deposition rate. Argon gas pressure was t ested in the range of 4 to 10 millitorr and the resulting deposition rates are given in Tab le 2. A minimum deposition rate of 80 /min was measured at an argon pressure of 4 millit orr, and it was found to increase to 123 /min when the pressure was increased to 10 mil litorr. Table 2. Effects of argon pressure on the depositio n rate of tungsten films. Time (min) Current (mA) Voltage (V) Pressure (milli torr) Deposition Rate (/min) 60 100 500 4 80 60 100 500 6 90 60 100 500 10 123 Comparable results have been reported by Nakano et al., who observed that in a DC system, the deposition rates of Al, Cu and Mo wer e proportional to an increasing gas pressure up to a maximum deposition rate found arou nd 7.5 millitorr. The deposition rate

PAGE 52

35 then decreased as gas pressure was increased beyond 7.5 millitorr [30]. The dependence of deposition rate on gas pressure can be attribute d to two factors: 1) a change in target current and 2) a change in the thermalization profi le. The effective electrical current density at the target, j which is proportional to the etch rate, can be ex pressed as v q n je = (9), where n e is the electron concentration, q is the electron charge and v is the electron velocity. The increasing gas pressure will initial ly increase the electron concentration which in turn results in more atomic ionization. T he increase in ionization effectively increases the etch and deposition rates. A transit ion point in deposition rate will then be reached when the frequency of collisions between sp uttered atoms and ambient gas is increased. Both experimental and simulation results report a t ransition point that depends on the atomic mass of the target [30]. The atomic mas s affects this transition point because the mass of the target atoms will determine how far the atoms travel before thermalization occurs. Thermalization in a plasma is when the high energy sputtered atoms and reflected Ar atoms reach thermal equilibr ium with the ambient environment, this is achieved by collisions in the plasma. The distance for thermalization to occur is proportional to the target’s atomic mass. At lower pressures, regardless of the target material, most of the sputtered atoms are still abl e to make it to the substrate with significant amounts of energy and there will be an increase in deposition rate up to the transition point. As gas pressure increases, so wi ll the frequency of collisions between sputtered atoms and the ambient gas. As gas pressu re continues to increase, there is a reduction in the mean free path of collision for th e sputtered atoms. This results in the

PAGE 53

36 thermalization profile converging on the target and at this point the deposition rate has hit its maximum and will start to decrease. So far, the effects of collisions between sputtered atoms and ambient gas on film thickness uniformity and deposition rates has been discussed. The collisions can also be credited with playing a role in the existence of re sidual stresses. Many authors have reported the effects of gas pressure on residual st ress in the sputter deposition of thin films [35-42]. Initial work on residual stress in thin films was motivated by the need to explain why cracks were observed in chromium thin f ilms sputtered onto plastic automotive parts. Hoffman and Thornton were at the head of this research and produced many publications in this area during the 1960s and 1970s. Their research focused on the effects of sputter deposition on the microstructure of thin films and the causes of residual stress. Their findings showed that the residual st ress in sputtered films had a strong dependence on the working gas pressure. Lower work ing gas pressures resulted in highly compressive residual stresses, up to 2 GPa [37]. A s the gas pressure increased there was a sharp transition from compressive to tensile resi dual stresses over a small pressure range. If the gas pressure continued to increase, the tensile residual stresses would start to decrease in magnitude. The results in Table 3 summarize the effects of ar gon pressure on residual stresses in sputter deposited tungsten films. All sputtering parameters other than gas pressured remained constant to ensure the test cons istency and to separate out the effects of changing gas pressure on residual stress. The r eported stress values in Table 3 were calculated using a curvature method that will be ou tlined in Chapter 3.

PAGE 54

37 Table 3. Effects of argon gas pressure on tungsten residual stress. Pressure (millitorr) Stress (MPa) Current (mA) Volta ge (V) Time (min) 2 Delamination 100 500 60 4 -1500 100 500 60 6 -500 100 500 60 10 1000 100 500 60 The residual stresses measurements listed in Table 3 confirm what was reported by Hoffman and Thornton: substantial amounts of com pressive residual stress are present in sputtered films at low working gas pressures and a transition to tensile residual stress was measured at higher working gas pressures. Figu re 17 shows the quick transition from compressive to tensile residual stress over a short range of argon pressure. Reducing the argon pressure below 2 millitorr was c hallenging because it was difficult to maintain a plasma discharge and film delamination f rom the substrate was common. The 2 GPa of stress at 2 millitorr Ar pressure is only an estimate chosen by following the observed relationship of stress and gas pressure. Delamination of the tungsten films at approximately 2 millitorr was unavoidable. Gas pre ssures above 10 millitorr were not tested because the intended future use of the tungs ten films required them to be in compression. Later, compressively stress tungsten films will be used in the superlayer indentation test for calculating film/substrate int erfacial toughness and for forcing film delamination to create microchannels. Therefore, f or the Ar pressure tests here, it was only necessary to know the transition point between compressive and tensile residual stresses.

PAGE 55

38 -2500 -2000 -1500 -1000 -500 0 500 1000 1500 024681012Stress (MPa)Pressure (millitorr) TensionCompression Figure 17. Residual stress dependence on argon pres sure. A summary of the Hoffman and Thornton findings can be found in Figure 18. There is a similar trend noticed in the results her e and in Figure 18 a). It can be observed that at lower argon pressures the deposited films a re in compression and then there is a quick transition to tensile stresses as the argon p ressure increases. The transition point for tungsten with argon as the working gas was meas ured to be about 3 millitorr less here, than what was reported by Hoffman and Thorton (Figu re 18 b)). The differences in transition points between their findings and the re sults here can be attributed to different sputtering system configurations and current and vo ltage settings [41]. An increase in voltage and current leads to reflected species with higher energies. Increases in current are more substantial with a cylindrical magnetron t han compared to a planar magnetron and this would account for the lower transition pre ssure noticed here.

PAGE 56

39 Figure 18. Hoffman and Thornton findings: a) Residu al stress of Cr films b) Transition points for various targets (Graphs reproduced from [36, 37]). Compressive stress at low gas pressures is primaril y attributed to atoms and backreflected neutral gas atoms reaching the substrate with substantial amounts of kinetic energy. As gas pressure is reduced, the gas scatte ring is reduced resulting in an increase of the normal flux component and the particle energ y striking the film. This suggests an impact that is sufficient enough to disturb the pre viously condensed material, packing it together by “atomic peening”. This atomic peening, or forward sputtering theory, suggests that atoms are displaced from their equili brium positions through a series of primary and recoil collisions. As the collisions c ontinue, the equilibrium positions are changed, resulting in a volumetric distortion. Convincing evidence to support the idea of atomic p eening was conducted by Hoffman and Gaerttner [43]. They measured the resi dual stress in evaporated chromium films, which had a unique system setup that allowed for the evaporation of chromium and introduction of an ion beam simultaneously. Normal ly evaporated films exhibit tensile residual stress, which is comparable to conditions observed in sputter deposition at high a) b) -1500 -1000 -500 0 500 1000 0.1110Stress (MPa)Ar pressure (Pa) TensionCompression 0.01 0.1 1 10 6090120150180Ar pressure (Pa)Atomic mass W Ta Gd Mo Cr

PAGE 57

40 gas pressures. During film deposition, Hoffman and Gaerttner simultaneously bombarded the film with a beam of accelerated inert gas ions. The independent control of metal and inert gas ions impinging upon the grow ing films enabled investigation of the influence of bombarding ions. They observed that w ith the addition of the ion beam, compressive residual stresses were present in the e vaporated chromium films. The addition of the ion beam mimics conditions that wou ld be expected in low pressure sputtering where a majority of the sputtered and ba ck-reflected gas atoms reach the film with substantial amounts of energy. This suggests that the presence of compressive stress in sputtered films is a momentum and energy driven process. Tensile stress will be expected in sputtered films at higher gas pressure due to the increase in collisions taking place in the ambient gas. As the gas pressure is increased during sputtering, gas scattering increases leading to a more significant oblique component of the particle flux. An increased obliq ue component will result in the particle energy and flux being attenuated. When th e particle energy is fully reduced by gas scattering, thermalization has taken place. Th e terminal energy of a sputtered atom is predominately determined by the product of the gas pressure and target to substrate distance [25]. For most sputtering systems the min imum distance between the target and the substrate is 5 cm, which corresponds to nearly all the sputtered and back-reflected particles being thermalized at a sputtering pressur e above 7.5 millitorr. An argon pressure of 7.5 millitorr was observed to be the tr ansition pressure for tungsten in Figure 17. As thermalization increases, there will be a transi tion between compressive to tensile stress. The sputtered atoms and back-refle cted gas ions and neutrals will have

PAGE 58

41 reduced amount of energy due to collisions with the ambient gas. This dramatically reduces the atomic peening effect that resulted in compressive stresses at lower gas pressures. Reduced energy in the sputtered atoms m eans that as the atoms reach the substrate surface, they will have less atomic mobil ity. As the film growth progresses through morphological stages (isolated atomic clust ers, nuclei, island film, continuous film), interatomic attractive forces acting across the gaps between contiguous grains cause an elastic deformation of the grain walls. T he grain boundary deformation is balanced by the intragrain tensile forces imposed b y the constraint exerted by the adhesion of the film to the substrate. Hoffman and coworkers [44, 45] have related the intragrain strain energy to the difference in the s urface energy of the adjacent crystallites and the energy of the resultant grain boundary. Th ey proposed that the elastic strain, in the film is related to the unstrained lattice const ant, a and the variation of the lattice constant, (x-a) or to and d which are the grain boundary relaxation distance a nd the final grain size, respectively. The elastic deform ation, is responsible for the macroscopically observed tensile stress, which is given by d v E a a x v E v E D = = = ) 1( ) 1( ) 1(e s (10), where E and n are the film’s Young’s modulus and Poisson’s ratio respectively. As the working gas pressure is increased further, the low energy sputtered atoms continue to produce tapered columnar structure grow ing side by side but separated by deep crevices and micropores [47-49]. The result o f the tapered columnar structure is a less dense, discontinuous film that cannot support lateral tensile stress and that is why there is a reduction in tensile stresses at high ga s pressures in Figure 18. In addition to the tensile stresses usually found in films sputter deposited at high gas pressures, because

PAGE 59

42 of the tapered columnar structure, the films tend t o have less optical reflectance and higher resistivities [40, 41]. 2.4 Film Structure Previously stated, there are primarily three steps in making a film. A source of film material is provided, the material is transpor ted to the substrate and then the final step is deposition. So far the first two steps hav e been covered in relation to DC magnetron sputter deposition. The third step will now be discussed and a connection will be made with its effect on film structure. A thoro ugh understanding of this step must be acquired because the film structure directly affect s the thin film properties. The process starts with the deposited atoms collidi ng with the substrate surface and starting off as isolated atomic clusters. The clusters will begin to coalesce to form larger islands and then the islands will join to fo rm a film. The efficiency of the atoms to stick together will determine the microstructure. Figure 19 helps to define the different microstructures commonly observed when using PVD pr ocesses. One axis of the graph is the ratio of substrate temperature, T to film melting temperature, T m and the other axis is the working gas pressure. Normally at low depos ition temperatures the mobility of arriving atoms is limited. Therefore, the resultin g film is expected to be less dense, with columnar growth structures separated by voids. Thi s type of structure would account for zone 1 in Figure 19, consisting of tapered columns with domed tops defined by voided growth boundaries. As the temperature increases, t he columns increase in width and are defined by metallurgical grain boundaries and this is zone 2 of Figure 19. The high temperature zone 3 of Figure 19 has a structure tha t consists of equiaxed grains, which increases in size in accordance with activation ene rgies typical of bulk diffusion.

PAGE 60

43 Figure 19. Microstructure zones from sputter deposit ion (Schematic reproduced from Thornton [47]). The trend in device fabrication towards lower proce ssing temperature means that coatings will often be deposited at substrate tempe ratures that are relatively low compared to the coating material melting point. No rmally, this would lead to zone 1 columnar growth structure with voids and would be u ndesirable because this type of structure tends to have an anisotropic character in terms of magnetism and lateral current transport [50]. But for magnetron sputtering, wher e low working gas pressures are used, sputtered atoms reach the surface with high energie s in the 10 – 40 eV range. These high energies lead to increased atomic mobility and the result is a denser film with smaller columnar grains represented by zone T in Figure 19. Along with the increased atom mobility, the atomic peening effect also plays a ro le in producing denser films. To get a better picture of the effects of argon pre ssure on film properties surface, topography scans of sputter deposited tungsten film s were taken and are presented in

PAGE 61

44 Figure 20. It is observed that there are no notice able differences in topography for the tungsten films deposited at 4 and 10 millitorr. Bo th films are thought to be representative of zone T in Figure 19 and were measured to have a surface roughness around 2 nm. The small oval shaped domes that are seen in Figure 19 are thought to be the tops of small densely packed columnar structures and were measure d to be about 300 nm in width. Figure 20. Surface scan of sputter deposited tungst en films; a) Argon pressure of 4 millitorr b) Argon pressure of 10 millitorr. Topographic images of the two tungsten films did no t reveal any noticeable difference between the films. Therefore, to furthe r examine the tungsten films, it was necessary to test the mechanical properties of the films using nanoindentation. A test method was setup that performed a total of 40 inden ts per sample in different locations and varying loads. The method consisted of indenti ng each sample in 5 different locations across a 1 cm 2 area. Eight indents were performed at each locati on in a two rows by four columns pattern, with six microns sepa rating each indent. The indentation load was varied between 1000 and 8000 N with the loading segment times held constant at 10 seconds. 1 m 1 m 4 millitorr 10 millitorr a) b)

PAGE 62

45 After examining the indentation results it was imme diately noticed that there are slight differences in the load-displacement curves of the two tungsten films (Figure 21). The two indents shown in Figure 21 were performed t o the same maximum load, with all the same loading conditions, but the indents reache d different maximum depths. The tungsten film deposited at 10 millitorr argon press ure had a final indentation depth about 10 nm deeper than the tungsten film deposited at 4 millitorr argon pressure. 0 1000 2000 3000 4000 5000 6000 020406080100120 4 millitorr 10 millitorr Load ( m N)Depth (nm) Figure 21. Comparison of the load-displacements cur ves for tungsten films deposited with different argon pressures. Since there was a difference in final indentation d epth, a difference in hardness of the two films would be expected and was measured (F igure 22). Hardness is calculated by knowing the maximum load P max and dividing it by the contact area of the indent er tip A c : cA P Hmax= (11).

PAGE 63

46 Since the contact area will be a function of the de pth of the indenter tip, it is understandable to see a difference between the two tungsten films after observing the difference in load-displacement curves. The tungst en film deposited at 4 millitorr was measured to have an average hardness 4 GPa higher t han the 10 millitorr film. This difference in hardness is the result of different e nergies for the bombarding atoms and ions of the two films. The lower pressure film wou ld be expected to see higher energy atoms and ions colliding with the surface causing m ore atomic peening of the film. This data could be beneficial if an application required a higher hardness film, but it also comes with the consequence of high amounts of compr essive residual stress. 14 16 18 20 22 24 26 28 020406080100 10 millitorr 4 millitorr H (GPa)h c (nm) Figure 22. Hardness of tungsten films deposited at different argon pressures. Along with hardness measurements the stiffness and modulus of the films were tested. Stiffness is plotted in Figure 23 and is d efined as the change in load divided by the change in depth:

PAGE 64

47 dh dP S = (12). The stiffness of both tungsten films matched up and showed no dependence on the argon pressure. Since the stiffness of the films was com parable, it’s expected that the reduced modulus measured as a function of the indent depth, would also show no significant differences for the two tungsten films (Figure 24). The reduced modulus E r can be expressed as the following: c r A S E 2 =g p (13), where is a correction factor that depends on the strain imposed by the indenter and the Poisson’s ratio of the sample. The reduced modulus takes into account any compliance of the indenter and it can be related to the sample ’s modulus by the following expression: i i s s r E v E v E ) 1( ) 1( 1 2 2 + = (14), where E s and v s are the elastic modulus and Poisson’s ratio for th e sample, respectively. E i and v i are the same properties, but for the indenter tip which is usually diamond. Both films were measured to have a maximum reduced modul us of approximately 230 GPa for contact depths between 20 and 40 nm. The reduced m odulus then decreased as a function of the contact depth to a minimum value of approxim ately 215 GPa at contact depths around 100 nm for both films.

PAGE 65

48 60 80 100 120 140 160 020406080100120 10 millitorr 4 millitorr S (dP/dh)h c (nm) Figure 23. Stiffness of tungsten films deposited at different argon pressures. 210 215 220 225 230 235 240 020406080100 10 millitorr 4 millitorr Er (GPa)h c (nm) Figure 24. Reduced modulus of tungsten films deposi ted at different argon pressures.

PAGE 66

49 The large variation in hardness and reduced modulus for both of the tungsten films in Figure 22 and Figure 24 is primarily thoug ht to be the result of the sputtering system used. A dynamic environment exists inside o f a DC magnetron sputtering system. Factors such as a non-uniform magnetic field, will lead to non-uniform sputtering rates, film thicknesses and particle energies across the s puttering target and substrate. These non-uniformities mean that this system is difficult to predict and it will be expected to see variations in film microstructure and residual stre ss across the area of a wafer. Some of the data variance at the shallower indentation dept hs is the result of the measurement technique and will be discussed later. 2.5 Summary of Sputtering Results The basics of sputtering have been covered here, wi th more specific details focused on DC planar magnetron sputtering. Similar to other types of film deposition, sputtering has its advantages and disadvantages. O ne major advantage of this deposition method is that sputtering is not limited to one typ e of deposited material. Depending on the type of power source used, sputtering can depos it insulating materials and refractory metals that are normally a challenge for other depo sition methods. By using magnetron sputtering, film deposition rates are relatively hi gh and deposition temperature can be kept low. The disadvantages of magnetron sputterin g should not necessarily be thought of as disadvantages, but things to be aware of. If film thickness uniformity is a major concern, special care must be taken in choosing the appropriate system setup and geometry. Options such as rotating the substrate/s ubstrates, changing the anode to cathode distance, adjusting the magnetic field and inserting meshes are all possibilities

PAGE 67

50 for improving film thickness uniformity. Depending on the system configuration, film thickness has been observed to vary by 45 % across the radius of a 4” diameter wafer. It has been shown that working gas pressure affects the deposition rate, residual stress and microstructure of a film. The gas press ure influences the transport behavior of sputtered atoms through the ambient gas and onto th e films surface. If gas pressures are low, there will be fewer collisions in the ambient gas. This allows for more energy upon impact of the film, resulting in denser films that will typically be in compression. The main theory behind the introduction of compressive stress at low sputtering pressures is atomic peening. When the gas pressure is low, sput tered atoms and back-reflected gas particles will reach the film surface without losin g significant amounts of energy to collisions in the ambient gas. The high momentum/e nergy impacts result in an atomic packing of the film. As gas pressure increases, there will be more colli sions of the sputtered atoms and back-reflected gas particles with the ambient gas, resulting in less dense films that will typically be in tension. The arriving atoms have l ess atomic mobility resulting in a tapered columnar film structure, which is filled wi th micropores and voids separating the columns.

PAGE 68

51 Chapter 3 Residual Stresses in Thin Films 3.1 Thin Film Residual Stress Desirable or not, internal or residual stress is a lmost always going to be present in thin films. Stress may be present in thin films wh ether or not external loads are applied and may be due to a variety of reasons that are int roduced during film deposition, which include: differential thermal expansion of the film /substrate, mismatches between the lattice parameter of the film and the substrate, at omic peening, incorporation of foreign atoms, microscopic voids, variation of interatomic spacing with crystal size, recrystallization processes, crystallite coalescenc e at grain boundaries and phase transformations [50-52]. To clarify between common ly used terms when discussing stress in thin films, residual stress, r will be used as a more inclusive term. It will include the contributions of both thermal stress, (T) and intrinsic stress, i Thermal stress in thin films will develop because of differ ential thermal expansion of a substrate/film system. Differential thermal expans ion of the film and the substrate is due to a mismatch in coefficients of thermal expansion (CTE). When a film/substrate composite experiences a change in temperature, the two different materials are going to expand or contract by different amounts. However, continuity of strain must be preserved, which means that both materials will be constrained, resulting in thermal stress. Intrinsic stress is defined as the interna l stress created as a result of the growth

PAGE 69

52 processes during film deposition. Therefore, the r esidual stress can be defined as the sum of the two types of internal stresses: i r Ts s s+ = ) ( (15). Residual stress in films can be either compressive or tensile. If the stress is large enough, it could lead to fracture of the substrate, film or substrate/film interface. According to the theorem of minimum energy, the equ ilibrium state of an elastic solid body is when the potential energy of the system is at a minimum. For a system that is experiencing externally applied forces or residual stress, the system may find an equilibrium position if rupture has occurred reduci ng the potential energy of the system [53]. Summarizing the theorem of minimum energy, t he strain energy caused by residual stress may be reduced by the rupture or delaminatio n of the film. In extreme cases tensile residual stress may lead to film cracking and peeli ng away from the substrate [54] and compressive residual stress may lead to film buckli ng and delamination from the substrate (Figure 25). Figure 25. a) Low-k dielectric film in tension [54] and b) tungsten film in compression. a) b) 100 m 30 m

PAGE 70

53 Besides the extreme cases just mentioned, residual stresses may also lead to the generation of crystalline defects, imperfection of epitaxial layers and the formation of film surface features such as hillocks and whiskers [11]. These less obvious results of residual stress may affect material properties such as magnetization, reflectivity and electrical conductivity [36, 51]. 3.2 Measuring Residual Stress Completely avoiding residual stresses in thin film s is impossible to do. For many applications small amounts of residual stress may b e tolerable and may not have any significant effects on the operation and reliabilit y of the device. For ensuring device operation and for optimizing deposition parameters, it is necessary to measure the amount of residual stress in thin films. Techniques for m easuring residual stress will be different from the techniques used for measuring the stress a s the result of externally applied forces. For externally applied loads there will be a direct cause and effect that is in general, easily measured. For example, if an exte rnal force is uniaxially applied to an arbitrary body, the result will be a deformation of the body that is proportional to the applied force. The amount of deformation can be re lated to the initial dimensions of the body, and is defined as the strain, : 0 0 0 l l l ld e= = (16), where l’ and l 0 are the deformed and initial body lengths, respect ively, and is the absolute deformation. If the strain is kept within elastic limits, the bo dy will return to its initial shape upon unloading and the material is said to be perfe ctly elastic. In most cases the strain

PAGE 71

54 can be directly measured during loading and unloadi ng by the use of extensometers or strain gages. By the use of Hooke’s law, which def ines stress as being proportional to strain, the stress can then be calculated. For res idual stress in thin films, a simple measurement of the strain produced during depositio n is not as straight forward. Residual stress produced during sputter deposition is an example where strain gages and extensometers cannot be used to get a direct measur ement of strain. One tell-tale sign of having large amounts of resid ual stress in a film is by observing the effects it has on its substrate. In extreme cases the film will spontaneously delaminate from the substrate, where in other cases there may be apparent bending of the film/substrate. In the mid 1800s to early 1900s, m any scientists observed these unwanted results when electrolytically depositing metallic f ilms [55, 56]. Since those early observations, calculating residual stress in films by measuring the change in curvature of the substrate before and after film deposition has been a popular method. The use of Xray diffractometry has also become an accepted tech nique for determining residual stress in crystalline films where a direct determination o f elastic strain is possible. 3.2.1 Curvature Method The majority of formulas used in the determination of thin film residual stress by curvature techniques are variations of an equation first given by G. Stoney in 1909 [56]. The derivation of the formula is relatively straigh t forward and is based on a mechanics of materials approach. Hypothetically starting wit h a film under compressive residual stress, an exaggerated film/substrate pair would ap pear as shown in Figure 26. The compressive stress is the result of the film wantin g to expand, but it is being constrained

PAGE 72

55 by the substrate. Therefore, the system would be c oncave downward with a negative curvature. Figure 26. Schematic of film/substrate bending due to compressive residual stress in the film. A solution for solving the stress in the thin film can be started by first maintaining mechanical equilibrium, which requires that the net force F vanish on any film/substrate cross section: = A dA Fs (17), where s is the stress and A is the cross sectional area. A free body diagram of the system is represented in Figure 27, where statically equiv alent combinations of forces and moments have replaced the interfacial set of forces The force and moment of the film are represented by the symbols F f and M f respectively, and F s and M s are for the substrate. The force F f must be equal to the force F s and can be imagined to act uniformly over the cross sectional area, tw ( w is the film width), giving rise to the film stress, f The moments are responsible for the bowing of th e film/substrate system their sum must also be equal to zero, yielding the expres sion: s f f s fM M d t F d F t F + = + = + 2 2 2 (18), where t and d are the film and substrate thicknesses, respective ly. substrate film

PAGE 73

56 Figure 27. Free body diagrams of the film and subst rate with indicated forces and moments. Since the film/substrate pair is not restrained fro m moving, it will bend to counteract the unbalanced moments and it can treate d as a beam with the curvature, k, where the curvature is defined as the following pre sented in Figure 28: 2 2 1 dx y d C ds d R k = = =q (19). ()[] 2/3 2/ 1 1 dx dy C + = (20). For conditions of small defections (dy/dx << 1) it is assumed that C = 1 and the curvature can be approximated as: 2 2 dx y d k = (21). F f F f F s F s M f M f M s M s

PAGE 74

57 Figure 28. Elastic bending of a beam under an appli ed moment. As the deflection increases the value of C will change and can no longer be assumed to be 1. Table 4 shows the change in C with an increase in the slope of a beam. An increase in the slope of the beam, dy/dx, corres ponds to an increasing deflection. In one of the more extreme cases of wafer bowing seen later, dy/dx was measured to be 0.000583. Therefore, it was safe to assume C = 1 for all cases here. Table 4. Small-deflection assumptions C = 1. dy/dx 0.01 0.05 0.10 0.25 0.50 1.00 2.00 (deg) 0.6 2.9 5.7 14.0 26.6 45.0 63.4 C 0.9999 0.9963 0.9852 0.9131 0.7155 0.3536 0.0894 The longitudinal strain will vary linearly with the distance from the neutral axis and is proportional to the curvature of the beam. By applying Hooke’s law for the normal bending stress: d t R M x y M

PAGE 75

58 y k E m =s (22), where E is the elastic modulus of the substrate material a nd y is the distance from the neutral axis. The bending moment corresponding to this stress distribution across the beam section will be: 12 3 2 2/ 2/ 2/ 2/ d w k E dA y k E dA y M d d d d m = = = --s (23). Extending this result for both the film and substra te: 12 12 3 3d w k E M t w k E Ms s f f = = (24). Substitution of this last expression back into equa tion (18) and assuming biaxial stress rather than uniaxial stress, where E is replaced with E/(1n ) gives: () () s s s f f f d w k E v t w k E d t Fn + = + 1 12 1 12 2 3 3 (25), where nf and ns are the film and substrate Poisson’s ratios, respec tively. Since d is usually much larger than t the film stress is solved to be: () t v k d E w t F s s f f = = 1 6 2s (26). Equation (26) is the Stoney formula, where f is calculated from the measured change in curvature before and after film depositio n, knowing the film and substrate thicknesses and the substrate mechanical properties Some care must be taken when using the Stoney equation for determining residual stress in the deposited film because the derivation of the formula used the following as sumptions: 1) Both the film and substrate are homogeneous, isotropic and linearly e lastic materials, 2) small deformation is present in the substrate (dy/dx << 1), 3) unifor m curvature with the system’s curvature

PAGE 76

59 components being equi-biaxial, 4) uniform film and substrate thickness with t f << t s 5) the film stress states are equi-biaxial while the o ut of plane stress and shear stresses are zero and 6) perfect adhesion between the film and t he substrate. 3.2.2 Stress Calculation Assuming Uniform Curvature and Film Thickness There are many tools that work well for calculatin g residual stress in thin films based on the curvature method previously discussed. For many of the tools available, the assumptions used when deriving the Stoney formula a re also made for the stress calculation. For example, the user will be asked t o input the substrate and film thicknesses and the substrate mechanical properties E and n From there it is assumed that materials are isotropic and homogeneous and th at the thicknesses are uniform. The only measurement that is taken by the equipment wil l be the curvature before and after film deposition. The method used for measuring the curvature will vary from manufacturer to manufacturer and include optical, m echanical, magnetic and electrical methods. A Flexus 2-300 is one of the tools used here, whic h utilizes an optical method for measuring the curvature in order to calculate the t hin film residual stress. It uses a single laser and a series of mirrors and optics to split t he beam into two parts and direct them down at the sample surface. If the sample surface is optically smooth, the two beams will be reflected off the sample surface and detected by two light sensors that record the beams’ position. As the curvature of the sample ch anges, the position of the reflected light beam on the light sensor will also change. B y knowing the geometry of the system, presented in Figure 29, the curvature can be calcul ated for the sample. The curvature is straightforward to calculate by knowing two distanc es: 1) the distance between the wafer

PAGE 77

60 and light detectors and 2) the distance between the two points where the laser beam hits the wafer. From there, the angles and in Figure 29 can be determined, which can be related to the slope of the wafer at the two points ) ( tan 2 1A slope-= p a (27), ) ( tan 2 1B slope-= p b (28). With those two angles known, the angle can be found, which is used with the distance between the two laser beams, D to calculate the radius of curvature: b a p = F (29), D R F = (30). This geometric proof is only valid for small angles where the straight line D can be assumed to be equal to the arc length. Figure 29. Geometry of the Flexus 2-300 curvature c alculation. The sample holder for the Flexus 2-300 requires 4” or 6” wafers and it can be rotated in 45 increments. It also has a heating t able built into the sample holder so that thermal stress can be calculated. Since the radius of curvature is found by using two D A B reflected beams incoming beams sample surface detectors

PAGE 78

61 points from the wafer and geometric relations of th e system, the Flexus cannot account for changes in the curvature across the wafer. The refore, a uniform film thickness and curvature is assumed at each 45 increment of rotat ion. At best, an average stress can be reported by averaging the stress calculated from th e four different possible directions of rotation. In the case of axisymmetric curvature an d stress, the curvature and stress only depend on the radial position. Therefore, no chang es in curvature and stress will be noticed in the circumferential direction, which cor responds to the rotation of the wafer on the Flexus stage. So it would be possible to have the residual stress be reported equal for all four stage rotations, even though the residual stress is non-uniform in the radial direction. Figure 30. Flexus 2-300 stage rotation. In general, the Flexus system is reliable and simp le to use, but is limited if there are significant non-uniformities of film thickness, radius of curvature and residual stress. The user is confined to assuming uniformity which m ay be very costly in the end when considering the future application of the film/subs trate combination. Given these limitations a different method for measuring the ra dius of curvature was needed. 45 R 1 n 1 R 2 n 2 R 4 n 4 R 3 n 2

PAGE 79

62 3.2.3 Accounting for Non-uniformities Unfortunately, there are many thin film deposition methods currently used that make it difficult to agree with all the assumptions used in the Stoney equation. For example, depending on the system parameters of magn etron sputter deposited films, film thickness, quality and deposition rates may be diff icult to keep uniform across the area of a substrate. Magnetron sputtering systems have foun d wide application in commercial coating processes, particularly for the deposition of thin metallic films. Their acceptance is due to the possible combinations of high current densities at moderate voltages and reduced gas scattering of the sputtered atoms at lo w operating pressures, which results in higher depositions rates than non-magnetron systems However, magnetron systems do have some disadvantages when it comes to film thick ness uniformity. It has been widely studied that film thickness uniformity can be affec ted by non-uniform magnetic fields, gas pressure, target to substrate distance and shea lth thickness in magnetron systems [2833]. In order to maintain the desired film properties, n on-uniformities in film thickness and stress must be first quantified and then contro lled through the deposition process. With such non-uniformities being present, the tradi tional approach of using Stoney’s formula may not be adequate. In order to compensat e for non-uniformities in film thickness and curvature, a localized approach using the Stoney formula has been attempted. Instead of ignoring the assumptions mad e in the derivation of the Stoney equation, the Stoney equation was applied to smalle r areas of the wafer where variations in curvature and film thickness were minimal. Ther efore, the Stoney equation assumptions would be satisfied in the localized are as.

PAGE 80

63 To carry out this localized approach, samples were profiled before and after film deposition using a Tencor P-20h profilometer. Init ial tests were performed on 4” (100) silicon wafers that were later coated with tungsten films using a DC magnetron sputtering system. The goal of the initial tests was to deter mine whether or not there was uniformity in the radius of curvature across a wafer. Uniform ity was not expected because it had already been observed that film thickness varied ra dial when using the CRC-100 sputtering system (Figure 15). The total scan length of the initial wafer profiles was 6 cm taken at 15 increments. This was done to map the changes in cu rvature over a large portion of the wafer surface. The scan speed was 2 mm/sec with a sampling rate of 50 Hz. The scan speed and the sampling rate were chosen to ensure c lean data and to keep the total number of data points within a reasonable size ( 1000 pts.). Since the profilometer stage was flat, the wafers were setup on a tripod configu ration using 3 steel balls mounted to the profilometer stage. This configuration ensured that the wafers would not rock on the stage because of their curvature. Modifications had to be made to the profilometer stage in order to achieve a repeatable placement of the w afers before and after film deposition. To do this, metal stops were mounted to the profilo meter stage so that the wafer placement would be confined in two directions. Two stops were placed close together in order to mate up with the flat side of the wafer an d maintain rotational confinement and a third stop was used to maintain directional confine ment. The setup and stage layout for scanning 4” wafers can be seen in Figure 31.

PAGE 81

64 Figure 31. Profilometer stage layout for 4” wafers. A profile taken from a wafer before and after film deposition is shown in Figure 32. The scan was started 3 cm to the left of the w afer center, with the scan direction moving to the right, crossing through the center of the wafer and having a total scan length of 6 cm. Deflection of the wafer in the y-d irection after film deposition appears more extreme than what the true deflection is becau se of the placement of the coordinate origin in Figure 32. This is the result of the pro filometer software automatically assigning the x and y-coordinates, (0, 0), at the s tarting point of the scan. The way in which the coordinates are defined by the profilomet er is of no consequence in the determination of the film’s residual stress since a change in curvature is required when using the Stoney equation. For this example a tung sten film was sputter deposited at a low argon pressure (4 millitorr), introducing a sig nificant amount of compressive residual stress. The final wafer shape is bowed concave dow nwards because of the compressive residual stress, resulting in a negative curvature. The x-axis was also adjusted in Figure 32 to place the center of the wafer at an x-positio n equal to zero. 15 Stops 4” Wafer Stage rotation Steel balls

PAGE 82

65 -30 -25 -20 -15 -10 -5 0 5 10 -3-2-10123 Before AfterProfile ( m m)x-pos (cm) Figure 32. Profiles of a wafer before and after fil m deposition. With a relatively small maximum displacement, the s econd derivative of the profile can be considered equal to the curvature wi thout introducing a significant amount of error (Table 4). To continue with the localized approach, the profiles in Figure 32 where broken into 20 segments of 3 mm lengths. Eac h 3 mm length was curve fitted with a second order polynomial (Figure 33). A second or der polynomial was sufficient for the 3 mm profile lengths and a correlation coefficient > 0.9999 was consistent for all segments. The second derivative of the curve fit wa s taken to be equal to the curvature of the segment. The difference in curvature before an d after film deposition was used in the calculation of the residual stress in the film segm ent using equation (24).

PAGE 83

66 -7 10-7-6 10-7-5 10-7-4 10-7-3 10-70.0030.0040.0050.006 Profile data Curve fit Profile (m) x-pos (m) Y = M0 + M1*x + ... M8*x 8 + M9*x 9 7.192e-08 M0 -0.00010717 M1 -0.0042264 M2 0.99991 R Figure 33. Finding the curvature of 3 mm segments. The change in curvature from before and after film deposition across the wafers was more significant than originally hypothesized. A plot in the change of curvature for a tungsten film deposited at 4 millitorr Ar pressur e is shown in Figure 34. The error bars in Figure 34 represent the deviation in curvature m easured as the wafer was rotated at 15 increments. The deviation from the average value i s less than 10 % and can be primarily attributed to the center of wafer not being aligned with the center of the sputtering target during film deposition. A small deviation could al so be expected from the center of rotation during profiling being slightly off from t he center of the wafer. With that in mind, it can be established that the curvature is a xisymmetric and is a function of the radial position. Any deviation observed in the cir cumferential direction is thought to be

PAGE 84

67 the result of the off-centered wafer placement duri ng film deposition and profile measurement. -0.035 -0.03 -0.025 -0.02 -0.015 -0.01 -0.005 -3-2-10123 x-pos (cm)Curvature (m-1) Figure 34. Change in wafer curvature after film dep osition at 4 millitorr Ar pressure. A maximum absolute value of the curvature change oc curs at the wafer center in Figure 34 and then decreases with an increasing rad ial position. Figure 35 is a plot in the change of curvature for a tungsten film deposited a t an Ar pressure of 10 millitorr. As observed in Figure 34, there is a maximum absolute value of the curvature change at the center of the wafer. An interesting transition occ urs in Figure 35 where there is a point of inflection and the curvature changes from a positiv e to negative as the radial position is increased. This transition indicates that there is a change from tensile to compressive residual stress. The transition in curvature adds to the dynamic nature possible by magnetron sputtering systems that was confirmed in Chapter 2 of the manuscript.

PAGE 85

68 -0.012 -0.008 -0.004 0 0.004 0.008 0.012 0.016 0.02 -3-2-10123Curvature (m -1 )x-pos (cm) Figure 35. Change in wafer curvature after film dep osition at 10 millitorr Ar pressure. Before the residual stress could be calculated, the change in film thickness had to be accounted for. The film thickness profile was f ound earlier to be axisymmetric and only dependent on the radial position. In order to assign a film thickness to each of the individual profile segments, a fourth order polynom ial was fitted to the film thickness profile data obtained from the sputtering experimen ts (Figure 36). This allowed for the film thickness to be calculated at any radial posit ion, assuming that the shape of the profile does not change from experiment to experime nt. The center point of each localized segment was used for calculating its film thickness, and was assumed uniform for the entire segment. The film thickness differe nce across a 3 mm segment was found to vary by less than 1 % at the center portion of t he wafer, up to approximately 4 %, 4 cm out from the wafer center (Figure 36).

PAGE 86

69 4.5 10 -7 5.5 10 -7 6.5 10 -7 7.5 10 -7 8.5 10 -7 -0.5-0.2500.250.5 Thickness data Curve fitFilm thickness (m) x-pos (m) Y = M0 + M1*x + ... M8*x 8 + M9*x 9 7.9638e-07 M0 5.9621e-09 M1 -2.09e-06 M2 -5.9581e-08 M3 2.9184e-06 M4 0.99059 R Figure 36. Fourth order polynomial used to fit the thickness profile. To account for differences in film thickness betwee n sputtering runs, a small piece of a glass slide was placed on the outer edge of the 4” wafers before film deposition. After film deposition the glass piece was removed and a profilometer was used to measure the step height in film thickness a t the outer edge of the wafer. Differences measured in the outer edge film thickne sses compared to the fitted thickness profile could be adjusted for by changing the M0 ter m in the fourth order polynomial shown in Figure 36. M0 is the constant in the polyn omial equation and allows for the curve adjustment in the y-direction. By accounting for film thickness differences this way, the profile shape is assumed to be constant, w hich is a source of small error in calculating film thickness.

PAGE 87

70 By using the approach outlined above, each segment will have a unique curvature and film thickness, which is only dependent on its radial position. Equation (26) was applied to each segment to calculate the residual s tress in the film. Results of using the localized approach are shown in Figure 37 and Figur e 38. As observed in the curvature figures, error bars are used to show the variation in residual stress measured at the different 15 rotation increments. Figure 37 is a plot of the residual stress calculated in a tungsten film that was deposited at 4 millitorr Ar pressure. A maximum residual stress of approximately -1500 MPa is located at the center of the wafer, which coincides with the maximum change in curvature plotted in Figure 34. As the radial position is increased, there is a sharp decrease in residual stress which hits a minimum of approximately -600 MPa at a radial position of 3 cm. Figure 38 is a plot of the residual stress calculat ed in a tungsten film that was deposited at 10 millitorr Ar pressure. A maximum t ensile residual stress of approximately 1000 MPa is located at the center of t he wafer, which coincides with the maximum positive change in curvature plotted in Fig ure 35. As the radial position is increased, there is a sharp transition in residual stress towards compressive stress. A maximum compressive residual stress was calculated to be approximately -800 MPa at a radial position of 3 cm.

PAGE 88

71 -1600 -1400 -1200 -1000 -800 -600 -3-2-10123Stress (MPa)x-pos (cm) Figure 37. Residual stress in a tungsten film depos ited at 4 millitorr Ar pressure. -1000 -500 0 500 1000 -3-2-10123Stress (MPa)x-pos (cm) Figure 38. Residual stress in tungsten film deposit ed at 10 millitorr Ar pressure.

PAGE 89

72 After examining the results plotted in Figure 34 th ru Figure 38, there are two significant effects to be noticed. First, it was o bserved that the film thickness, change in curvature and residual stress were all axisymmetric about the wafer center. There was some deviation in the rotational direction, but tha t would be expected with a slightly offcentered film deposition and wafer prolife. Theref ore, the deviation is thought to be caused by experimental setup and could be reduced w ith future modifications to wafer placement. Second, there was a significant change in stress as a function of the radial position, which in one case changed from tensile to compressive. Because of these observations, it was decided to ma ke changes to the profiling method. To further examine the change in curvature and residual stress at larger radial positions, the total scan length was increased to 8 cm. Along with an increased scan length, the scan speed was increased to 5 mm/sec to keep the total number of data points at 1000. Due to the axisymmetric results observed, the rotation increment was increased to 45. The individual segment size was also incre ased from 3 to 4 mm, while the total number of segments for each scan was kept at 20. T hese changes allowed for a larger profile of the wafer to be taken without collecting as many data points as in the initial tests. Along with a change in the profile method, a change in Ar pressure was made for the next test. Previous trials resulted in tungsten films that were predominately either in compressive or tensile residual stress. Therefore, an Ar pressure of 6 millitorr was chosen to try and deposit a film with little or no residual stress present. As before, the sputtering current was kept at 100 mA, the voltage was 0.5 kV and the deposition time was 60 minutes. Figure 39 displays the change in c urvature results for a tungsten film

PAGE 90

73 deposited at 6 millitorr. Similar to the 10 millit orr film, there is a combination of both positive and negative curvatures. A negative curva ture was measured within approximately 1 cm of the center of the wafer and t hen at larger radial positions there is a transition to a positive curvature. At approximate ly 2 cm out, the curvature hits a maximum and then starts to decrease in magnitude wi th an increasing radial position. As expected, the residual stress follows the same patt ern as the change in curvature across the wafer (Figure 40). There is a maximum compress ive stress of approximately -450 MPa at the wafer center decreasing to zero stress ap proximately 1 cm out from the center. A maximum tensile stress of about 900 MPa was calcul ated between 2 and 3 cm out form the center. -0.015 -0.01 -0.005 0 0.005 0.01 0.015 0.02 0.025 -4-3-2-101234Curvature (m -1 )x-pos (cm) Figure 39. Change in wafer curvature after film dep osition at 6 millitorr Ar pressure.

PAGE 91

74 -600 -400 -200 0 200 400 600 800 1000 -4-3-2-101234Stress (MPa)x-pos (cm) Figure 40. Residual stress in tungsten film deposit ed at 6 millitorr Ar pressure. Addition proof of the residual stress axisymmetric state seen in Figure 34-Figure 40, can be observed in Figure 41, where spontaneous delamination of a tungsten film happened immediately after sputter deposition. The tungsten film in Figure 41 was deposited at 2 millitorr Ar pressure, with a sputte ring current of 100 mA, a voltage of 0.5 kV and a deposition time of 60 minutes. It was dep osited onto a 4” (100) silicon wafer and it was estimated to have maximum compressive st ress around 2 GPa. Delamination was noticed within seconds of the power being turne d off and it occurred while the system was being vented. Complete delamination of the film was confined to about a 1.25” diameter area, where delaminations of various morphology can be observed heading in all directions. Continuing from approxi mately 1.25” from the wafer center to about 2”out, telephone cord delaminations take over and extend outward in the radial direction.

PAGE 92

75 Figure 41. Delamination of a tungsten film deposite d at 2 millitorr Ar pressure. To test the effect of segment size selection on the curvature and residual stress results, a comparison was performed on the tungsten film deposited at 4 millitorr in one of the scan directions. One trial was with the seg ment size increased to 10 mm, which resulted in the profile being broken down into 6 se gments. The stress calculation method remained the same as in the 20 segments procedure, where a film thickness was calculated at the center of segment and assumed to be uniform. A second trial was performed where the curvature was continuously defi ned across the wafer by fitting a fourth order polynomial to the profile data. This allowed the curvature to be defined at any radial position because the second derivative d id not reduce the curvature fit down to a constant. By using the continuous curvature prof ile in conjunction with the thickness variation, the stress was calculated continuously a cross the wafer by using equation (26). The results are presented in Figure 42. 2”

PAGE 93

76 -1500 -1000 -500 0 500 -3-2-10123 Continuous 20 segments 6 segments Stress (MPa)x-pos (cm) Figure 42. Effects of using different segment sizes on the stress results. There was not a significant difference observed in the stress results when using 3 and 10 mm segment sizes. For both segment sizes a maximum compressive stress of approximately 1500 MPa was calculated in the center of the wafer and a minimum compressive stress of approximately 800 MPa was calc ulated at the outer segments. The biggest difference in stress results was observed w hen the continuous calculation method was used. It resulted in a maximum compressive str ess of about 1000 MPa at the center, which is 30 % less than what was calculated with th e 3 and 10 mm segment sizes. Even larger differences in the calculated residual stres s were observed at the outer edges of the scan. For the continuous calculation there was a t ransition from compressive stress to tensile stress, which was not observed using the 3 and 10 mm segment sizes. The reason for the discrepancies at the center and the outer e dges is due to the fourth order

PAGE 94

77 polynomial deviating from the experimental data at those locations. This was not noticed at first because the fourth order polynomial select ed had a correlation coefficient of 0.99969. It wasn’t until a closer look was taken a t the sections in question and a deviation in the curve fit and experimental data wa s noticed (Figure 43). Figure 43. Deviations of fourth order polynomial cu rve fit from experimental data. Even though there is only a 10 % difference in the y-position noticed in Figure 43, it is the second derivative that is used in calcula ting stress. Therefore, the difference in 0 1 10 -6 2 10 -6 3 10 -6 4 10 -6 5 10 -6 6 10 -6 7 10 -6 8 10 -6 -0.03-0.02-0.0100.010.020.03y-pos (m)x-pos (m) Y = M0 + M1*x + ... M8*x8 + M9*x9 7.6233e-06 M0 2.3317e-05 M1 -0.010591 M2 -0.027774 M3 2.5381 M4 0.99969 R 7.4 10-67.5 10-67.6 10-67.7 10-67.8 10-67.9 10-600.0020.004y-pos (m)x-pos (m) -1 10-70 1 10-72 10-73 10-74 10-75 10-76 10-70.0280.0290.03y-pos (m)x-pos (m)

PAGE 95

78 stress is caused by taking the second derivative of a curve fit that is inaccurate at certain locations. It is concluded that separating the pro file scans into small segments is the best way to quantify changes in residual stress. Keepin g the segment size small allows for accurate determination of the curvature and film th ickness at the individual segments’ locations. To substantiate the stress results calculated using the Stoney equation on multiple segments, X-ray diffraction was also performed to c alculate the residual film stress. Similar to the previous methods, the stress can not be directly measured. With X-ray diffraction the change in lattice plane spacing is measured and is related to the film stress. 3.2.4 X-ray Diffraction By understanding the diffraction geometries betw een an X-ray beam and a material, X-ray radiation can be used to measure th e spacing between lattice planes in crystalline materials. When external loads are appl ied or residual stress is present in these materials, they will deform in response to the load s or residual stress. This strain will result in a change of the lattice planes spacing an d have an effect on the diffraction geometry. With the assistance of X-ray diffraction the change in interplanar spacing acts as an internal strain gage. By scanning the X-ray detector over a range of 2 angles (Figure 44), the interplanar spacing d can be found with the use of Bragg’s law: ( q l sin 2 = d) (31) where is the X-ray wavelength.

PAGE 96

79 Figure 44. Schematic of the diffractometer setup. The use of X-ray diffraction for residual stress me asurements can be made with the conventional powder X-ray diffractometer. It i s generally intended for polycrystalline materials with random grain orientation and well de fined elastic constants. Ordinarily a high Bragg angle plane is chosen and strain measure ments are made at several arbitrary angles (Figure 45) ranging from 0 to 90. This me thod of measuring the interplanar spacing at various angles is referred to as the sin 2 technique and has been used by many researchers for calculating the residual stres s in thin films [57-61]. By using the theory of elasticity, along with the lattice planes spacing measurements, the stress (residual or applied) acting on the lattice planes can be determined. By using the transformation of strain in a three di mensional body, the principal strains in the film can be solved for. To start, a coordinate system for the specimen must be defined and is shown in Figure 45. The specimen coordinate system is defined by the axis S i with S 1 and S 2 positioned on the specimen surface and S 3 is normal to the specimen surface. A reference coordinate system re lated to the X-ray equipment must 2 Detector X-ray tube

PAGE 97

80 also be defined and it is referred to as the labora tory system. It is defined by L i where L 3 is in the direction normal to the family of planes (hkl) and makes an angle with S 3 L 1 and L 2 are on the plane defined by S 1 and S 2 and make an angle with S 1 and S 2 respectively. It is important to have a clear defi nition of the specimen and laboratory coordinate systems because their relationships are needed for the transformation of strain. Figure 45. Sin 2 technique. Once the lattice spacing, d is obtained from the position of the diffraction peak for a given reflection (hkl), the strain along the L 3 direction may be obtained from: 0 0 33 ) ( d d d = FY FYe (32), where d 0 is the unstressed lattice spacing. The strain, ( 33 ) may be expressed in terms of the strains in the sample coordinate system by u tilizing the transformation rule for second rank tensors: kl l k a ae e3 3 33) ( =FY (33), S 2 S 1 S L 3 S 3 L 1 L 2

PAGE 98

81 where a 3k and a 3l are the direction cosines between L 3 and S k and S l respectively. To remain consistent from here on, the suffix notation will be used to describe the Cartesian tensors. To find the direction cosine matrix for t his case, the individual rotations need to be determined first. The first individual rotation is by about the S 3 axis, and is given by the matrix A3 : 1 0 0 0 cos sin 0 sin cos 3 F F F F = A (34), and the second individual rotation will be about the S 2 axis and is given by the matrix A2 : Y Y Y Y = cos 0 sin 0 1 0 sin 0 cos 2 A (35). The complete direction cosine matrix for the new co ordinate system is the product of the individual rotations given in equations (34) and (3 5): 3 2 A A a ik = (36), Y Y F Y F F F Y Y F Y F = cos sin sin sin cos 0 cos sin sin cos sin cos cos ik a (37). Substituting for a 3k and a 3l in equation (33) and using the double angle formul a for sine and cosine (t t t cos sin 2 sin = ) to simplify the expression, ( 33 ) can be solved for: 0 0 33) ( d d d =FY FYe = Y + Y F + Y F + Y F + Y F + Y F2 33 13 23 2 2 22 2 12 2 2 11cos 2 sin cos 2 sin sin sin sin sin 2 sin sin cose e e e e e (38).

PAGE 99

82 This is the fundamental equation of X-ray strain de termination and is a linear equation of six unknowns that may be solved if d is solved in six independent directions. When analyzing polycrystalline materials, it is possible to obtain a diffracted beam at all tilts (-90 90) and there will be three types of d versus sin 2 behavior (Figure 46). Figure 46. Types of d versus sin 2 plots observed in residual stress analysis from polycrystalline materials: a) equi-biaxial stress, b) shear strains are non-zero and c) anisotropic elastic constants. Figure 46 a) depicts a linear d versus sin 2 behavior that can be expected when the shear strains are zero. When the shear strains are non-zero, d measured at positive and negative will be different, causing a split in the data whi ch is shown in Figure 46 b). If there is a presence of a non-homogeneous st ress/strain state or anisotropic elastic constants, there will be an oscillation in the d versus sin 2 plot similar to that depicted in Figure 46 c). Once the strains are obtained, the stresses in the S i coordinate system may be calculated from the general form of Hooke’s law: kl ijkl ijCe s= (39), sin 2 d sin 2 d sin 2 d a) b) c)

PAGE 100

83 where the elastic coefficients, C ijkl are referred to the S i coordinate system. The stresses in any other coordinate system may be determined fr om the transformation rule for second rank tensors: ij nj mi mn a as s= (40). The inverse of equation (39) can be used to express the strains in the specimen coordinate system: kl ijkl ijSs e= (41), where S ijkl are the elastic compliances. By substituting equa tion (41) into equation (38) the stresses can be linked to the measured diffract ion data. It must be noted that the elastic compliances are also referred to the S i coordinate system and must be obtained from the elastic constants referred to the unit cel l axes. For anisotropic crystals the elastic compliance will be dependent on the crystal axis direction and this will be especially important in textured film [58, 59, 62]. This can be neglected in bulk materials because isotropic behavior is obtained when the ind ividual crystallites are oriented throughout space with equal directional probability Residual stress measurements of tungsten films wer e of interest here, therefore crystalline structure had to first be confirmed. T he tungsten film had the normal -2 ( = 0) scan performed to confirm that it was polycrys talline (Figure 47). It can be observed in Figure 47 that several 2 peaks are present, which indicate random crystal o rientation. Therefore, the sin 2 technique can be applied and based on the axisymme tric results found using the curvature technique in the previous section, a sin 2 plot similar to the one depicted in Figure 46 a) is likely.

PAGE 101

84 0 50 100 150 200 406080100120Counts2 Theta (110) (200) 112 reflection (220) (310) (222) (321) Figure 47. 2 Theta scan of tungsten film. The 40 peak was chosen first for the sin 2 technique on because it is the highest intensity peak corresponding to (110) planes spacin g. Next the elastic constant in the (110) direction had to be solved for. Since tungst en has a BCC crystal structure, there are only three independent compliance values, and they were found to be S 11 = 0.26 x 10 -11 Pa -1 S 12 = -0.07 x 10 -11 Pa -1 S 44 = 0.66 x 10 -11 Pa -1 [63]. With the plane direction chosen and the corresponding compliance values of the crys tal axes gathered, the compliance value in a new direction can be solved for using th e following equation: mnop lp ko jn im ijkl S a a a a S =' (42), where a im a jn a ko and a lp are from the transformation matrix given in equati on (40) which defines the orientation of our new coordinate syste m in relation to the specimen coordinate system (Figure 48).

PAGE 102

85 Figure 48. (110) plane and [110] direction of the n ew compliance value. 1 0 0 0 cos sin 0 sin cosg g g g= ij a (43). Solving for the compliance value in the direction n ormal to the (110) plane and contracting the tensor notation to matrix notation: ) sin (cos ) sin (cos 2 ) sin (cos 2 2 44 2 2 12 4 4 11 11g g g g g gS S S S + + + = (44), 1 11 11 11 ) 110 ( 10 26.0 1 = = = Pa S S E (45). Equations (44 and 45) confirm that tungsten is isot ropic and there is no directional dependence in the <110> direction. Therefore, 384 GPa can be used for the Young’s modulus of tungsten [63] and equation (38) becomes: kk ij ij ij E E vs n d s e+ = 1 (46), where ij is Kronecker’s delta defined as: 1 2 3 1’ r (110) [110]

PAGE 103

86 n = = l i j i ij ,0 ,1d (47). If the film is in a biaxial stress state and equati on (47) is substituted into equation (38), the follow expression is derived: ) ( sin 1 22 11 2 0 0s s y sf fy+ + = E v E v d d d (48). Equation (48) is a form of the traditional X-ray re sidual stress equation and it predicts a linear variation of d versus sin 2 The stress in the S direction can be obtained directly from the slope of the line fitted to the experiment al data measured at various if E n and the unstressed plane spacing, d 0 are known. Equation (48) is simplified further b y assuming a state of equi-biaxial stress where n 11 = n 22: ) 2 1( sin ) 1( 0 2 0s y sy E v d E v d d + + = (49). Figure 49 is a plot of a 2 scan, ranging from 39 to 41, with being increased from 0 to 30, in 10 increments. The film irradiated in Fig ure 49 was an 800 nm thick tungsten film that was deposited at 6 millitorr. Three thin gs can be observed in Figure 49: 1) there is a shift in the 2 peak with an increase in 2) there is a reduction in the intensity of the peak with an increase in and 3) there is a broadening of the peak with an i ncrease in

PAGE 104

87 0 200 400 600 800 1000 1200 3939.54040.541 Psi = 0 Psi = 10 Psi = 20 Psi = 30Counts2 Theta Figure 49. Peak shift with changing angle for the 6 millitorr tungsten film. The shift in the 2 peak is a result of the lattice plane spacing bein g strained and indicates the presence of residual stress. The shi ft of the peak position to the right in Figure 49 means that d is decreasing in length with an increase in the angle (Figure 50). Figure 50 is a representation of different gr ain orientations and depicts the effect of compressive residual stress on the (110) plane spac ing. At larger angles of there is a decrease in the (110) plane spacing compared to the unstressed d spacing. At smaller angles of there will be an increase in d compared to the unstressed spacing due to the Poisson’s effect. Therefore, the peak positions shi fting to the right signify that compressive residual stress is present in the film.

PAGE 105

88 Figure 50. Change in d-spacing with a change in The decrease in intensity is expected because an in crease in the angle will result in a reduction of diffracted X-rays reaching the detector. This reduction in diffracted X-rays is the result of a changing tilt of the sample surface, which leads to two problems: 1) the tilt of the surface creates a larg er beam size and 2) tilting of the sample surface increases the percentage of the X-rays that will be reflected off the surface. Both of these results will lead to a decrease in the int ensity of the diffracted X-rays. The peak broadening observed in Figure 49 has two m ajor contributors: 1) the presence of non-uniform strain or stress on the mac roscopic and microscopic scale and 2) size effects of the crystallites or grains. Macros copic stress will be defined here as the stress that extends over a distance that is large r elative to the grain size of the material, whereas microscopic stress will cover sizes equal t o or smaller than the grain size [6466]. The effect of macroscopic stress on peak broa dening is easy to envision when the beam area is considered along with the non-uniform curvature measured earlier on the tungsten samples (Figure 34 and Figure 35). By kno wing the geometry of the system being used, the X-ray beam area can be calculated. For the Philips X’Pert Pro the X-ray = 0 = 45 = 90 d =0 > d =45 > d =90

PAGE 106

89 beam length was calculated to be 16.33 mm when = 20, by use of the following equation: r = 2 sin sin sin sin2 2d w d w R L (50), where R is the radius of the goniometer, is the incident beam divergence and r is the angle between the incident beam and the sample surf ace. The width of the beam was calculated to be 19.08 mm by the following equation : ) ( )3 ( f R M W + = a (51), where M is the mask size, is the angle of the soller slits and f is the distance from the middle of the X-ray tube to the crossed slits. The beam area ( Y = cos / A A ) will have a further increase in size when the angle is increased. This is a fairly large X-ray beam area and should be considered when analyzing the Xray results for residual stress. Using the wafer curvature method for calculating stress, it was observed that the stress could vary by a few hundred mega-Pascals across a 1 to 2 cm length. With that in mind, a significant change in d would be expected across the beam area and would he lp explain the peak broadening. The effects of microscopic stress are a little less obvious to picture and can vary from point to point within the crystal lattice alte ring the lattice spacing. The microscopic stress may vary within the grain due to defects int roduced during deposition. This could include trapped foreign atoms and forward sputterin g effects. The source of trapped foreign atoms would be from the Ar working gas used during sputter deposition of the tungsten films. The atomic peening and forward spu ttering effects could also create a

PAGE 107

90 gradient in strain through the film thickness, addi tionally contributing to peak broadening. Small grain size will also cause a broadening of th e diffracted beam. The Scherrer formula can be used to estimate the averag e size, D of very small grains by measuring the breadth width at half the maximum int ensity, B : q l cos = B K D (52), where is the peak position, is the X-ray wavelength and K is dependent on the shape of the grains and is normally chosen to be 0.9 or 1 .0 [67]. By measuring the breadth width at half the maximum intensity for the = 0 peak in Figure 49, the average grain size, D was calculated to be 223 using the Scherrer for mula. Due to the reduction in peak intensity and increase in peak broadening at l arger angles, measurements were normally performed at < 45. Before the calculation of residual stress was made using the peak positions observed in Figure 49, a biaxial state of stress ha d to be confirmed. To do this, measurements were taken at equal positive and negat ive angles. If the film is in a state of biaxial stress, the d-spacing at negative and po sitive angles should be the same. The results of this test can be observed in Figure 51, confirming that the film is in a state of biaxial stress. If the residual stress of the film had not been biaxial, the plot would have formed an ellipse, similar to what was depicted in Figure 46 b).

PAGE 108

91 2.24 2.242 2.244 2.246 2.248 2.25 00.050.10.150.20.25 positive negatived (10 -10 m)sin 2 Y Figure 51. Sin 2 technique performed in the positive and negative directions. To accurately determine the position of the peaks i n Figure 49, there are several methods to choose from [68, 69]. Some common metho ds include half-value breadth method, centroid method, Gaussian fit and parabolic fit. No matter what method is chosen for the peak position determination, consist ency must be established during the sin 2 test when measuring the shift in 2 Figure 52 demonstrates the Gaussian and parabolic fit method for determining the 2 peak position. Only the top 15% of the peak intensity is used for determining the peak for both methods. For this case, the parabolic fit had a correlation coefficient of 0.99084 and th e Gaussian fit had a correlation coefficient of 0.99265. Both methods found the ide ntical 2 peak of 40.046

PAGE 109

92 960 1000 1040 1080 1120 39.94040.1 40.2 data gaussian fit parabola fitCounts2 Q Figure 52. Peak determination by fitting a parabola After the 2 peaks are found, the lattice plane spacing is calc ulated using Bragg’s law and is plotted against sin 2 The slope of the plot in Figure 53 is equal to: 0 2 1 sin d E v d + = Y F Ys (53), which can be rearranged to solve for the stress As predicted from equation (41), for an isotropic film that is in a state of biaxial str ess, there is a linear relationship between d and sin 2 Normally the lattice spacing measured at = 0 is substituted for d 0 because the unstressed lattice spacing may not be k nown. For most elastic materials the elastic strains may introduce at most, 0.1% differe nce between the true value of d 0 and d at any angle Since d 0 is a multiple to the slope, the total error introd uced by this assumption in the final stress value is less than 0 .1 % [69]. Determination of d 0 can also

PAGE 110

93 be made by knowing the lattice parameter of the mat erial and what type of unit cell it has. For the case of a cubic unit cell: 2 0 2 2 2 2 ) ( 1 a l k h d hkl + + = (54), where h k and l represent the Miller indices of the adjacent plane s being considered and a 0 is the lattice parameter. The lattice plane spaci ng for (110) planes in tungsten, with a lattice parameter of 3.1652 [70], was calculated to be 2.2381 . The unstressed lattice plane spacing can also be found with the use of equ ation (49) from the sin 2 technique. For = *, d = d 0 and assuming equi-biaxial stress, equation (49) b ecomes: E v E v /) 1( / 2 sin 2 + = Y (55). The angle (41) can then be solved for by inputting the values of the Young’s modulus and the Poisson’s ratio for tungsten, and w ould be the angle where d is equal to the unstressed d spacing. The sin 2 tests that were initially conducted on the (110) p eak for the tungsten samples all resulted in extremely high values of re sidual stress. This is due to the fact that the planes spacing will be measured less accur ately at smaller 2 angles [67]. The decreased accuracy at lower 2 angles is the result of the X-ray beam being out o f focus. The higher 2 angles had originally been avoided because of low intensity and broadened peaks. Since the (110) peak resulted in erroneous stress results the sin 2 test was conducted on the (321) peak at 2 = 131. Figure 53Figure 55 are the results of t he sin 2 test on tungsten films deposited at 4, 6 and 10 mi llitorr.

PAGE 111

94 0.848 0.8485 0.849 0.8495 0.85 0.8505 00.10.20.30.4 y = 0.85026 0.004976x R= 0.97859 d (10 -10 m)sin 2 Y s r = -1.76 GPa Figure 53. Sin 2 plot for tungsten film deposited at 4 millitorr Ar pressure. 0.8484 0.8486 0.8488 0.849 0.8492 0.8494 0.8496 00.10.20.30.4 y = 0.84949 0.0027161x R= 0.99354 d (10 -10 m)sin 2 Y s r = -755 MPa Figure 54. Sin 2 plot for tungsten film deposited at 6 millitorr Ar pressure.

PAGE 112

95 0.8474 0.8475 0.8476 0.8477 0.8478 0.8479 0.848 0.8481 0.8482 00.110.220.330.44 y = 0.8481 0.0017268x R= 0.96337 d (10-10 m)sin2Y sr = -698 MPa Figure 55. Sin 2 plot for tungsten film deposited at 10 millitorr A r pressure. The X-ray beam was focused on the wafer center for the tungsten film deposited at 4 millitorr Ar pressure. It resulted in a negat ive slope indicating compressive residual stress with the results presented in Figure 53. Th e -1.76 GPa of stress calculated using the sin 2 technique is approximately 200 MPa higher than wha t was calculated using the curvature technique. The results of the tungsten f ilm deposited at 6 millitorr Ar pressure are presented in Figure 54. Again, there is a decr ease in the interplanar spacing with an increase in the angle, which again indicates compressive residual stress. As before the X-ray beam was focused on the wafer center and the residual stress was calculated to be 755 MPa, which is approximately 200 MPa higher than the curvature results. The results presented in Figure 55 are for the tungsten film de posited at 10 millitorr Ar pressure, but unlike the two other samples the X-ray beam was not focused on the center of the wafer. The sample had been scribed and broken into two hal ves for mechanical testing with the

PAGE 113

96 Hysitron nanoindenter. Therefore, the sin 2 test was performed on the remaining half of the wafer with the X-ray beam focused approximately 2 cm from what would have been the wafer center. The residual stress at that loca tion was calculated to be -698 MPa, which is close to what the curvature technique resu lted in at the same location. 3.3 Summary of Stress Measurements The stress results from three different techniques for measuring film stress have been compiled in Table 5. The first column lists t he three different tungsten films that were analyzed. All deposition parameters were held constant for the three films, except for the Ar pressure. The second column lists the r esults using the Flexus 2-300, which is based on measuring a change in curvature before and after film deposition, assuming uniform film thickness and curvature. The stress r esults listed for the Flexus 2-300 are an average residual stress from 4 measurements taken a t 0, 45, 90 and 135 stage positions. The results of using the Tencor profilo meter are listed in column three of Table 5 5. The reported values are the stress results cal culated at the center and outer edge of the profiles. The values are also an avera ge residual stress taken by rotating the wafer in the circumferential direction. For the tu ngsten films deposited at 4 and 10 millitorr, the wafers were rotated in 15 increment s, whereas the 4 millitorr tungsten film was rotated by 45 increments. The third column li sts the results from the sin 2 technique using X-ray diffractometry. Only one mea surement for residual stress was reported for each sample. For the tungsten films d eposited at 4 and 6 millitorr Ar pressure the X-ray beam was focused on the wafer ce nters and for the tungsten film deposited at 10 millitorr Ar pressure the X-ray bea m was focused 2 cm from the wafer center.

PAGE 114

97 Table 5. Stress measurement results. Wafer Flexus (MPa) Profilometer (MPa) (Center to Edge) XRD (MPa) W 4 millitorr -893 5 -1500 to -500 -1760 (center) W 6 millitorr 257 23 -450 to 900 -755 (center) W 10 millitorr 190 47 1200 to -1000 -698 (R = 2cm ) At first glance, the stress results from the Flexus and the Tencor profilometer do not agree. This would be expected when considering the procedures used for calculating the change in curvature before and after film depos ition. The Flexus used two points on the wafer to calculate a single value of curvature for the entire wafer. The points it used for calculating a change in curvature were 1.25 cm from the center of the wafer. If the same points were chosen from the profilometer resul ts for the change in curvature, identical results would be obtained, with both piec es of equipment measuring a change in curvature of 0.025 m -1 at 1.25 cm from the wafer center for the tungsten film deposited at 4 millitorr Ar pressure. Figure 56 is a plot of th e change in curvature results from the Tencor profilometer with the curvature highlighted at a radial position of 1.25 cm. If the same film thickness and substrate properties were u sed at this point, the stress results would also be the same since both methods are based off the Stoney equation. A similar procedure for the tungsten films deposited at 6 and 10 millitorr can be conducted to compare the change in curvature and stress calculat ions when using the Flexus and Tencor tools.

PAGE 115

98 Figure 56. Comparing the curvature found with the F lexus and Tencor tools for the tungsten film deposited at 4 millitorr Ar pressure. When comparing the curvature methods to the X-ray analysis for calculating residual stress, the results did not compare for sm all 2 angles, but better results where obtained at larger 2 angles. When applying the sin 2 technique to a larger 2 angle (131), the residual stress was calculated to be hi gher than the wafer curvature techniques by up to 200 MPa. The disagreement in results is t hought to be caused by two reasons. First, the segment approach using the Stoney equati on is slightly off from the actual stress. Second, the equipment setup with the X-ray diffraction measurements can be improved. The main improvement would be to decreas e the spot size of the X-ray beam. A smaller spot size would reduce the peak broadenin g and complications caused by the curvature of the wafer. Because of the large beam area and curvature of the wafer, the diffracted beam is actually a sum of peaks (Figure 57). Each of these individual peaks k = 0.0225 Flexus results

PAGE 116

99 are the result of local strains in the film. There fore, the measured peak shape will depend on the range of local strains, which is dependent o n the area of the beam. That is thought to be the primary reason why there is an increase i n peak broadening with an increase in Figure 57. A diffraction peak made up of many peaks The curvature of the sample will also create errors in the peak positions due to small misalignments of the instrument and the speci men. One of the first adjustments to be made when loading a sample in the Philips XRD, i s finding the correct z-height of the stage. The correct z-height will place the sample surface in the diffractometer center plane. The samples analyzed were centered in middl e of the XRD stage to find the correct z-height. However, this guarantees that on ly the portion of the wafer that is in the XRD stage center is in the diffractometer center pl ane. Due to the curvature of the wafers and the size of the X-ray beam, most of the sample surface is slightly displaced from the diffractometer center plane. This will re sult in alignment issues in both the 2 I

PAGE 117

100 and axes of rotation. In order to correct this proble m, the beam area was reduced in size. Reduction of the beam area was possible by r educing the slits size and the angle of the divergence and receiving slits. However, by re ducing the mask size and the divergence and receiving slit angles, the intensity of the diffracted beam was also reduced to the point where peak determination was not possi ble. In general, the accuracy in determining the peak position is proportional to th e peak intensity. To improve the chances of successfully using X-ray diffraction for calculating residual stress in future experiments, a combinatio n of a smaller X-ray beam area and a higher intensity beam should be used. Beam sizes o n the order of 100 m or less in diameter would be ideal, and are normally called mi rcobeams. Beams with diameters on the order of 10 m are routinely used with synchrotron radiation, an d beams smaller than 1 m in diameter have been obtained. Along with reduc ed beam divergence, synchrotron radiation has several advantages over tube sources for X-ray diffraction. The intensity of X-rays delivered is far greater than that of other sources and synchrotron radiation can be tuned to the most advantageous X-ray wavelength nee ded for the particular application. An alternative to using synchrotron radiation would be to still use a monochromatic beam, but use a collimator or microfocus tube to he lp reduce the X-ray beam size. The draw back of using collimators is that they will pr oduce an X-ray beam that is weak, requiring very long exposure times. Microfocus tub es can help by reducing the focal spot size during X-ray generation, which results in a hi gher intensity.

PAGE 118

101 Chapter 4 Thin Film Mechanical Testing 4.1 Nanoindentation Nanoindentation is a convenient and widely used met hod for testing thin film mechanical properties at the submicron level. It i s possible because of high resolution testing equipment that can simultaneously measure f orce and displacement during an indent (Figure 59). The load-displacement data obt ained during one or more cycles of loading and unloading can be used to derive a varie ty of mechanical properties, including hardness and elastic modulus. The hardness of a ma terial, H is given by: c A P H max = (56), where P max is the peak indentation load and A c is the projected contact area under that load. There will be some compliance of the indente r that must be accounted for when using indentation, therefore a reduced modulus is d etermined and it can be related to the sample’s elastic modulus through the following expr ession: i i s s r E v E v E ) 1( ) 1( 1 2 2 + = (57), where E s and v s are the elastic modulus and Poisson’s ratio for th e sample. E i and v i are the same properties, but for the indenter tip mater ial, which is usually diamond. The reduced modulus E r is normally expressed as the following:

PAGE 119

102 c r A S E 2 =g p (58), where S is the stiffness and is a correction factor that depends on the strain imposed by the indenter and the Poisson’s ratio of the sample. Stiffness can be thought of as the slope of the initial portion of the unloading curve (Figure 58): dh dP S = (59) where P is the load and h is the indenter depth. Some indentation depths th at must be defined and are shown in Figure 58 are the maximum indentation depth, h max the contact depth, h c and the final indentation depth, h f 0 1000 2000 3000 4000 5000 6000 7000 8000 020406080100120140160Load (N)Depth (nm) S=dP/dh h c h max h f Figure 58. Load-displacement data for an indent int o tungsten. For cones and pyramids, the correction factor is given as: y gcot ) 1(4 2 1 1 v v + = (60),

PAGE 120

103 where v is the Poisson’s ratio of the material and is the indenter half angle. For spheres: R a v v ) 1( 3 ) 2 1(2 1 + =p g (61). Equation 58 has its origins in elastic contact theo ry and is appropriate for any indenter that can be described as a body of revolution of a smooth function and is not limited to a specific geometry. Figure 59 is a plot of four different types of mate rials that were indented to approximately the same maximum load. It can be see n that the load-displacement curves are quite different for the four different material s. The difference in the loaddisplacements curves is the result of different mec hanical properties. In the case of sapphire, which has a high modulus and hardness, th e loading and the unloading portions of the curve matched up resulting in a perfectly el astic indent. In comparison the low-k film has a relatively low modulus and hardness whic h results in large amounts of plastic deformation for the same maximum load. The amount of elastic recovery is seen in the load-displacement curve as the difference between t he maximum indentation depth and the final indentation depth. Along with determinat ion of thin film hardness and elastic modulus, additional film properties such as adhesio n and fracture toughness can be determined using nanoindentation.

PAGE 121

104 0 500 1000 1500 2000 020406080100120 Tungsten Sapphire Fused Quartz Low-kLoad ( m N)Depth (nm) Figure 59. Load-displacement plots for different ty pes of films. The contact mechanics of nanoindentation can be qui te complex, therefore, a detailed understanding of the information contained in the loading and unloading curves is required. The complexity of indentation is the result of both elastic and plastic deformation occurring during loading, as well as th e non-uniformity of stress and deformation fields in the vicinity of contact. For this reason, many of the methods used for assessing mechanical properties by nanoindentat ion are empirical. One such example is the determination of the tip area function. Sim ilar to hardness tests done at the macroscopic level, nanoindentation also requires kn owledge of the residual indent impression for determining mechanical properties. However, because of the nanometerscale of the indents, direct imaging of the residua l impression is not possible or inconvenient at the least.

PAGE 122

105 Due to the complexities discussed previously, extra ction of the necessary information from the indentation data requires prop er calibration of the equipment and knowledge of the materials being analyzed. This is of particular importance when the indentation depth is reduced to the sub 100 nm rang e. The tip contact depth and the contact area are two parameters on the equipment’s side of the analysis that require close attention. On the material’s side, the sample’s su rface roughness, existence of additional surface layers such as oxides or contaminates, sink -in and pile-up must be taken into consideration. Until proper equipment calibration is performed, a thorough understanding of the indentation process is acquire d and material effects are factored in, proper analysis of the mechanical properties will b e impossible. With that in mind, the first place to start will be discussing the main st eps in proper equipment calibration and understanding some of the assumptions made during t he analysis of the unloading portion of the load-displacement curve. 4.2 Indentation Calibration and Analysis No matter what type of experiment is being conducte d, or what physical quantity is being measured, proper calibration of the testin g equipment must be the first step in the process. If the final result depends on measuring multiple quantities, proper calibration is even more crucial to avoid an accumulation of error Nanoindentation is such a case where multiple quantities are needed for the final determination of mechanical properties. So far it has been mentioned that determination of the reduced modulus and hardness are based on the analysis of the load-displacement curv es. It will be shown that they are specifically dependent on accurate knowledge of the load, displacement and indenter

PAGE 123

106 contact area. If any of the three are inaccurate, it can be expected that there will be errors in the reported values of a material’s reduced modu lus and hardness. A Hysitron Triboindenter was used for the indentati on tests, which has a transducer that is based on a three-plate capacitiv e design that provides excellent resolution of force and displacement (Figure 60). An indenter tip is screwed into a tip holder, which is located on the center plate of the transducer. The center plate is spring mounted to the transducer housing. The indentation force is electrostatically actuated by applying a DC bias to the bottom plate of the capac itor. This creates an electrostatic attraction between the center plate and the bottom plate, pulling the center plate and the indenter tip downward. Figure 60. Schematic of the TriboIndenter transduce r. The indenter force can be calculated from the magni tude of the voltage applied using the following expression [72]: 2 V F F E = (62), where F E is the electrostatic force constant which depends o n the area, A of the plates, the spacing, d between the center and the outer plates and k is the dielectric constant of the air between the plates [73]: Indenter tip Drive plates Pick-up electrode Springs

PAGE 124

107 2 2 d A k F E = (63). The maximum force that can be applied by the transd ucer is about 10 mN, with a 1 nN resolution. The displacement of the tip is me asured by the transducer’s center plate which acts as a pickup electrode. The two outer pl ates, or drive plates, are driven by AC signals 180 out of phase with each other. Because the outer plates are 180 out of phase, the electric field potential is a maximum at the dr ive plates and zero at the center where the signals’ opposite polarity cancel each other. Since the plate spacing is relatively small compared to the lateral dimension, the electr ic field potential varies linearly between the plates. The displacement is easily det ermined since the pickup electrode is at the same electric potential as the electric fiel d between the outer plates. The maximum displacement of the transducer is 20 m, with a 0.0 4 nm resolution. Due to its capacitor-based operation, it is critica l to calibrate the transducer before each use. Temperature and humidity changes will af fect the capacitance properties of the transducer. Therefore, an air indent is performed prior to operation, which determines an electrostatic force constant and a displacement sca le factor. The electrostatic force constant relates the force output of the plate to a n applied voltage and the displacement scale factor relates the displacement of the center plate to a measured voltage output. Accurate calibration of the two constants is necess ary for correct determination of the load-displacement curve. Along with transducer cal ibration, the material stiffness, tip area function and machine compliance need to be det ermined for proper analysis of the reduced modulus and hardness.

PAGE 125

108 4.2.1 Indentation Stiffness As previously described in equation 58 of Chapter 2 the reduced modulus depends on the unloading stiffness and the contact area. The stiffness has been defined as the slope of the initial portion of the unloading c urve in equation 59 and was shown in Figure 58. The unloading portion of the load-displ acement plot is of interest because it only consists of the elastic recovery. Oliver and Pharr have shown that a power law relationship describes the top portion of the unloa ding data through the expression [74]: m f h h P ) ( =a (64), where P is the indentation load, h is the displacement, h f is the final displacement after complete unloading, and m are constants that depend on the indenter geometry and the material being tested. The top 65 % of an unloading curve from a 5300 N indent performed on fused quartz has been fitted with the Oliver-Pharr power law relationship in Figure 61. The final values of h f and m have been determined from regression analysis of t he experimental data, giving a correlation coefficient of 0.99942. The unloading stiffness, S can then be established by differentiating equation 64 and evaluating it at the maximum penetration depth, h max : max 1 ) ( h h m f h h m dh dP S = = =a (65).

PAGE 126

109 1500 2000 2500 3000 3500 4000 4500 5000 5500 100120140160180200Load (N)Depth (nm) y = m1*(m0-m2)^m3 Error Value 0.23684 1.1175 m1 2.6206 27.169 m2 0.036463 1.6722 m3 NA 4.7553e+05 Chisq NA 0.99942 R Figure 61. Oliver-Pharr power law fit for the top 6 5 % of an unloading curve from fused quartz. Pharr and Bolshakov used finite element simulations to reproduce the experimentally observed unloading behavior [75]. F rom those simulations a better understanding of the origin of the power law expone nts has been obtained. It is based on the concept of an “effective indenter shape”, with the indenter geometry determined by the shape of the plastic hardness impression formed during loading. Their model provides the means by which the material constants in the power law fit can be related to more fundamental material properties such as the el astic modulus and hardness. With the stiffness analysis now outlined, the only remaining variable for determining the reduced modulus is the indenter contact area.

PAGE 127

110 4.2.2 Tip Area Function Due to the small scale of nanoindentation, imaging of residual contact impressions is inconvenient at the least, therefore the determination of a tip area function as a function of indentation depth is necessary. T he contact area at peak load is used in calculating both the hardness and the reduced modul us. It is determined by the geometry of the indenter and the contact depth h c which is defined in both Figure 58 and Figure 62. The contact depth is the difference between the max imum displacement, h max which is experimentally measured, and the displacement of th e surface at the contact perimeter, h s which can be extracted from the load-displacement d ata. Figure 62. Schematic of indentation geometries. The displacement of the surface at the contact peri meter depends on the indenter geometry and for conical indenters Sneddon found th is to be [76]: ) ( )2 ( f s h h h =p p (66). Since Sneddon’s solution applies only to the elasti c component of the displacement, the quantity ( h-h f ) is used rather than h by itself. Additionally, Sneddon’s force-displace ment relationship for the conical indenter yields: a h c h h s h f Surface profile after indent Surface profile under load

PAGE 128

111 S P h h f 2 ) ( = (67). By substituting equation 67 into equation 66 and be cause the contact area of interest is determined at the peak load, the following expressi on for h s is derived to be: S P h s maxh= (68) where the constant depends on the indenter geometry. The indenter ge ometry constant has been determined to be 0.72 for conical tips, 0. 75 for Berkovich tips and 1.0 for a flat punch [74 76]. Combining equation 68 with the de finition of the contact depth, h c the following equation is derived: S P h h c max maxh= (69). An extended explanation of the contact depth was ne cessary to show that its derivation is empirically based, and any significant changes in t ip geometry must be accounted for. For example, a cube corner tip will have a differen t contact depth than a conical tip even if they are indented to the same maximum depth. Th is is important to note since the tip area function is defined in terms of the contact de pth. The tip area function is found experimentally by ca rrying out indents to various contact depths on a standard reference sample. Fus ed quartz is a common choice and is assumed to have a constant modulus and hardness as a function of depth. Determination of the area function should be confined to the dept h range of the intended indents in the sample of interest, with numerous indents performed Typical experiments conducted here to determine the area function included a tota l of 50 indents, broken up into 5 groups, performed at various locations on a fused q uartz sample with the contact depth

PAGE 129

112 ranging from 10 to 200 nm. The 5 groups of indents had the same load range and were intended to make sure that there was repeatability between the groupings. A Berkovich indenter was used for all the modulus and hardness tests here, and it has an ideal area function of 25. 24 ) ( c c h h A = The ideal area function will provide an accurate description of the contact geometry at larger contact depths, b ut will be grossly inaccurate at shallow indents. A comparison of the ideal and experimentally determ ined contact area for a Berkovich indenter is shown in Figure 63. It’s not until after a contact depth of approximately 220 nm is reached that the experiment ally determined contact area matches up with the ideal contact area. With the B erkovich geometry, inaccuracies will arise at the identer tip point, where manufacturing of a perfectly sharp tip is impossible. In reality, the indenter tip is blunted and can be described as having a radius. Oliver and Pharr have suggested the use of an eight parameter function to compensate for the differences between the ideal and actual tip geomet ry [74]: 128 /1 8 4/1 3 2 /1 2 1 1 256. 24 ) ( c c c c c c h C h C h C h C h h A + + + + + = (70), where C1 through C8 are constants that will be found through experimen tal fitting with a reference sample. The first term describes the per fect Berkovich geometry with the others describing the blunting of the tip.

PAGE 130

113 0 5 10 5 1 10 6 1.5 10 6 2 10 6 050100150200250 Ideal Exp Projected contact area (nm 2 )h c (nm) Figure 63. Ideal and experimentally measured Berkov ich tip contact areas. 4.2.3 Finding the Tip Radius One of the most crucial requirements in nanoindenta tion methods is knowledge of the indenter tip geometry. Many challenges are pre sented at shallow indentation depths due to deviation from the ideal tip geometry. Thes e deviations become increasingly apparent because an error in contact area will dire ctly affect the reduced modulus and hardness calculations. So far a method for determi ning a tip area function has been presented, which attempts to deal with these deviat ions. Through the use of atomic force microscopy observations, the tip of a Berkovich ind enter has been considered to have a spherical shape [77]. The spherical tip shape comp arison has been further backed by finite element simulations [78-80]. An attempt is made here to confirm the validity of

PAGE 131

114 treating the tip of the Berkovich indenter as a sph ere by applying Hertzian contact theory, where the radius of the tip can be solved for by st arting with the following equation: R a E P r = 3 4 3 (71), where, E r is the reduced modulus of the material being inden ted, a is the contact radius of the indenter and R is the indenter tip radius. It is more useful to relate the load, P to the indentation depth, h by eliminating a and getting a relationship between P and h in terms of only the reduced modulus and geometry: 2/3 2/1 3 4 h R E P r = (72). Using the Hertzian contact theory, indents were per formed on a fused quartz sample using both a Berkovich and cube corner inden ters. The manufacturer quoted the Berkovich indenter to have a tip radius between 100 and 200 nm and the cube corner tip radius is quoted to be around 50 nm. The indent lo ads were kept within a range that would result in a perfectly elastic contact. To ac hieve a perfectly elastic indent, the loading and unloading portions of the load-displace ment curve should coincide. This would result in a final contact depth, h f of zero. Figure 64 is the load-displacement curv e of a 210 N indent in fused quartz with a cube corner tip. T he experimental data is plotted as the open circles and the Hertzian contac t with a tip radius of 90 nm was plotted as the solid black line in Figure 64. It can be ob served that by assuming a tip radius of 90 nm for the cube corner indenter, the Hertzian conta ct theory matched up with the experimentally observed data. The same procedure w as performed in Figure 65 for the Berkovich indenter, where a tip radius of 170 nm ma tched up with the experimentally

PAGE 132

115 obtained data. For both figures only a percentage of the data points have been plotted, but both show the loading and the unloading data. 0 50 100 150 200 0510152025 Exp Hertz (90nm)Load ( m N)Depth (nm) Figure 64. Hertzian contact fit for a cube corner t ip. 0 100 200 300 400 500 600 0510152025303540 Exp Hertz (170nm) Load ( m N) Depth (nm) Figure 65. Hertzian contact fit for a Berkovich tip

PAGE 133

116 An alternative way to confirm the tip radius of the indenter is by utilizing an area function that was developed by Thurn and Cook [81]. They developed a two parameter function corresponding to the effective tip radius and effective cone angle of the indenter. They found that the projected area of a tip can be given by a “simplified area function”: y p p y p2 2 2 2cot 4 4 cot ) ( + + = R h R h h A c c c (73), where h c is the contact depth, R is the tip radius and is the included half angle of the equivalent cone. The first term of the expression relates to the ideal cone shape and in the case of a Berkovich tip, would be 70.3, and is equal to the ideal Berkovic h area function, where256. 24 ) ( c c h h A = The remaining terms account for the tip rounding The final term is a constant that prevents the cont act area from going to zero as the contact depth approaches zero. Figure 66 is a plot of the experimentally measured contact area for a Berkovich indenter and the two p arameter area function from Thurn and Cook. Using a tip radius of 170 nm that was de termined using the Hertzian contact theory, along with the included angle, = 70, the experimentally measured contact area and expression developed by Thurn and Cook have bee n compared. One immediate benefit of using equation 72 over equation 69 for m odeling the contact area is seen when the contact depth approaches zero. Equation 69 forc es the contact area to be zero, at zero contact depth, which creates an inconsistency in th e area function at contact depths below 10 nm. Thurn and Cook’s model handles the shallow contact depths better by starting with an initial contact by the use of the final ter m in equation 69. Although the Thurn and Cook model was preferred here at shallower cont act depths, significant deviation from the experimentally measured contact area was o bserved at larger indentation depths.

PAGE 134

117 0 5 10 4 1 10 5 1.5 10 5 2 10 5 01020304050 Exp Thurn [81]Ac (nm 2 )h c (nm) Figure 66. Comparison of Thurn and experimentally m easured area function at shallow depths. The discontinuity in the area function at shallow i ndentation depths created by equation 69 could explain why there is a larger var iation in calculated hardness in this region. Difficulties in compensating for the spher ical tip geometry using equation 69 could also explain why the hardness often initially increases with the indentation depth in the nanometer regime. Figure 67 is a plot of hardn ess results as a function of contact depth for a 200 nm thick gold film on silicon. The hardness was calculated to be 2 GPa at a contact depth of 15 nm and it plateaus out at a maximum hardness of 3.5 GPa starting at a contact depth of 100 nm. Xue et al. have deve loped a model to explain the depth dependence of the nano/micro indentation hardness b ased on a theory of strain gradient plasticity [82]. This result contradicts many obse rvations at the microindentation scale, where the hardness decreases with an increase in in dentation depth [83, 84]. The main

PAGE 135

118 contributor suspected in those cases is geometrical ly necessary dislocations (GNDs) that accumulate underneath an indenter, providing additi onal work hardening of the material. It is thought that the density of GNDs is inversely proportional to the indentation depth, causing increased hardness at shallower contact dep ths. With the complexity of the indenter tip described a nd its possible effects on modulus and hardness covered, the only calibration procedure remaining is the machine compliance. So far it has been observed that the l oad and displacement are continuously being measured during indentation. It must be poin ted out that some of the displacement will be contributed by the equipment and it must be accounted for. If not, it will be shown that inaccuracies in the reduced modulus and hardness will occur. 1.5 2 2.5 3 3.5 4 020406080100120140160H (GPa)h c (nm) Figure 67. Increase in hardness for a 200 nm gold f ilm as a function of contact depth.

PAGE 136

119 4.2.4 Machine Compliance of the Indenter The total amount of compliance experienced during i ndentation will be a combination of two constituent parts, the specimen and the testing equipment. The contribution of the equipment (machine) compliance is especially important when conducting deep indents and analyzing high modulus materials. The significance of not accounting for machine compliance on a high modulus material can be observed in Figure 68. In Figure 68 indents were executed to a range of loads in an 850 nm tungsten film. There is approximately a 50 GPa difference i n the reduced modulus when not compensating for machine compliance. 180 190 200 210 220 230 240 250 260 405060708090100 Mach. comp. = 0 nm/mN Mach. comp. = 3 nm/mN Er(GPa) h c (nm) Without machine compliance With machine compliance Figure 68. Effect of machine compliance on high mod ulus material. Using an incorrect machine compliance may go unnoti ced for some time depending on the types of materials that are being tested. Fused quartz is a typical

PAGE 137

120 reference sample used for calibrating the tip area function, but it is relatively compliant compared to many other materials. When only examin ing the results for the reduced modulus of fused quartz, inaccurate machine complia nce may go unnoticed as can be seen in Figure 69. It’s not until the hardness dat a is analyzed will discrepancies appear for fused quartz (Figure 70). Not only are the har dness values overestimated when using the wrong machine compliance value, but the hardnes s data shows a more significant change as a function of the contact depth. 67 68 69 70 71 72 020406080100120140 Mach. comp. = 0 nm/mN Mach. comp. = 3 nm/mNEr (GPa)h c (nm) Figure 69. The effect of machine compliance on the reduced modulus of quartz. One way to initially determine the correct machine compliance when testing fused quartz is by an iteration method. The objective of the method would be to adjust the value for machine compliance until the calculated h ardness values start to level off at deeper contact depths. In general, an indentation depth that is less than 1/3 of the tip radius will show considerable change in hardness. This effect can be seen in Figure 70

PAGE 138

121 when using the correct machine compliance of 3 nm/m N. By compensating for machine compliance the hardness of fused quartz starts to l evel off after the first 50 nm of contact depth. The manufacturer suggests that the hardness of fused quartz should be between 9 and 13 GPa when using a Berkovich indenter. Over t ime the tip will continue to wear down, which increases the tip radius and results in a higher value of hardness. 8 10 12 14 16 18 020406080100120140 Mach. comp. = 0 nm/mN Mach. comp. = 3 nm/mNH (GPa)h c (nm) Figure 70. The effect of machine compliance on the hardness of fused quartz. A more conclusive way to determine the machine comp liance is by modeling the load frame and the specimen as two springs in serie s, in which case: m s C C C + = (74), where C is the total measured compliance, C s is the sample compliance and C m is the machine compliance. Since the sample compliance du ring elastic contact is given by the inverse of the contact stiffness, S equation 55 and equation 74 combine to yield:

PAGE 139

122 c r mA E C C 1 2 + =p (75). If the reduced modulus is constant, a plot of C versus A c -1/2 should be linear for a given material and C m can be found as the y-axis intercept (Figure 71). 3 4 5 6 7 8 9 00.0010.0020.0030.0040.005C (nm/mN)A-1/2 (nm-1) Machine compliance Figure 71. Machine compliance check. With the proper machine compliance determined, all the necessary equipment calibrations have been covered. Proper equipment c alibration is often taken too lightly, resulting in poor confidence in the final data. So metimes the testing of new materials will lead to unique results that the user has not s een in the past. Before a hypothesis can be drawn relating the results to material propertie s, the user must be sure that the results are not equipment related. It is also possible to see some material effects that result in misleading results.

PAGE 140

123 4.3 Material Effects Along with the equipment effects already discussed, calculation of a film’s modulus and hardness will also be affected by film and substrate material effects. When reporting thin film modulus and hardness, it is com mon to report them as a function of the contact depth. Very rarely will the thin film modulus and hardness be constant through the range of contact depth. This lack of c onsistency through a range of contact depths is more than likely caused by material effec ts, assuming that all equipment calibration has been done correctly. One possible material effect was mentioned in section 4.2.3, where the hardness changed at variou s contact depths due to the density of geometrically necessary dislocations [83, 84]. The influence of geometrically necessary dislocations is not being disputed, but the variati on of hardness as a function of depth could also be caused by other more obvious reasons. Going back to the definition of hardness, which is load divided by the contact area and taking into consideration that the contact area is dependent on the contact depth, mat erial effects such as pile-up and sinkin will change the final results for reduced modulu s and hardness. Pile-up and sink-in will produce an actual contact depth that differs f rom the instrumentation found contact depth, resulting in the wrong analysis of hardness. In addition to pile-up and sink-in, there are other material effects to be considered. Many of these, such as mismatches between substrate and film properties [85, 86], will lead to misleading reduced modulus and hardness res ults that show a strong dependence on the contact depth. To avoid this, most tests ar e kept to indentation depths less than 20 % of the total film thickness. The only material e ffect that will be focused on here is pile-up, with the others being left for future rese arch.

PAGE 141

124 4.3.1 Pile-up During Indentation Pile-up and sink-in are two material-based response s that will create errors in the reported contact area used for calculating the redu ced modulus and hardness using nanoindentation. A generalization can be made that pile-up occurs during indentation of soft films and that sink-in occurs during indentati on of hard films. The Oliver-Pharr method for determining the contact depth in equatio n 69 only accounts for small amounts of sink-in. Their method is accurate for a large n umber of materials, but will lead to inaccuracies when indenting soft or very hard films For a soft film, as the indenter is driving further into the film some of the displaced material will pile-up around the sides of the indenter. This results in an underestimation of contact depth and area, and an o verestimation of the hardness and reduced modulus. An example of pile-up is shown in Figure 72 and Figure 73. These images were obtained after a 1600 N indent had been made in a 200 nm thick gold film on a silicon substrate. Figure 72 gives a 3-dimens ional view of the gold surface where the residual indentation imprint and surrounding pi le-up can be seen. In Figure 73 the topographical heights were measured and a maximum p ile-up height of 34.6 nm was found for the 1600 N indent. These AFM-like images were made using th e same equipment used to produce the indent. This is poss ible because the Hysitron transducer is mounted to piezoelectric material that allows scann ing in the surface plane, while the capacitive based transducer measures topographic ch anges.

PAGE 142

125 Figure 72. Topographic scan showing pile-up from a 1600 N indent in gold. Figure 73. Pile-up measurement from a 1600 N indent in gold: a) topographic image and b) line profile taken across the indent. a) b)

PAGE 143

126 Bolshakov and Pharr simulated the effects of pile-u p and sink-in on the accuracy of the calculated reduced modulus and hardness usin g FEM [87, 88]. Their simulations found that as the result of pile-up, the hardness a nd modulus may be overestimated by as much as 50 %. The ratio of the final displacement to the maximum displacement, h f /h max which can be measured experimentally, is a useful i ndicator of when pile-up may be a significant factor (Figure 74). They found that an h f /h max ratio of 0.7 is the critical point when pile-up will start to be an influencing factor especially if the material does not work harden. 0 200 400 600 800 1000 1200 1400 1600 050100150Load (N)Depth (nm) hmaxhf Figure 74. Load-displacement plot of a 1600 N indent in 200 nm thick gold film. To apply their findings to the gold results found h ere, Figure 74 is a plot of the load-displacement curve from a 1600 N indent. The maximum displacement was measured to be 138 nm and the final displacement up on unloading was 100 nm. This results in an h f /h max ratio of 0.7246, which is just above the critical point that Bolshakov and Pharr found in their FEM simulations. Unfortun ately, one can not predict if a

PAGE 144

127 material work hardens solely on the load-displaceme nt data. With that said, no evidence was found in the literature on whether or not pure gold work hardens. Therefore, it must be assumed that the film does not work harden and t he hardness and reduced modulus values of gold will be overestimated. In Figure 75 the ratio of h f /h max has been plotted as a function of the maximum indentation load, P max It can be observed that the experimentally found h f /h max ratio for the 200 nm thick gold film quickly approaches the B olshakov and Pharr ratio of 0.7. Therefore, pile-up should be expected to affect the determined values of reduced modulus and hardness for the 200 nm thick gold film. 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 05001000150020002500hf/hmaxP max ( m N) Figure 75. The ratio of h f to h max versus the maximum indentation load for a 200 nm t hick gold film. In Figure 76 the height of the pile-up has been plo tted as a function of the maximum indentation load. The results were obtaine d by scanning the residual indentation impressions after each indent, similar to the pictures shown in Figure 72 and

PAGE 145

128 Figure 73. There appears to be a fairly linear rel ationship between the amount of vertical pile-up and the maximum indentation load. Since pi le-up will affect the contact depth, new values for reduced modulus and hardness were ca lculated by first determining the actual contact depth. This was accomplished by add ing the pile-up height to the contact depth and using the new adjusted contact depth to c alculate a new contact area. The new contact area was then used to determine reduced mod ulus and hardness. 0 10 20 30 40 50 05001000150020002500 pile-upHeight (nm)Pmax ( m N) Figure 76. Pile-up as a function of the contact dep th for a 200 nm thick gold film. Figure 77 and Figure 78 compare the hardness and re duced modulus for the 200 nm thick gold film when taking into consideration t he additional contact area due to material pile-up. Using the new contact area, the hardness decreased by approximately 1 GPa after maximum indentation loads of 1500 N. For indents at lower loads, the difference was not as significant. The difference in reduced modulus as the result of using a new contact area was more significant than what was noticed for the hardness.

PAGE 146

129 1.5 2 2.5 3 3.5 4 05001000150020002500 H H(pile-up)H (GPa)P max ( m N) Figure 77. Corrected gold film hardness compensatin g for pile-up. 65 70 75 80 85 90 95 05001000150020002500 Er Er(pile-up)Er (GPa)P max ( m N) Figure 78. Corrected gold film reduced modulus comp ensating for pile-up.

PAGE 147

130 A good comprehensive study of the determining facto rs causing pile-up has been conducted by Taljat and Pharr [89]. With the use o f finite element analysis, they concluded that pile-up and sink-in are not only dep endent on strain hardening, but also on the relative amount of elastic and plastic deformat ion as characterized by the nondimensional material parameter, E/ n y the non-dimensional depth of penetration, h/R, an d the friction coefficient, One effect that they did not mention, which may play a role in the amount of pile-up, is the film thickness. Futu re tests will be conducted to determine the effect of film thickness on the amount of verti cal pile-up. It is expected that indents performed to the same indentation depth, may produc e a larger amount of vertical pile-up in thinner films. The thinner films will have in a larger indentation depth to film thickness ratio, h/t, and the substrate may act as a barrier preventing material displacement, resulting in greater amounts of pileup. 4.4 Dynamic Testing As device sizes decrease, there will be a need for thinner film thicknesses. As the film thickness is decreased, there is an increasing challenge in obtaining reliable indentation results. Difficulties in defining a ti p area function for shallow indents and the influence of substrate properties have been discuss ed. Up until this point all indentation results have been obtained by using a quasi-static method of indentation, where a load is applied and then fully removed. Another option is to perform dynamic indentation testing, where a dynamic mechanical analysis can be used. For dynamic mechanical analysis (DMA), a small sinusoidal AC force is supe rimposed on the DC applied load. This is achieved by summing the DC and AC voltages, which is applied to the drive

PAGE 148

131 plates. For a superimposed driving force,) sin( 0 t F Fw= the equation of motion of the indenter relative to the indenter head is modeled a s: ) sin( 0 t F kx x C x mw= + + (76), where m is the indenter mass, C is the damping coefficient, is the frequency in rad/sec and k is the spring constant. The solution to equation 7 6 is a steady-state displacement oscillation at the same frequency as the excitation : ) sin( f w = t X x (77), where X is the amplitude of the displacement oscillation a nd f is the phase shift of the displacement with respect to the excitation force. The amplitude and phase shift can be used to calculate the contact stiffness in a dynami c model. The indenter and the sample are represented by the components in the dynamic mo del shown in Figure 79. The standard analytical solution for this model, assumi ng that the machine frame stiffness is infinite is as follows, where the amplitude of the displacement signal is: ()()[] 2 2 2 0 0w ws iC C m k F X + + = (78), where C i is the damping coefficient of the air gap in the d isplacement transducer, C s is the damping coefficient of the sample and the combi ned stiffness ( K s + K i ) is k The phase shift between the force and displacement is: ( ) 2 1 tan w w f + = m k C Cs i (79).

PAGE 149

132 Figure 79. Modeling the dynamic test method. Similar to the calibrating procedures used for the quasi-static testing, in order to determine the material’s reduced modulus, the tip a rea function, indenter compliance and phase shift as a function of driving frequency must be determined. From there, the specimen stiffness (contact stiffness) is proportio nal to the reduced modulus: pc r sA E K = 2 (80). The advantage of DMA is that the contact stiffness is obtained continuously during indentation allowing the reduced modulus to be determined throughout the indent cycle. The technique can also be extended to study the viscoelastic properties of polymeric materials. The ultimate sensitivity and useful frequency range of the technique depends on the mass, the damping coefficient and st iffness of the indenter. A low mass, low damping coefficient and optimum stiffness of th e indenter will significantly improve sensitivity. There will also be a reduction in pla sticity effects, such as reverse plasticity, which is effectively the same as putting a hold tim e at the peak load during a quasi-static test. C i C s K s K i m

PAGE 150

133 The main benefit by of using the dynamic method ove r the static method was observed here during shallow indent depths of thin films under 200 nm in thickness. Not only was the reduced modulus as a function of conta ct depth obtained more quickly, but there was less deviation of the results noticed acr oss multiple tests. A comparison of the dynamic and quasi-static indentation tests for dete rmining the reduced modulus is shown in Figure 80 and Figure 81. 10 20 30 40 50 60 70 80 90 1020304050607080 Static Dynamic Er (GPa) hc (nm) Figure 80. Comparison of dynamic and quasi-static i ndentation results of Er for a 140 nm thick low-k film. In Figure 80 the deviation in reduced modulus for a 140 nm thick low-k film using the quasi-static indentation test was found t o be 5 GPa compared to 2 GPa for the dynamic indentation test. Figure 81 plots the results of quasi-static indentations factoring in pile-up and dynamic tests for determin ing the reduced modulus of a 200 nm thick gold film. Again, the deviation was less usi ng the dynamic test compared to the quasi-static test.

PAGE 151

134 60 65 70 75 80 85 90 020406080100120140160 Static(pile-up) DynamicEr (GPa)h c (nm) Figure 81. Comparison of dynamic and quasi-static i ndentation results of Er for a 200 nm thick gold film. The decision is left up to the user to determine wh at indentation method they prefer, either quasi-static or dynamic. There have been two advantages observed here for using the dynamic method on thin films. One is tha t only one indent test needs to be performed to determine the reduced modulus as a fun ction of contact depth. Second, there is less deviation in the results over a colle ction of tests. Additionally, the dynamic method also gives the user the option of analyzing viscoelastic properties, but this option was not necessary here. The dynamic indentation me thod is typically not used when analyzing thin film adhesion and fracture toughness Since the max indentation load and contact depth are the only quantities required from the indentation data, the quasi-static method is preferred for determining those propertie s.

PAGE 152

135 4.5 Non-traditional Tests The usefulness of indentation for determining the m odulus and hardness of thin films has been thoroughly covered in the previous s ections. It should also be realized that indentation can be used for determining thin film a dhesion and fracture toughness. Knowledge of a thin film’s adhesion and fracture to ughness is beneficial when reliability issues are of concern. As discussed before, method s will differ between macroscopic and microscopic tests. For example, at the macroscopic level there are two standard specimen configurations for determination of the plane-strai n fracture toughness outlined by American Society of Testing and Materials (ASTM) st andards; the single edge notched bend (SENB) and the compact tension (CT) specimen [ 90]. However, due to the film thicknesses that are of interest, the ASTM standard specimens are not an option for determining fracture toughness. The same size challenges are presented with adhesio n testing, although adhesion testing of thin films has a few more options availa ble at the microscale than fracture toughness. A good outline of the different possibi lities has been presented by Volinsky et al. [91]. Along with indentation, the four point b end and microscratch tests deserve recognition as popular methods of determining thin film adhesion [92, 93]. There is some debate on which method provides the best quant itative results for adhesion, but the choice of method will more than likely come down to what equipment is available. Because of that, indentation is used quite often be cause of its popularity for testing thin film modulus and hardness. Analysis of the indentation load-displacement curve was all that was needed for determining thin film modulus and hardness. For de termining thin film adhesion and

PAGE 153

136 fracture toughness, analysis of the load-displaceme nt curve will be necessary along with additional information obtained from post-indentati on analysis of the film surface. The following sections will describe the procedures nee ded for determining a thin film’s adhesion and fracture toughness using indentation. As before, challenges will be faced when the thin film thickness is decreased to the su b-micron level. 4.5.1 Adhesion Measurements Adhesion can be described as the mechanical strengt h or bond strength between two joined bodies. Good adhesion of a film to a su bstrate is of obvious importance and is believed to be caused by a few different reasons: 1 ) atomic bonds created by the interaction of the two surfaces, 2) mechanical lock ing and friction due to surface texture and 3) a transition layer produced by the diffusion of one material into the other [11]. The debate exists on how to quantitatively measure adhesion with numerous approaches spanning from the atomic to macroscopic levels. A more academic approach could be taken, where theoretical bond strengths and perfect materials are considered, or a more pragmatic approach could be used where large area m echanical tests are used. Depending on the approach used, a difference of two orders of magnitude can be observed [11]. From a thermodynamic perspective, the “true” work o f adhesion at the interface is the amount of energy required to create free surfac es from the bonded materials. In an ideal case, the true work of adhesion is defined wh en brittle fracture occurs and there is no energy dissipated due to plastic deformation or friction. Therefore, all energy is conserved as new surfaces are formed: fs s f A Wg g g+ = (81),

PAGE 154

137 where gf is the film surface energy, gs is the substrate surface energy and gfs is the interfacial energy. The interfacial energy can be found by knowing the surface energies of the film and the substrate and using the contact angle technique schematically presented in Figure 82: Q = cos f s fsg g g (82), where Q is the contract angle between the droplet free sur face and the substrate. With the surface energies and contact angle known the YoungDupr equation can be used to find the true work of adhesion: ( ) Q + = + = cos 1 f fs s f A Wg g g g (83). Figure 82. Contact angle technique. In a perfect situation we could say that the true w ork of adhesion is equal to the film/substrate adhesion. This follows the idealize d case of Griffith fracture where the fracture resistance i is assumed to be equal to the thermodynamic true work of adhesion W A The true work of adhesion does not account for e nergy loss due to plastic deformation or friction. Even as fracture occurs i n a brittle material there will always be a small plastic zone ahead of the crack tip that ma y extend from a single bond to over several atomic spacings [94, 95]. The small nonlin ear plastic zone immediately surrounding the crack tip will be followed by a lin ear elastic zone that serves the function Q g f g fs g s

PAGE 155

138 of transmitting the applied stresses to the inner r egions. A more sensible value of adhesion is the “practical” work of adhesion: ( ) s f A A P A U U W W W + + =, (84), where W A is the true work of adhesion, U f is the energy per unit area spent due to plastic deformation in the film and U s is the energy per unit area spent due to plastic d eformation in the substrate. The practical work of adhesion W A,P is also called the interfacial toughness or the resistance to crack propagation of the film and the substrate pair. Now that the basic definitions of adhesion are esta blished, fracture mechanics will be considered. This connection is necessary becaus e many of the methods used for determining adhesion are based on fracture mechanic s. The field of fracture mechanics emerged from the study of solid mechanics, with a g rowing desire to characterize fracture and crack growth. In an attempt to provide quantit ative answers of the material strength as a function of crack size, two main approaches ha ve been taken; an energy balance approach and a stress intensity approach. The ener gy balance approach was first developed by A.A. Griffin, who modeled a static cra ck as a reversible thermodynamic system. He sought a configuration that minimized t he total free energy of the system, where the crack would be in a state of equilibrium and thus be on the verge of extension. He started by defining the total energy of the syst em as being made up of two individual energy terms: s M U U U + = (85), where U M and U S are the mechanical and surface energy terms, respe ctively. The mechanical energy also consists of two parts and is defined as: A E M U U U + = (86),

PAGE 156

139 where U E is the potential strain energy stored in the elast ic medium and U A is the potential energy of the applied loading system. Th ermodynamic equilibrium is reached by balancing the mechanical and surface energy term s over a virtual crack extension da Figure 83 is schematic representing Griffith’s crac k system where a is the crack length, da is the crack extension, u 0 is the crack opening displacement, S is the crack surface and P is the applied load. The elastic body in Figure 83 can be treated as an elastic spring in accordance with the Hooke’s law: P u =l0 (87), where = (a) is the elastic compliance. The strain energy of t he system is equal to the work of elastic loading: 0 0 0 0 2 1 ) (0u P du u P U u E = = (88). The change in elastic energy, dU E can be described for two conditions; the fixed gr ips or the constant load conditions. Under fixed grips co ndition the applied loading system experiences zero displacement as the crack extends ( u 0 = constant) and the elastic strain energy will decrease with crack extension. With fi xed grip conditions the energy changes are as follows: 0 = A dU (89), l l l d P d u dU E 2 2 2 0 2 1 2 1 = = (90). The total mechanical energy is therefore: ld P dU M 2 2 1 = (91).

PAGE 157

140 Figure 83. Static crack system for defining the mec hanical energy release rate. For the constant load condition, the potential ener gy of the applied load decreases and the elastic strain energy increases: ld P Pdu dUA 2 0= = (92), ld P dU E2 2 1 = (93) Therefore, the total mechanical energy is: ld P dUM 2 2 1 = (94). Since equation 91 and equation 94 are identical, it has been shown that the mechanical energy released during incremental crack extension is independent of the loading configuration. The strain energy release rate, G can be defined as the rate of change of the stored elastic strain energy with respect to th e crack area under fixed grips conditions [96]: 0u E A U G = (95). P a da S u 0 P

PAGE 158

141 In 1920 Griffith formulated that a crack will conti nue to grow as long as the strain energy release rate from the surrounding elastically strai ned material is equal to the energy required to form new surfaces [53]: iG G = (96), where i is the material’s resistance to crack growth The other approach for characterizing fracture and crack growth follows the crack stress field analysis and the next few equations ar e classic equations for a straight crack of length a : a K I =p s 22 a K II =p s 21 a K III =p s23 (97), where K is the stress intensity factor for mode I (opening mode), mode II (shear mode), mode III (twisting mode), ij are the stresses far from the crack tip and a is the crack length. Modes one, two and three describe how the loads are being applied to the crack. Figure 84 represents the different modes of fractur e and if the stress intensity factor K is greater than the critical stress intensity factor K c the crack will propagate. The Griffith and stress intensity approaches were combined by Ir win [94]: E K K K G III II I ) 1( ) 1( ) 1(2 2 2 2 2u n n+ + + = (98), where E is the Young’s Modulus and n is the Poisson’s ratio of the bulk material.

PAGE 159

142 Figure 84. Modes of fracture: a) Mode I b) Mode II c) Mode III. So far, the fracture analysis assumed the elastic b ody to be homogeneous and isotropic. Experimental evidence suggests that cra cks in brittle, isotropic, homogeneous materials propagate such that pure mode I condition s are maintained at the crack tip. However, when discussing a layered material system, there will be an interface and mismatches in material properties resulting in a co mbination of modes at the crack tip. A measure of mode II and mode I loading acting on the crack is defined by the phase angle : = Y-I II K K 1 tan (99). Application of equation 99 reveals that = 0 for mode I loading and = 90 for mode II loading. In general, anytime there is modulus m ismatch between two joined bodies a combination of modes will always exist. The Dundur s’ parameters, and are used to + x 2 x 1 a a) b) c) P P P P P P

PAGE 160

143 describe the elastic mismatch between the film and the substrate. The Dundurs’ parameters for plane strain are [97]: ( ) ( ) ( ) ()()() 1 2 2 1 2 1 2 11 1 / 1 1 /u u m m u u m m a+ = ( ) ( ) ( ) ()()() 2 1 2 1 1 2 2 11 1 / 2 1 2 1 / 2 1u u m m u u m m b+ = (100) where and n are shear modulus and Poisson’s ratio, and the subs cripts 1 and 2 refer to the upper and lower bimaterial layers. Because of the mode mixity, the interfacial toughness of the film and the substrate varies with as seen in Figure 85. Figure 85. Strain energy release rate as a function of A new criterion for the initiation of crack growth at an interface when the crack tip is loaded in mixed mode is characterized by as: ) ( Y G = G (101), where ( ) is defined as the toughness of the interface and can be thought of as an effective surface energy that depends on the mode o f loading. A comprehensive study of G IC 0 90 Y G Energy Dissipation Thermodynamic Work of Adhesion

PAGE 161

144 multiple mixed mode loading configurations has been compiled by Hutchinson and Suo [98]. Marshall and Evans have been able to apply a fractu re analysis to indentationinduced delaminations of thin films. They were abl e to solve for the fracture toughness of the interface in terms of the equilibrium crack length, indenter load and geometry, the film thickness, the mechanical properties and the r esidual stress. To do this they treated the section of film above the delaminating crack in duced by indentation and residual stress as a rigidly clamped disc shown in Figure 86 [99]. In order to help explain their derivation, the solution has been broken down into 4 steps. The first step in Figure 86 a delaminated section is hypothetically taken out to show the effects of a compressive residual stress. If the section was going to be pl aced back into the sample, the section would have to be recompressed with an edge stress r The work done would be: ( ) r r p a h Ue s p2 = (102), where r = R /a and 2a is the crack length. This is equivalent to the re sidual strain energy stored within the delaminated section before remova l. The total energy of the system, U R = U S + U p is independent of crack length for an unbuckled p late. Therefore, the strain energy in the remainder of the film, U S = U R U p must depend on the delamination radius, where U R can now be treated as a constant.

PAGE 162

145 Figure 86. Hypothetical operations used to calculat e the strain energy associated with an indentation-induced delamination in a stressed film In the second step, the indentation is made, whi ch creates a plastic zone of deformation leaving a permanent impression of volum e V I It is assumed that volume is conserved and results in radial displacements at th e crack tip. It is modeled as an internally pressurized cylinder inducing a radial e xpansion I at the edges equal to: a h V I I = Dp 2 (103), where the indentation strain is defined as I = I / a and the stress required to recompress the section I is: () () v a h E V v E I I I = = 1 2 1 2p e s (104). D D D D R D D D D R +D +D +D +D I D D D D R +D +D +D +D I s s s s s s s s s s s s R s s s s R s s s s R s s s s R s s s s R s s s s R D D D D R 1) 2) 3) 4)

PAGE 163

146 The internally pressurized cylinder has a radius-de pendent elastic strain energy distribution with a total work done: () r = 2 1 2 v a h U I I Ep e s (105). In the third step the expanded section is recompres sed by a combination of the residual and indentation stresses. Compensating fo r the possibility of the edge stress exceeding the critical buckling stress the strain e nergy induced in step 3 is: ( ) ( ) ( ) ( ) ( ) [ ] B R I B R I R I R I RI a h Ue e e s s s a e e s s p+ + + + + = 1 2 (106), where represents the slope of the buckling load versus t he edge displacement upon buckling: () f v + = 1 902 .0 1 1 1a (107). In step four there is reinsertion and the total str ain energy is the sum of the strain energies just described. The sum of the strain ene rgies can be differentiated with respect to the crack area A in order to find the strain energy release rate G [99]: ()RI E S U U U dA d G + + = (108), ( ) () ( ) () ( ) ( ) f f B I f f R f f I E v h E v h E v h G + = 1 1 1 1 2 12 2 2 2s s a s a s (109). Films that are thin, ductile or strongly adhering a re likely to cause problems when using the single layer indentation test. These pro blems can be avoided by using a superlayer deposited over the film of interest. Th e superlayer is typically a refractory metal that can be deposited by means of relatively low temperature physical vapor deposition technique such as sputtering, where the temperature is not high enough to alter

PAGE 164

147 the microstructure or interface of the original fil m. The superlayer can be tailored to optimize conditions for film thickness and residual stress, which allows for greater driving force for the same penetration depth to fil m thickness ratio. One condition that must be met for the superlayer indentation method t o work is that the superlayer must adhere to the film more strongly than the film adhe res to the substrate. If this condition is not met, the measurement obtained from the adhesion test will be for the superlayer to the film and not the adhesion of the underlying film to the substrate. Kriese and Gerberich have combined the idea of a su perlayer test with the Marshall and Evans findings by applying the laminat e theory in order to calculate the strain energy release rate for a multilayer sample [100, 101]. For many cases the superlayer is much thicker than the underlayer and the test can be treated the same as the single layer test defined by Marshall and Evans. T he superlayer indentation test has been applied here for determining the interfacial toughn ess of copper and organo-silicate glass (OSG) films. Cooper and OSG films are commonly found in IC techn ology for a variety of reasons. OSG is a low-k dielectric film that is ty pically used as an insulating layer. The use of low-k dielectrics in the IC industry became popular about the same time as copper’s replacement of aluminum for interconnects took place [102]. Both were driven by the desire to decrease RC delays, crosstalk nois e and power dissipation. Although the speed of the devices increases as the feature size decrease, the interconnect delays become the major fraction of the total delay and li mits the improvement in device performance. The RC delay is dependent on the meta ls’ resistivity, the dielectric constant and the packing density [103]. As the pac king density increases there is a

PAGE 165

148 reduction in the wiring pitch (sum of the metal lin e width and the spacing between the metal lines) which results in a larger delay. This delay is a result of an increase in capacitance between the tightly packed metal lines and the increase in resistance due to smaller pitch lines. Before the introduction of low-k dielectrics, SiO 2 was the popular choice as an interlayer material between interconnect structures The immediate advantage of using a low-k is the reduction in dielectric constant and f or most low-k materials it is below 3. On the down side, structural integrity becomes an i ssue due to reduced thermal and mechanical properties. Thermal and mechanical stab ility are important because low-k materials need to withstand the elevated processing temperatures and high stresses that can occur in the interconnect structures [104]. Re sistance to thermal decomposition is important because decomposition can severely degrad e the dielectric’s material properties and lead to outgassing and film delamina tion. Because of these reasons, adhesion testing of copper and low-k films is of in terest. The first step in determining the adhesion of coppe r and low-k films was to deposit a tungsten superlayer. For both films a tu ngsten superlayer was sputter deposited, followed by the use of wafer curvature techniques f or determining residual stress. Crack propagation and delamination of the films were then induced by indentation. After delamination the blister radius and contact depth a re required to calculate the strain energy release rate. The delamination blister radi us is found using an optical microscope with a micron ruler superimposed on the lens in the eye piece. A maximum magnification of 200X was used, as an increase in m agnification decreases the ability to see height changes in the film. At 200X magnificat ion, the radii measurements could be

PAGE 166

149 taken with an accuracy of approximately 1 m. Th e contact depth can be found using the Oliver-Pharr method from the load-displacement curve. A typical delamination blister resulting from the superlayer indentation t est is shown in Figure 87. The delamination blister and contact radii are labeled x and a, respectively. Figure 87. Delamination blister from the superlayer indentation test. To compensate for the localized effect of the test and determine an average value of film adhesion, 4 trials of indents were made at different locations on each sample. Each trial consisted of 5 to 10 indents at varying loads, with the same load variation being used for each trial. Indentation was perform ed under load control, with the total indent time remaining the same for all indents on t hree different samples. To ensure that usable measurements were taken, it was necessary to keep the maximum loads within a certain range. If the loads applied were too small no delamination blisters appeared. If loads were too high, extensive radial cracks appear ed in the thin film along with substrate fracture, making adhesion calculations less accurat e. Figure 88 is the strain energy release rate for a 9 7 nm thick copper film plotted against x/a. For smaller indents and x/a larger st rain energy release rates were 50 m x a

PAGE 167

150 consistently measured and as the indents were made to greater depths and larger x/a ratios, the strain energy release rate decreased. Steady state cracking is assumed when the strain energy release rate starts to plateau of f at larger x/a ratios, which means that the driving force and interfacial toughness become inde pendent of the delamination length and initial flaw geometry [98]. 0 2 4 6 8 10 12 6789101112 Cu 97 nmG (J/m2)x/a Figure 88. Strain energy release rate for 97 nm thi ck Cu film. For the results in Table 6 it was assumed that the steady state strain energy release rate had been reached for x/a ratios greater than 9 and the average of these values were assumed to be the interfacial toughness of the film /substrate. The low-k film was measured to have an interfacial toughness of 0.69 J /m 2 which was comparable to results found in literature [105]. The interfacial toughne ss of the copper films was measured to be 2.98 and 2.74 J/m 2 for the film thicknesses of 67 and 97 nm, respecti vely. The increase in interfacial toughness with increasing f ilm thickness was expected and

PAGE 168

151 compares to results found in literature [91]. The increase in interfacial toughness with an increasing film thickness is thought to be caused b y greater amounts of plastic deformation possible in the thicker films resulting in plastic energy dissipation. Table 6. Strain energy release rates results for co pper and OSG low-k films. Film Film thickness (nm) x/a W residual stress (MPa) W thickness (nm) G (J/m 2 ) Cu 67 9-12 320 1100 2.74 0.86 Cu 97 9-12 320 1100 1.98 0.82 OSG low-k 140 9-11 500 463 0.69 0.74 4.5.2 Fracture Toughness Measurements Fracture toughness is a material property that char acterizes a material’s resistance to crack propagation. As with the previously discu ssed mechanical properties, testing procedures used for measuring the fracture toughnes s of bulk materials and thin films are not the same. The pre-cracked three point bend tes t is an example of a test method used for measuring bulk materials’ fracture toughness, b ut it will be limited when testing films below several microns in thickness. A comprehensiv e review of fracture toughness measurement for thin films has been conducted by Zh ang et al. and it describes several methodologies for testing thin films [106]. These methodologies were separated into five different categories, which include: bending, buckl ing, scratching, tensile and indentation tests. All of the methods had their pros and cons, but collectively shared the difficulty in testing thin films with thicknesses below about 100 nm. The indentation test is the most popular method for brittle materials and was reprod uced here with its challenges presented and discussed.

PAGE 169

152 To make a connection between radial crack patterns observed as a result of indentation and fracture toughness, an understandin g of the complex elastic/plastic field introduced during the indentation cycle had to be d eveloped. In order to accomplish this, initial models were based on experiments with soda lime silica glass. Soda lime glass proved to be a convenient sample because of its abi lity to be well polished and transparent and has been tested by many [107-112]. Much of the initial modeling of the sequential steps observed during crack propagation was based on experiments with soda lime glass. However, more recent findings conclude d that no general theory can be used to predict crack morphology. There are five major types of crack morphology that are commonly generated in brittle materials by indentat ion contact. The expected crack type, and sequence of crack formation will depend on the indenter tip geometry, the mechanical properties of the material and the inden tation load [107]. Four of the cracks types are commonly observed when the contact is elasticplastic using pyramidal shaped indenter tips, inclu ding radial, median, half-penny and lateral cracks. There is a fifth type of crack cal led a cone crack and it is normally generated by the elastic loading of spherical or fl at punch indenters. Cone cracks typically spread away from the material surface at a characteristic angle to the load axis after nucleation of a ring crack at the periphery o f contact. Radial cracks are generated parallel to the load axis and remain close to the s urface, starting at the edge of the plastic contact impression. They are thought to be generat ed by flaws at the deformation zone boundary and are driven by the residual stress fiel d arising from the strain mismatch of the plastically deformed zone embedded in the surro unding elastically restraining area [108]. Unlike radial cracks, median cracks will be generated beneath the plastic

PAGE 170

153 deformation zone and are in the form of full circle s or circular segments truncated by the deformation zone boundary or material surface. Alt hough the median cracks are nucleated at the deformation zone boundary, they ar e thought to be driven by the stress field arising from the elastic loading of the inden ter onto the surface [109]. The most commonly seen crack morphology is that of a half-pe nny and it is depicted in Figure 89. In Figure 89, a half section of an elastic-plastic indent using a pyramidal shaped indenter tip is presented schematically. A portion of the f inal indent impression can be observed with a residual plastic zone located beneath the in dent impression. The half-penny crack morphology is depicted as the dotted regions extend ing out from the indent impression corners and forming a half-circle shape into the ma terial. Like median cracks, lateral cracks are also generated beneath the deformation z one, running parallel to the surface and are circular in shape. Figure 89. Half-penny fracture morphology. c

PAGE 171

154 Lawn, Evans and Marshall were the first to relate a materials’ fracture toughness to the maximum applied load, P and the radial crack length, c [110-112]: 2 /3 2 /1 c P H E K c =z (110), where E and H are the Young’s modulus and hardness of the materi al, is a material independent constant based on the indenter tip, whi ch for Berkovich and Vickers indenters is = 0.016 and for a cube corner tip = 0.04 [113]. Initial indentation tests for calculating fracture toughness were performed on bu lk sapphire to gain familiarity with the testing procedure. The modulus and hardness of the sapphire sample was first determined by indentation and the results for the r educed modulus and hardness are presented in Figure 90 and Figure 91. 325 330 335 340 345 350 102030405060Er (GPa)h c (nm) Figure 90. Reduced modulus of sapphire.

PAGE 172

155 25 30 35 40 45 102030405060H (GPa)h c (nm) Figure 91. Hardness of sapphire. After the modulus and hardness were determined, a s eries of indents ranging from 300 mN to 500 mN were performed using a Berkovich t ip and Hysitron’s multi-range transducer. The multi-range transducer is meant fo r indents that require larger loads (1 N) and displacements (80 m). This load and displacement range is ideal for harder and thicker films. Indents below 300 mN were not used in calculating the fracture toughness of sapphire because they did not produce clearly de fined radial cracks that could be observed in the optical microscope. Following inde ntation, an optical microscope was used to determine the radial crack length, c and the results of a 500 mN indent can be observed in Figure 92. For each indent, all three of the radial cracks were measured and the average was used for c in equation 107. The average fracture toughness f or the sapphire sample was calculated to be 1.2 MPam 1/2 which is lower than what was found in the literature (2.1 MPam 1/2 )[ 111, 114].

PAGE 173

156 Figure 92. Berkovich indent into sapphire: a) loaddisplacement curve and b) corresponding optical micrograph. The tests of sapphire provided confidence in using nanoindentation for calculating fracture toughness, but the goal was to use the met hod on films with thicknesses around 100 nm. Of particular interest was testing the fra cture toughness of a 140 nm thick low-k dielectric film. The first challenge was to determ ine if radial cracks could be produced at such low loads. A problem arises because indentati on cracking will occur at material specific cracking thresholds. The cracking thresho ld will not only be dependent on the indentation load, but on the geometry and condition of the indenter tip. Harding et al. found that the indentation cracking threshold could be significantly reduced by employing a sharper indenter tip. Their work focus ed on the geometries of a cube corner and Berkovich tips. When comparing indents to the same contact area, the cube corner tip will displace three times as much volume as a B erkovich tip. This results in greater stresses and strains in the surrounding material le ading to a reduction in the cracking threshold load. 0 1 1052 1053 1054 1055 10505001000150020002500Load (N)Depth (nm) 10 m a) b) c

PAGE 174

157 Initial comparison of the two different tip geometr ies was done by comparing the load-displacement curves for the same indentation l oad. It can be observed in Figure 93 that for the same maximum indentation load of a 100 0 N, the maximum indentation depths for the two tips are the same and the final indentation depth is slightly different. This indicates that the Berkovich indenter resulted in more elastic recovery upon unloading. This would be expected due to the large r included angle of the Berkovich indenter producing less stress and strain in the su rrounding material. 0 200 400 600 800 1000 020406080100 Cube corner BerkovichLoad (N)Depth (nm) Figure 93. Load-displacement curve for a 1000 N indent with a Berkovich and cube corner tips. A more significant difference in the effects of the two tips could be seen after making topographic scans of the residual indents. Figure 94 a) and b) are 5 x 5 m 2 topographic scans of the residual fractures left by 2000 N indents using a Berkovich and cube corner indenters. The radial cracks appear to be slightly more defined in the

PAGE 175

158 residual indent left by the cube corner tip. The ra dial cracks were also more consistent in length when comparing all three corners of the inde nt impression. For the Berkovich tip, there were two radial cracks that always appeared l onger than the third one. Using the results obtained for the indentation tests and topo graphy scans, an average fracture toughness of low-k film was calculated to be 0.13 M Pam 1/2 The fracture toughness of the low-k film was measured to be higher than what was found in the literature, where fracture toughness of OSG low-k film varied between 0.01 and 0.05 MPam 1/2 [105]. Figure 94. Topographic scan of 2000 N indent in low-k film using a) Berkovich and b) cube corner tip. Some improvements could be made to the testing proc edure used here and the main one would be obtaining better images of the re sidual impressions. Using the Hysitron Triboindenter to scan the material surface is limited by the tip sharpness. The tip radii of the Berkovich and cube corner tips wer e found earlier to be 170 and 90 nm, respectively. The Hysitron transducer has excellen t resolution in the vertical direction but will be limited in the lateral directions, espe cially when trying to measure crack a) b) 1 m 1 m

PAGE 176

159 lengths and width. In the future, it would be idea l to use SEM to measure the crack lengths. The only problem would arise when trying the find the indents on the surface of the film since they are approximately 1.5 m in diameter. There is a major concern about the significance of substrate constraint on the developing half-penny cracks. Equation 107 is base d on the assumption that “well developed” half-penny cracks are created by indenta tion, but because of the limited film thickness of 140 nm, crack development in the low-k layer may be constrained by the substrate. However, there was still a linear relat ionship between the maximum indentation load and the crack length to the 3/2 po wer, which was observed by Lawn et al. for well developed cracks (Figure 95) [110]. Th e ideal crack should also satisfy a minimum requirement of the radial crack radius, c to tip imprint radius, a being at least 2. For the indents here, the ratio was closer to 1 .5. Future work will be needed to check the validity of using equation 107 on ultra thin fi lms such as the ones tested here. 1 1.2 1.4 1.6 1.8 2 2.2 0.40.50.60.70.80.91Pmax (mN)c 1.5 ( m m 1.5 ) Figure 95. Maximum indentation load as a function o f c 3/2

PAGE 177

160 Chapter 5 Delaminated Film Buckling Microchannels 5.1 Introduction So far residual stress in thin films has been prima rily shown to result in negative consequences that include wafer bowing, film cracki ng and delamination. However, depositing a film with compressive residual stress has been demonstrated to be a benefit when using the superlayer indentation for determini ng thin film interfacial toughness. A similar concept can be employed for creating microc hannels. When the strain energy release rate, G exceeds the interfacial toughness, i of a film/substrate, delamination will occur. A simplified form of the strain energy rele ase rate in a stressed film is [98]: f fE h Z G2s= (111), where f is the stress in the film, h is the film thickness, E f is the modulus of elasticity and Z is a dimensionless parameter that depends on the g eometry. In thin film systems with biaxial compressive stres s, various shapes of delaminated regions evolve. These shapes include l ong straight-sided, circular and telephone cord delaminations, which is the most com monly observed morphology. Delamination shape and size will depend on factors such as the film stress, thickness and interfacial toughness. Most importantly, their pro pagation depends on the interfacial toughness that increases as the mode mixity acting on the interface ahead of the

PAGE 178

161 delamination crack shifts from mode I towards mode II. Interfacial failure starts with the film delaminating from the substrate, then the buck ling loads the edge of the interfacial crack causing it to spread, resulting in a failure phenomenon that couples buckling and interfacial crack propagation. To create useful microchannels from film delaminati ons, the direction and morphology of the delaminations needs to be control led. The easiest way to control delamination is by controlling the interfacial toug hness. This can be done by creating adhesion reducing layers that have a lower interfac ial toughness than surrounding areas. A compressively stressed film can be used in conjun ction with a patterned adhesion reducing layer as a future method for creating micr ochannels. This method of creating microchannels could replace existing methods that tend to be time consuming and cumbersome. A currently u sed method of creating microchannels is by etching trenches in a substrate such as glass or silicon. The layout of the etched trenches is created using lithography te chniques and the process is completed by bonding a glass or silicon wafer to the etched s ubstrate. Drawbacks of using the wafer to wafer bonding technique include misalignment and voids trapped during the bonding processes that can change the desired shapes and fu ture device function. Using delaminations will hopefully solve the existing cha llenges and provide an alternative method to create microchannels. 5.2 Creating Patterns To create the adhesion reducing layers, standard ph otolithography techniques are employed, with the simplest approach using the patt erned photoresist as the adhesion reducer. Photolithography is a technique similar t o photography, where an original image

PAGE 179

162 or pattern is transferred to a photosensitive mater ial. The basic steps in lithography include the following: 1) The application of a phot osensitive material (photoresist), 2) soft bake of the photoresist, 3) exposure of the ph otoresist, 4) development of the exposed pattern and 5) hard bake of the remaining p attern. Figure 96 is a depiction of the basis lithography steps used here along with the ad ditional step of depositing a compressively stress film for creating microchannel s using film delaminations. Figure 96. Process of creating microchannels. There are two types of photoresist to choose from: positive and negative photoresist. Positive photoresist is exposed to UV light wherever it is to be removed. In positive photoresist, exposure to the UV light chan ges its chemical structure so that it becomes more soluble in a developer, opposite to th e negative resist. The exposed resist is then washed away by a developer solution, leavin g areas of the bare underlying material. Therefore, the mask contains an exact co py of the pattern which is to remain on the wafer. In general positive resists provide cle arer edge definition than negative resists. Si wafer Mask Exposure Spin coating Develop W deposition W delamination Photoresist Soft bake Hard bake

PAGE 180

163 The better edge definition by positive resists make s them a better option for high resolution patterns. Negative photoresists behave in the opposite manner Exposure to the UV light causes the negative resist to become polymerized, a nd more difficult to dissolve. Therefore, the negative resist remains on the surfa ce wherever it is exposed, and the developer solution removes only the unexposed porti ons. Therefore, masks used for negative photoresists contain the inverse of the pa ttern to be transferred. Shipley 1813 was used here, which is a positive photoresist that is optimized for G-line exposure (436 nm wavelength). Normally to start the photoresist application proce ss, the wafer surface is prepared in a specific way in order to remove surface moistu re and contaminants. In order to remove moisture, the wafers are baked and then prim ed with an adhesion promoter. Hexamethyldisilazane (HMDS) is normally used as the adhesion promoter and is applied at reduced pressure to form a monomolecular layer o n the wafer surface, making the wafer hydrophobic, which prevents moisture condensa tion. These wafer preparation steps were ignored here since the goal of the photo resist layer was to be an adhesion reducer and only a proof of concept was intended. Spin coating is used to apply the photoresist with thicknesses ranging from a few hundred nanometers to a few microns. If thicker co atings are required, electrochemical coatings, spray coatings and casting processes are used [115]. A Laurell Technologies WS-400A-8NPP/Lite Spin Processor was utilized here and can handle wafers up to 8” in diameter. It uses a vacuum chuck to hold the wafer s in place and the spin speed can range from 0 to 6000 rpm. Acceleration profiles, s peed changes and spin times can all be

PAGE 181

164 programmed by the user. By adjusting the spin spee d the photoresist thickness can be controlled. The manufacturers supplied thickness v ersus spin speed for Shipley 1813 is shown in Figure 97. They suggest that Shipley 1813 has the best coating uniformity between spin speeds of 3500 and 5500 rpm. 800 1000 1200 1400 1600 1800 2000 1000300050007000Thickness (nm)Spin Speed (rpm) Figure 97. Photoresist thickness as a function of s pin speed for Shipley 1813. The spin speed and time used here were 4000 rpm for 40 sec, with a ramp speed of 1000 rpm/sec. Based on the manufacture’s suppli ed data for the resist thickness versus spin speed, it was expected to have a resist thickn ess of approximately 1.3 m after application. However, the resist thickness was mea sured to be approximately 1.5 m with relatively good thickness uniformity across th e wafer diameter. Spin-on deposition of resist was a tricky process because the resist w as applied manually. First, the wafer surface had to be thoroughly cleaned of any debris to avoid streaking of the photoresist during spinning. After surface cleaning the wafer had to be centered on the vacuum

PAGE 182

165 chuck to avoid uneven distribution of the photoresi st. A drop of photoresist was then placed in the center of the wafer and a few additio nal drops were added during the first 5 seconds of ramping the wafer up to full spin speed. Upon completion of the spin-on deposition, the wafer was placed on a hot plate for 90 seconds at 90 C. It is suggested for future tests that an oven be used instead of th e hot plate for soft and hard bake because of the hot plate uneven temperature distrib ution. After photoresist soft bake, a range of exposure ti mes was attempted in order to find the optimum for the resist thickness. The lig ht source used for resist exposure was a mercury vapor lamp that provides a wavelength spect rum from 310 to 440 nm. A Karl Suss MA 56 Mask Aligner was used in hard contact mo de for the mask and wafer alignment. The mask used had a repeating pattern w hich consisted of two straight lines running parallel, where the line width was measured to be 250 m with 30 m separation. Results of resist profiles after a range of exposur e times can be seen in Figure 98 and Figure 99. The resist width and thickness varied u p to 10 % across the 4” wafer diameter.

PAGE 183

166 0 0.5 1 1.5 050100150200 10 sec 8 sec 6 sec 4 secHeight ( m m)Width ( m m) Figure 98. Photoresist profiles after different exp osure times. At the shortest exposure time of 4 seconds, the rem aining developed resist measured 1.5 m in height and 218 m in width. However, on most of the wafer there also remained a thinner layer of resist between the parallel lines. It was concluded that an exposure time of 4 seconds at 275 W was inadequate. From there the exposure time was increased in 2 second increments, with the final re sist height and width being inversely proportional to exposure time. Along with decreasi ng line height and width, the resist profile ended up being more rounded as the exposure time was increased. After exposure, the wafers were placed in a develop er bath for 30 seconds and then rinsed with de-ionized water. Nitrogen was us ed to remove majority of the excess moisture on the wafer and then it was hard baked on a hot plate at 110 C for 100 seconds.

PAGE 184

167 Figure 99. Effect of exposure time on the final pho toresist thickness: a) 10 sec, b) 8 sec, c) 6 sec, and d) 4 sec. Overall the lithography techniques used here were a dequate for the objective of creating simple patterns on a wafer. However, it i s suggested that a more thorough approach be taken in the future for optimizing spin speed and time, bake time and temperature, exposure and developer time. It must be understood that the line widths created here are relatively large compared with wha t lithography techniques are capable of. Therefore the quick optimization steps used he re were adequate. If smaller line widths and heights were required a more meticulous approach would be needed. The final step in the process was to deposit a tungsten film that is forced to have compressive residual stress. Before those results are presente d, a closer look at delamination morphology must be taken. 218 m 96 m 118 m 142 m a) b) c) d)

PAGE 185

168 5.3 Delamination Morphology As stated before, various shapes of buckled regions evolve in film/substrate systems that are in a state of biaxial compression. Details of their shape and size will depend on factors such as the film stress, thicknes s and interfacial toughness. The geometry of the buckles can be used to assess inter facial toughness. In straight-sided delaminations, also called Euler mode, the buckling stress can be found using the following expression [98]: () 2 2 21 12 = b h EBn p s (112), where h is the film thickness, b is the delamination half-width, E is the film’s modulus and n is the film’s Poisson ratio. Figure 100 is a pict ure of three straight-sided delaminations of a tungsten and diamond like carbon (DLC) film stack on a silicon wafer. Figure 100. Straight-sided delaminations of a W/DLC film on Si. x y 50 m

PAGE 186

169 The compressive stress, r is responsible for producing the buckling delamin ations and can be found using the following expression [98]: + = 1 4 32 2hB rd s s (113), where d is the delamination height. The film’s steady sta te interfacial toughness, ss is independent of the mode mixity and is defined in th e direction of delamination propagation (y-direction) [98]: ( ) 2 2 21 2 1 = Gr B r SSE hs s s n (114). The mode-dependent interfacial toughness, ( ), in the buckling direction (x-direction) perpendicular to delamination propagation is define d as [98]: () ( ) ()()B r B r E hs s s s n + = Y G 3 2 12 (115). Assuming that fracture happens at the interface, eq uations 112 through 115 can be applied to solve for the interfacial toughness betw een the photoresist and the tungsten film when straight-sided delaminations are present. One of the initial deposition tests was on a silicon wafer patterned with the larger 200 m width photoresist lines. The tungsten film was deposited for 50 minutes with an argon pre ssure of 5 millitorr. This resulted in straight-sided delaminations forming across the wid th of the photoresist line as shown in Figure 101 a). The profile of the straight-sided d elamination widths is shown in Figure 101 b). Using the delamination height, d, delamination half width, b and equations 112115, the critical buckling stress was calculated to be 194 MPa, the residual stress of the film was 313 MPa, the steady state interfacial toug hness was 0.0114 J/m 2 and the modedependent interfacial toughness was 0.0859 J/m 2

PAGE 187

170 Figure 101. Tungsten delamination a) Optical image of delamination morphology, and b) Profile of delaminations. The steps just taken for calculating interfacial to ughness assumed that fracture took place at the tungsten/photoresist interface, b ut this has not been confirmed. There is also a possibility that the crack propagates in the photoresist, at the interface between the photoresist and the silicon substrate, or a combina tion of above mentioned. No matter where the crack is propagating, the important thing is that the interfacial toughness between the tungsten film and the silicon substrate which has been reported in literature to be 1.73 J/m 2 [101], is stronger than that measured in the photo resist areas. Future experiments need to be conducted to determine the e xact origin and path of the crack propagation. Moon et al. have found that the delamination morpho logy can be predicted when the film stress is compared to the buckling stress [116]. For r / B < 6.5 straight-sided delaminations are predicted and for r / B < 6.5 telephone cord delaminations are predicted. For the delaminations in Figure 101, r / B = 1.6, which agrees with the Moon a) b) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 050100150 height ( m m) x-pos ( m m) 2b d Scan direction 200 m

PAGE 188

171 et al. findings. Their predictions of delamination morphology were based on similar experimental methods that utilized lithography tech niques for applying patterned areas of low interface adhesion surrounded by areas of high adhesion. By controlling the width of the low adhesion strips, the buckle morphology was controlled. Ideally the delaminations would propagate parallel to the photoresist lines as opposed to perpendicular to them as seen in Figure 101. The main reason preventing this from happening is that the photoresist line is too wide. The photoresist is so wide that it exceeds the critical buckling width and there is en ough room for the straight-sided delaminations to run perpendicular to the lines. F igure 102 a) and b) show two different delamination morphologies that are possible when th e photoresist line is decreased in width. Telephone cord delamination morphology can be observed in Figure 102 a) when the photoresist width was approximately 120 m. When the photoresist width was reduced to approximately 80 m in Figure 102 b), a straight sided delamination w as created. Unfortunately in Figure 102 b) tungsten d elamination also occurred in-between the photoresist lines. Figure 102. Delamination morphology with different photoresist widths: a) telephone cord delamination and b) straight-sided delaminatio n. a) b) 120 m 80 m

PAGE 189

172 Delamination morphology that was observed in Figure 102 would be necessary if the delaminations were to find future use in transp orting fluids. Continued work is necessary to further experiment with photoresist wi dth and its effect on delamination morphology. Attention to deposition parameters for controlling residual stress was found to be more important when using the adhesion reduci ng layers. Not only was delamination occurring in the patterned areas, but it was also common to see the delamination propagate across other areas of the wa fer. The adhesion reducing areas acted as crack initiation sites that helped spawn d elamination upon film deposition. There appears to be a fine line between creating de laminations on the patterned areas and delaminations on the rest of the wafer. Controllin g the exact amount of compressive residual stress is critical for this method to work and be used for creating microchannels. 5.4 Delamination Microchannel Conclusions By using photolithography to create adhesion reduc ing layers, buckling delaminations have been controlled and show potenti al use as microchannels. Delamination morphology depends on two conditions: 1) the buckling stress which is controlled by the adhesion reducing layers width an d 2) the amount of compressive residual stress in the thin film. Here, telephone cord delaminations were observed at larger photoresist widths and straight-sided delami nations were observed for smaller photoresist widths. Line widths between 80 and 220 m were created here, but future work could included line widths that are a few micr ons.

PAGE 190

173 Chapter 6 Summary and Future Work 6.1 Summary The research conducted here was separated into 4 ma in Chapters. Starting with Chapter 2, sputter deposition along with film thick ness and residual stress effects were covered. Chapter 3 discussed different methods of measuring residual stress including film thickness non-uniformities in the calculations Thin film characterization using nanoindentation was discussed in Chapter 4. The la st topic was film delamination and its possible use as microchannels, which was covered in Chapter 5. The common thread between the Chapters is that thin film deposition a nd characterization is important when considering thin film use in microelectronics and M EMS applications. 6.1.1 Sputter Deposition An in-depth look at DC magnetron sputter deposition has been taken and its effects on residual stress and film thickness unifo rmity have been examined. Because DC magnetron sputtering is not limited to depositin g specific material types, has relatively high deposition rates and low deposition temperatures, it has become a popular method for film deposition. Depending on the syste m configuration, film thickness and residual stress have been measured to vary signific antly across a 4” diameter (100) Si wafer. This variation is caused by the magnet, the same system component that is responsible for high deposition rates and low depos ition temperature. The addition of a

PAGE 191

174 magnet allows for a combination of magnetic and ele ctric fields, which gives the system its advantages over basic DC sputtering systems. H owever, the changing interaction between the magnetic and electric fields across the target surface will result in nonuniform deposition rates and residual stresses. A profile of the target surface was related to the non-uniform film thickness in the presence of a changing magnetic field. The profile showed a racetrack erosion pattern on the target surface that matched the areas where the magnetic and electric fields are perpendicular, creating an area of high current den sity. Based on the position of the erosion track, the target to substrate distance and by assuming a cosine sputter yield distribution, a theoretical deposition profile was determined and compared with the experimental data. Theoretical and experimental re sults show that for the given sputtering system configuration and a 4” wafer, the film thickness will vary from 33 to 45 % between the wafer center and edge. Film thicknes s uniformity can be improved if modifications are made to the system configuration. It has been shown that the determining parameter fo r controlling residual stress is the working gas pressure. In general, low gas pres sure will produce compressively stressed films and higher gas pressure will lead to films with tensile residual stress. In extreme cases, a combination of tensile and compres sive residual stress has been observed. Reliability issues may exist if thin fil m residual stress is sufficiently large, where film cracking and delamination may be a mecha nism for energy release. High levels of residual stress are unwanted when discuss ing device reliability, but are desirable when using the superlayer indentation test to deter mine film/substrate interfacial toughness. The compressively stressed superlayer a ssists indentation stresses in crack

PAGE 192

175 propagation to purposely delaminate a film from a s ubstrate. Following delamination, analysis of the load-displacement curve and delamin ation blister are conducted to calculate interfacial toughness. 6.1.2 Residual Stress Measurement In most cases high amounts of residual stress are u ndesirable and need to be quantified. Two methods have been used here to mea sure thin film residual stress. One is based on measuring the change in wafer curvature before and after film deposition and the other uses X-ray diffraction to measure the lat tice planes spacing. The curvature method was modified to account for changes in film thickness and wafer curvature by profiling the wafer before and after film depositio n and reducing the profile into segments. Each segment had its own unique film thi ckness and curvature and by using the Stoney equation the residual stress for each se gment was calculated. The stress results obtained using the curvature met hod were compared with stress calculations using the sin 2 technique. The sin 2 technique uses X-ray diffraction to measure the lattice planes spacing, which can be re lated to the film stress if the elastic constants are known. The sin 2 technique provided comparable results to the curva ture method at larger 2 peaks, but proved unsuccessful at smaller 2 peaks. The technique could be improved by reducing the X-ray beam spot s ize and increasing the beam intensity. Unfortunately, that was not an option g iven the equipment available. 6.1.3 Thin Film Characterization using Nanoindentat ion Nanoindentation is widely used for determining thin film mechanical properties, namely hardness and reduced modulus. It was shown here that nanoindentation can also

PAGE 193

176 be used for determining film/substrate adhesion and fracture toughness. No matter what test is being performed, proper equipment calibrati on must be the first priority. The significance of the tip area function and machine c ompliance were thoroughly discussed, with different calibration methods demonstrated for each. The tip area function is of particular importance because it compensates for de viation between the intended and actual tip geometries. The biggest challenge in ma nufacturing pyramidal indenter geometry will be at the indenter tip, where it is i mpossible to manufacture a perfectly sharp tip. The resulting indenter tip geometry is commonly described to be spherical in shape. The spherical shape comparison has been con firmed here for a cube corner and Berkovich indenter by using Hertzian contact theory The current challenge for nanoindentation is testin g films below 100 nm in thickness. Uncertainties in the tip geometry, surf ace roughness and substrate effects are all influencing factors at this indentation depth. At shallower indentation depths, dynamic mode testing was found to provide more reli able results with less scatter than quasi-static testing. An additional advantage of d ynamic testing is that the reduced modulus can be measured continuously during an inde ntation, which significantly reduces testing time. When indenting soft films on hard substrates, pileup is commonly observed. The Oliver-Pharr method for determining contact depth d oes not account for pile-up, it assumes a small amount of sink-in. A possible solu tion to compensate for film pile-up was explored. A topographic scan was performed aft er each indent in order to measure the amount of pile-up. There vertical amount of pi le-up was used to determine a new contact depth. The new contact depth was then used to calculate a new contact area,

PAGE 194

177 which is used in the analysis for film hardness and reduced modulus. By compensating for pile-up and using a new contact area, there was a 15 to 30 % difference in reduced modulus and hardness results. 6.1.4 Creating Microchannels from Controlled Film D elaminations By using standard lithography techniques, areas of low adhesion were created to control delamination morphology. This could be use d as a new method for creating microchannels for transporting, mixing and storing fluids in microfluidic devices. Current methods for creating microchannels involve etching and wafer bonding. The advantages of the new method are in its ease of man ufacturing and cost effectiveness. Proof of concept was provided here by using photore sist as the adhesion reducing layer. By controlling the photoresist line width, delamina tion morphology was controlled. 6.2 Future Work Much of the work presented here addressed current c hallenges in sputter deposition and film characterization using nanoinde ntation. Some steps were taken to overcome those challenges, but more work is still r equired. The following sections outline some ideas that the author would like to ad dress personally or see future graduate students pursue. 6.2.1 Pop-in Phenomenon Load excursions or pop-ins are interesting events t hat are sometimes observed in load-displacement curves. Pop-in events are happen during load-controlled indentation and are sudden bursts of displacement at specific i ndentation loads, which produce discontinuous steps in the load-displacement data. In crystalline materials without

PAGE 195

178 surface oxides and other contaminating surface laye rs, the first pop-in event signifies the transition from purely elastic to elastic/plastic d eformation and is thought to be associated with the nucleation and propagation of dislocations [117-119]. The local maximum shear stress generated under the indenter at pop-in event s is frequently close to the material’s theoretical strength, G/2 where G is the shear modulus [120, 120]. This wo uld suggest that deformation at the nano-scale is controlled by the homogeneous nucleation of dislocations and not the motion of pre-existing dis location structures. Some of the parameters thought to be influencing the pop-in phe nomenon are the load applied, loading rates, tip radius, crystal orientation and pre-existing dislocations [119, 120]. Even in a brittle material like sapphire, plastic d eformation is initiated prior to the onset of fracture if the indenter tip is sharp. Th e load at which the pop-in event is observed is found to be very repeatable as in the c ase of sapphire in Figure 103. The pop-in events in Figure 103 are for three indents a nd the load at which pop-in occurs varies between 7900 and 8200 N.

PAGE 196

179 0 2000 4000 6000 8000 020406080100 1 2 3Load (N)Depth (nm) Figure 103. Pop-ins observed at the same load for a sapphire sample using a Berkovich indenter. To confirm that the pop-in phenomenon was a transit ion from elastic to elastic/plastic contact, an indent was performed to a maximum load just below the load pop-in events were noticed. Figure 104 is a 7300 N indent that shows perfectly elastic contact behavior. The loading and unloading portio ns of the load-displacement curve were plotted with different markers to help indicat e this. Since there was no plastic deformation this would indicate that no dislocation s were generated. Additional proof of the pop-in being an elastic to plastic transition i s by use of Hertzian contact theory applied to the loading portion of the curve prior t o the pop-in. Equation 72 from Chapter 4 was used to plot the Hertzian contact model again st the loading portion of the loaddisplacement curve in Figure 105.

PAGE 197

180 0 1000 2000 3000 4000 5000 6000 7000 01020304050607080 Unloading LoadingLoad ( m N)Depth (nm) Figure 104. Perfectly elastic indent prior to pop-i n loads. 0 1000 2000 3000 4000 5000 6000 7000 8000 020406080100 Experimental HertzLoad (N)Depth (nm) Figure 105. Hertzian fit prior to pop-in event mode ling elastic loading. The resolution of current nanoindenters allows for exploring elastic and plastic deformation of solids at the nanometer level. Futu re work would involve using the pop-

PAGE 198

181 in events to calculate the maximum shear stress at the elastic threshold, which could be compared to the theoretical strength of a material. 6.2.2 Microfluidic Devices Microfluidics has been a rapidly growing field alon g with the rest of the microelectronics boom. In the late 1980s the early stages of microfluidics were dominated by the development of microflow sensors, micropumps and microvalves [122]. Like many different areas of engineering, h aving everyone agree on a set definition is sometimes difficult and microfluidics does not differ in that sense. But one point that the majority can agree upon is that a mi croscopic quantity of a fluid is the key issue in microfluidics. One main advantage of micr ofluidics is utilizing scaling laws for achieving better sensor performance. This can be s een in the following example regarding diagnostic sensitivity, where the sample volume V and the sensor efficiency s are inversely related [122]: i A sA N V = 1h (116), where N A is Avogadro’s number and A i is the concentration of analyte i From equation 116, the sensor efficiency increases with decreasin g the sample volume. As the fluid volume is decreased, there will also be a need to d ecrease the size of the channels the fluid is transported in. Some possible delaminatio ns sizes created here are shown in Figure 106. The delamination channel width was var ied from 25 to 60 m and the height was varied from 0.75 to 2 m.

PAGE 199

182 0 0.5 1 1.5 2 0102030405060 W/Si W/PhotoresistHeight ( m m)Width ( m m) Figure 106. Different delamination channels profile s. An interesting effect has been observed with the in troduction of water at the film/substrate interface of highly compressed films Water appears to reduce interfacial toughness and spontaneous delamination propagation was initiated with the introduction of water. Figure 107 shows the propagation of a te lephone cord delamination over a 90 second time interval when water was introduced at t he lower left hand corner. In this case (Figure 107), the delamination microchannels c ould be used as a one time use, disposable microfluidic devices.

PAGE 200

183 Figure 107. Delamination propagation induced by the introduction of water. Using film delaminations to create microchannels sh ows promise in the field of microfluidics. The key to creating the microchanne ls is by utilizing areas of reduced adhesion to control the delamination morphology. P ossible areas for future work could be in finding better choices for adhesion reducing layers and developing more complex delamination patterns. Creating the microchannels is only a small component of the overall picture if they are to be used in microflui dic devices. Integration of the microchannels onto a “lab on a chip” type device is the goal, but many questions still need to be answered on how the fluid will be placed into the microchannels and how the fluid with be transported once inside the microchan nels. 90 sec 60 sec 30 sec 0 sec 50 m

PAGE 201

184 References 1 International Roadmap Committee, International technology roadmap for semiconductors 2007 edition (2007) 2 M. M Vai,., VLSI design Boca Raton, CRC Press (2001) 3 W. D. Nix, Mechanical properties of thin films Metallurgic Trans. A, 20A, 2217 (1989) 4 B. Jacoby, A. Wienss, R. Ohr. M. von Gradowski, H. Hilgers, Nanotribological properties of ultra-thin carbon coatings for magnet ic storage devices Surface and Coatings Technol., 174, 1126 (2003) 5 S. J. Lim, S. Kwon, H. Kim, ZnO thin films prepared by atomic layer deposition and RF sputtering as an active layer for thin film transistor Thin Solid Films, 516, 1523 (2008) 6 X. Liang, G. Zhan, D. King, J. A. McCormick, J. Zha ng, S. M. George, A. W. Weimer, Alumina atomic layer deposition nanocoatings on pri mary diamond particles using a fluidized bed reactor Diamond and Related Materials, 17, 185 (2008) 7 N. Yu, A. Polycarpou, T. F. Conry, Tip-radius effect in finite element modeling of sub-50 nm shallow nanoindentation Thin Solid Films, 450, 295 (2004) 8 K. D. Bouzakis, N. Michailidis, S. Hadjiyiannis, G. Skordaris, G. Erkens, The effect of specimen roughness and indenter tip geome try on the determnation accuracy of thin hard coatings stress-strain laws b y nanoindentation Materials Characterization, 49, 149 (2003) 9 R. Gunda, S. K. Biswas, S. Bhowmick, V. Jayaram, Mechanical properties of rough TiN coating deposited on steel by cathodic ar c evaporation technique J. Am. Ceram. Soc., 88(7), 1831 (2005) 10 H. Bei, E. P. George, J. L. Hay, G. M. Pharr, Influence of indenter tip geometry on elastic deformation during nanoindentation Physical Review Letters, 95, 045501 (2005) 11 M. Ohring, Materials science of thin films San Diego, Academic Press (2002)

PAGE 202

185 12 B. Kindler, W. Hartmann, J. Klemm, B. Lommel, J. St einer, Preparation of targets by sputter deposition , Nucl. Instr. And Meth. In Phys. Res. A, 521, 22 2 (2004) 13 W. R. Grove, On the electro-chemical polarity of gases Phil. Trans. Roy. Soc. London, 142, 87 (1852) 14 A. W. Wright, On the production of transparent metallic films by electrical dischage in exhausted tubes Amer. J. Sci. Arts, 13, 49 (1877) 15 P. Sigmund, Phys. Rev., 184, 383 (1969) 16 M. A. Makeev, A. L. Barabasi, Effect of surface morphology on the sputtering yields. I. Ion sputtering from self-affine surfaces Nucl. Instr. And Meth. In Phys. Res. B, 222, 316 (2004) 17 M. A. Makeev, A. L. Barabasi, Effect of surface morphology on the dputtering yields. II. Ion sputtering from rippled surfaces Nucl. Instr. And Meth. In Phys. Res. B, 222, 335 (2004) 18 C. Huyghebaert, T. Conard, W. Vandervorst, Energy and angular dependence of the sputter yield and ionization yield of Ge bombar ded by O 2 + Applied Surface Science, 231, 693 (2004) 19 J. E. Mahon, A. Vantomme, A simplified collisional model of sputtering in the linear cascade regime J. Vac. Sci. Technol. A, 15(4) 1976 (1997) 20 R. V. Stuart, G. K. Wehner, J. Appl. Phys. 33, 2345 (1963) 21 Y. Matsuda, Y. Yamamura, Y. Udeda, K. Uchino, K. Mu raoka, M. Maeda, M. Akazaki, Jpn. J. Appl. Phys, Energy dependence of angular distributions of sputtered particles by ion-beam bombardment at norm al incidence 25, 8 (1986) 22 S. Mahieu, G. Buyle, D. Depla, S. Heirwegh, P. Ghek iere, R. De Gryse, Monte Carlo simulation of the transport of atoms in DC ma gnetron sputtering Nucl. Instr. and Meth. in Phys. B, 243, 313 (2006) 23 G. Buyle, D. Depla, K. Eufinger, J. Haemers, W. De Bosscher, R. De Gryse, Simplified model for the DC planar magnetron discha rge Vacuum, 74, 353 (2004) 24 T. P. Drusedau, M. Lohmann, F. Klabunde, T. M. John Investigations on energy fluxes in magnetron sputter-deposition: Implication s for texturing and nanoporosity of metals Surface and Coatings Technology, 133, 126 (2000)

PAGE 203

186 25 R. E. Somekh, The thermalization of energetic atoms during the sp uttering process J. Vac. Sci. Technol., A2(3), 1285 (1984) 26 J. M. Harper, J. J. Cuomo, R. J. Gambino, H. R. Kau fman, R. S. Robinson, Mean free path of negative ions in diode sputtering J. Vac. Sci. Technol., 15(4), 1597 (1978) 27 R. S. Robinson, Energetic binary collisions in rare gas plasmas J. Vac. Sci. Technol., 16(2) 185 (1979) 28 T. Smy, L. Tan, S. S. Winterton, S. K. Dew, M. J. B rett, Simulation of sputter deposition at high pressures J. Vac. Sci. Technol., A15(6), 2847 (1997) 29 G. M. Turner, S. M. Rossnagel, J. J. Cuomo, Measured radial and angular distributions of sputtered atoms in a planar magnet ron discharge J. Appl. Phys. 75(7), 3611 (1994) 30 T. Nakano, S. Baba, Gas pressure effects on thickness uniformity and circumvented deposition during sputter deposition p rocess Vacuum, 80, 647 (2006) 31 S. Hong, E. Kim, B. Bae, K. No, S. Lim, S. Woo, Y. Koh, A Simulation model for thickness profile of the film deposited using plana r circular type magnetron sputtering sources J. Vac. Sci. Technol. A, 14(5) 2721 (1996) 32 K. S. Fancey, A coating thickness uniformity model for physical v apor deposition systems: Overview Surface and Coatings Technol., 71, 16 (1995) 33 S. Hong, E. Kim, Z. Jiang, B. Bae, K. No, S. Lim, S Woo, Y. Koh, Effects of gas ring position and mesh introduction on film quality and thickness uniformity Mat. Sci. Eng., B45, 98 (1997) 34 R. A. Vidal, B. D. Teolis, R. A. Baragiola, Angular dependence of sputtering yield of water ice by 100 keV proton bombardment Surface Science, 588, 1 (2005) 35 S. Inoue, T. Ohba, H. Takata, K. Koterazawa, Effects of partial pressure on the internal stress and the crystallographic structure of RF reactive sputtered Ti-N films Thin Solid Films, 343, 230 (1999) 36 D. W. Hoffman, Perspective on stresses in magnetron-sputtered thin films J. Vac. Sci. Technol. A, 12(4), 953 (1994)

PAGE 204

187 37 D. W. Hoffman, J. A. Thornton, Internal stresses in sputtered chromium Thin Solid Films, 40 355 (1977) 38 J. A. Thornton, J. Tabock, D. W. Hoffman, Internal stresses in metallic films deposited by cylindrical magnetron sputtering Thin Solid Films, 64, 111 (1979) 39 P. V. Plunkett, R. M. Johnson, C. D. Wiseman, Stresses in sputter-deposited nickel and copper oxide thin films Thin Solid Films, 64, 121 (1979) 40 D. W. Hoffman, J. A. Thornton, Compressive stress and inert gas in Mo films sputtered from cylindrical-post magnetron with Ne, Ar, Kr, and Xe, J. Vac. Sci. Technol., 17(1), 380 (1980) 41 J. A. Thornton, D. W. Hoffman, The influence of discharge current on the intrinsic stress in Mo films deposited using cylind rical and planar magnetron sputtering sources J. Vac. Sci. Technol. A, 3(3), 576 (1984) 42 H. Windischmann, Intrinsic stress in sputter-deposited thin films Critical Reviews in Solid State and Materials Sciences, 17(6 ), 547 (1992) 43 D. W. Hoffman, M. R. Gaerttner, Modification of evaporated chromium by concurrent ion bombardment J. Vac. Sci. Technol. 17(1), 425 (1980) 44 J. D. Finegan, R. W. Hoffman, Stress and stress anisotropy in evaporated iron films J. Appl. Phys., 30, 597 (1959) 45 F. A. Doljack, R. W. Hoffman, The origin of stressing thin nickel films Thin Solid Films, 12, 71 (1972) 46 H. Windischmann, Temperature dependence of intrinsic stress in Fe, S i, and AlN prepared by ion beam sputtering J. Vac. Sci. Technol. A, 7(3), 2247 (1989) 47 J. A. Thornton, The microstructure of sputter-deposited coatings J. Vac. Sci. Technol. A, 4(6), 3059 (1986) 48 J. A. Thornton, Influence of apparatus geometry and deposition cond itions on the structure and topography of thick sputtered coating s J. Vac. Sci. Technol., 11(4) 666 (1974) 49 J.A. Thornton, Ann. Rev. Mater. Sci. 7, 239, 1977 50 W. Buckel, Internal stresses J. Vac. Sci. Technol. 6, 606 (1969) 51 R. W. Hoffman, Stresses in shin films: The relevance of grain bou ndaries and impurities Thin Solid Films, 34, 185 (1976)

PAGE 205

188 52 W. D. Nix, B. M. Clemens, Crystallite coalescence: A mechanism for intrinsic tensile stresses in thin films J. Mater. Res., 14(8), 3467 (1999) 53 A. A. Griffith, The phenomena of rupture and flow in solids Phil. Trans. Roy. Soc. London Series A, 221, 163 (1921) 54 A. A. Volinsky, Fracture patterns in thin films and multilayers Mat. Res. Soc. Symp. Proc., 795, U3.8.1 (2004) 55 G. Gore, On the properties of electro-deposited antimony Phil. Trans. Roy. Soc. London, 148, 185 (1858) 56 G. G. Stoney, The tension of metallic films deposited by electrol ysis Proc. Roy. Soc. London. Series A, 82, 172 (1909) 57 M. Gelfi, E. Bontempi, R. Roberti, L. E. Depero, X-ray diffraction debye ring analysis for stress measurement (DRAST): a new meth od to evaluate residual stress Acta Mater., 52, 583 (2004) 58 L. Meda, K. Dahmen, S. Hayek, H. Garmestani, X-ray diffraction residual stress calculation on textured La 2/3 Sr 1/3 MnO 3 thin film J. Crystal Growth, 263, 185 (2004) 59 C. V. Falub, A. Karimi, M. Ante, W. Kalss, Interdependence between stress and texture in arc evaporated Ti-Al-N thin films Sur. Coat. Technol., 201, 5891 (2006) 60 E. Atar, C. Sarioglu, U. Demirler, E. Kayali, H. Ci menoglu, Residual stress estimation of ceramic thin films by X-ray diffracti on and indentation techniques Scripta Mater., 48, 1331 (2003) 61 B. Girault, P. Villian, E. Le Bourhis, P. Goudeau, P. Renault, X-ray diffraction analysis of the structure and residual stresses of W/Cu multilayers Sur. Coat. Technol., 201, 4372 (2006) 62 J. Zhang, Y. Zhang, K. Xu, V. Ji, General compliance transformation relation and applications for anisotropic cubic metals Materials Letters, 62, 1328 (2008) 63 R. W. Hertzberg, Deformation and Fracture Mechanics of Engineering M aterials Wiley, New York (1976) 64 G. Maeder, M. Barral, J. L. Lebrun, J. M. Sprauel, Study of the mechanical behavior of materials by using synchrotron radiatio n The Rigaku Journal, 3(2), 9 (1986)

PAGE 206

189 65 H. Araki, Micro area X-ray diffraction techniques The Rigaku Journal, 6(2), 34 (1989) 66 D. Balzar, N. C. Popa, Analyzing microstructure by Rietveld refinement The Rigaku Journal, 22(1), 16 (2005) 67 B. D. Cullity, S. R. Stock, Elements of X-ray diffraction Prentice Hall, Upper Saddle River, NJ (2001) 68 H. Behnken, V. Hauk, Determination of steep stress gradients by X-ray diffraction results of a joint investigation Mater. Sci. Eng. A, 300, 41 (2000) 69 I. C. Noyan, J. B. Cohen, Residual stress: Measurement by diffraction and interpretation Springer-Verlag, New York (1987) 70 D. R. Askeland, The science and engineering of materials PWS Publishing Co., Boston (1994) 71 B. D. Cullity, S. R. Stock, Elements of X-ray diffraction Prentice Hall, Upper Saddle River, NJ (2001) 72 S. A. Syed Asif, K. J. Wahl, R. J. Colton, Nanoindentation and contact stiffness measurement using force modulation with a capacitiv e load-displacement transducer Review of Scientific Instruments, May (1999) 73 Hysitron Triboindenter manual 74 W. C. Oliver, G. M. Pharr, An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments J. Mater. Res., 7(6), 1564 (1992) 75 G. M. Pharr, A. Bolshakov, Understanding nanoindentation unloading curves J. Mater. Res., 17(10), 1660 (2002) 76 I. N. Sneddon, The relation between load and penetration in the ax isymmetric Boussinesq problem for a punch of arbitrary profile Int. J. Enging. Sci., 3, 47 (1965) 77 J. Y. Kim, D. Read, D. Kwon, Depth-dependent hardness characterization by nanoindentation using a Berkovich indenter with a r ounded tip Mat. Res. Soc. Symp. Proc., Vol. 875, O2.4 (2005) 78 K. D. Bouzakis, N. Michailidis, S. Hadjiuiannis, G. Skordaris, G. Erkens, The effect of specimen roughness and indenter tip geome try on the determination accuracy of thin hard coatings stress-strain laws b y nanoindentation Materials Characterization, 49, 149 (2003)

PAGE 207

190 79 N. Yu, A. A. Polycarpou, T. F. Conry, Tip-radius effect in finite element modeling of sub-50 nm shallow nanoindentation Thin Solid Films, 450, 295 (2004) 80 Y. T. Cheng, C. M. Cheng, Further analysis of indentation loading curves: Effects of tip rounding on mechanical property meas urements J. Mater. Res., 13(4), 1059 (1998) 81 J. Thurn, R. F. Cook, Simplified area function for sharp indenter tips in depthsensing indentation J. Mater. Res., 17(5), 1143 (2002) 82 Z. Xue, Y. Huang, K. C. Hwang, M. Li, The influence of indenter tip radius on the micro-indentation hardness J. Eng. Mat. Technol., 124, 371 (2002) 83 Y. Huang, F. Zhang, K. C. Hwang, W. D. Nix, G. M. P harr, G. Feng, A model of size effects in nano-indentation J. Mech. Phys. Solids, 54, 1668 (2006) 84 G. Feng, W. D. Nix, Indentation size effect in MgO Scripta Mater., 51, 599 (2004) 85 R. Saha, W. D. Nix, Effects of the substrate on determination of thin f ilm mechanical properties by nanoindentation Acta Mater., 50, 23 (2002) 86 S. M. Han, R. Saha, W. D. Nix, Determining hardness of thin films in elastically mismatched film-on-substrate systems using nanoinde ntation Acta Mater., 54 1571 (2006) 87 A. Bolshakov, G. M. Pharr, Influences of pileup on the measurement of mechanical properties by load and depth sensing ind entation techniques, J. Mater. Res., 13, 1049 (1998) 88 G. M. Pharr, Measurement of mechanical properties by ultra-low l oad indentation Materials Science and Engineering A, 253, 151 (19 98) 89 B. Taljat, G. M. Pharr, Development of pile-up during spherical indentation of elastic-plastic solids International J. of Solids and Structures, 41, 38 91 (2004) 90 R. J. Sanford, Principles of fracture mechanics Prentice Hall, Upper Saddle River, NJ (2003) 91 A. A. Volinsky, N. R. Moody, W. W. Gerberich, Interfacial toughness measurements for thin films on substrates Acta Mater., 50, 441 (2002) 92 P. G. Charalambides, J. Lund. A. G. Evans, R. M. Mc Meeking, A test specimen for determining the fracture resistance of biomater ial interfaces J. Appl. Mech., 56, 77 (1989)

PAGE 208

191 93 S. K. Venkataraman, D. L. Kohlstedt, W. W. Gerberic h, Metal-ceramic interfacial fracture resistance using the continuou s microscratch technique Thin Solid Films, 223, 269 (1993) 94 G. Irwin, Analysis of stresses and strains near the end of a crack traversing a plate J. Appl, Mech. 79, pp. 361-366 (1957) 95 B.R. Lawn, An atomistic model of kinetic crack growth in britt le solids J. Mat. Sci. 10, pp. 469-480 96 B. Lawn, Fracture of brittle solids Cambridge University Press, Great Britain (1993) 97 J. Dundurs, Edge-bonded dissimilar orthogonal elastic wedges un der normal and shear loading J. Appl. Mech. 36, pp. 650-652 (1969) 98 J.W. Hutchinson, Z. Suo, Mixed mode cracking in layered materials Adv. Appl. Mech. 29, pp. 63-191 (1992) 99 D. B. Marshall, A. G. Evans, Measurement of adherence of residually stressed thin films by indentation. I. Mechanics of interfac e delamination J. Appl. Phys., 56(10), 2632 (1984) 100 M. D. Kriese, W. W. Gerberich, N. R. Moddy, Quantitative adhesion measures of multilayer films: Part I. Indentation mechanics J. Mater. Res., 14(7), 3007 (1999) 101 M. D. Kriese, W. W. Gerberich, N. R. Moddy, Quantitative adhesion measures of multilayer films: Part II. Indentation of W/Cu, W/W Cr/W J. Mater. Res., 14(7), 3019 (1999) 102 P.S. Ho, J. Leu, W.W. Lee, Low Dielectric Constant Materials for IC Applications Springer, Verlag Berlin Heidelberg (2003) 103 T. Sakurai, T. Iizuka, Gate electrode RC delay effects in VLSI’s, IEEE J. of Solid State Circuits, 20(1), 290 (1985) 104 W.D. van Driel, Facing the challenge of designing for Cu/low-k reliability, Microelectronics Reliability, article in press (200 7) 105 A. A. Volinsky, J. B. Vella, W. W. Gerberich, Fracture toughness, adhesion and mechanical properties of low-k dielectric thin film s measured by nanoindentation Thin Solid Films, 429, 201 (2003) 106 S. Zhang, D. Sun, Y. Fu, H. Du., Toughness measurement of thin films: a critical review Surface Coatings Technology, 198, 74 (2004)

PAGE 209

192 107 R. F. Cook, G. M. Pharr, Direct observation and analysis of indentation crac king in glasses and ceramics J. Am. Ceram. Soc., 73(4), 787 (1990) 108 B. R. Lawn, T. P. Dabbs, C. J. Fairbanks, Kinetics of shear-activated indentation crack initiation in soda-lime glass J. Mater. Sci., 18, 2785 (1983) 109 B. R. Lawn, M. V. Swain, Microfracture beneath point indentations in brittle solids J. Mater. Sci., 10, 113 (1975) 110 B.R. Lawn, A.G. Evans, D.B. Marshall, Elastic/plastic indentation damage in ceramics: The median/radial crack system, J. Am. Ceram. Soc. 63 [9] 574-581 (1980) 111 G.R. Anstis, P. Chantikul, B.R. Lawn, D.B. Marshall A critical evaluation of indentation techniques for measuring fracture tough ness: I, direct crack measurements, J. Am. Ceram. Soc., 64 [9] 533-538 (1 981) 112 P. Chantikul, G.R. Anstis, B.R. Lawn, D.B. Marshall A critical evaluation of indentation techniques for measuring fracture tough ness: II, strength method J. Am. Ceram. Soc., 64 [9] 539-543 (1981) 113 D.S. Harding, W.C. Oliver, G.M. Pharr, Mater. Res. Soc. Symp. Proc. 356 (1995) 114 T. Scholz, G. A. Schneider, Fracture toughness from submicron derived indentation cracks Appl. Phy. Let., 84(16), 3055 (2004) 115 S. Franssila, Introduction to micro fabrication John Wiley and Sons, Ltd, West Sussex, England (2004) 116 M. W. Moon, K. R. Lee, K. H. Oh, J. W. Hutchinson, Buckle delamination on patterned substrates Acta Mater., 52, 3151 (2004) 117 W. W. Gerberich, J. C. Nelson, E. T. Lilleodden, P. Anderson, J. T. Wyrobek, Indentation induced dislocation nucleation: The ini tial yield point Acta Mater., 44(9), 3585 (1998) 118 Y. L. Chiu, A. H. W. Ngan, Time-dependent characteristics of incipient plastic ity in nanoindentation of a Ni 3 Al single crystal Acta Mater., 50, 1599 (2002) 119 W. Wang, C. B. Jiang, K. Lu, Deformation behavior of Ni 3 Al single crystals during nanoindentation Acta Mater., 51, 6169 (2003) 120 H. Bei, E. P. George, J. L. Hay, G. M. Pharr, Influence of indenter tip geometry on elastic deformation during nanoindentation Phy. Rev. Letters., 95, 045501 (2005)

PAGE 210

193 121 T. A. Michalske, J. E. Houston, Dislocation nucleation at nano-scale mechanical contacts Acta Mater., 46(2), 391 (1998) 122 N.T. Nguyen, S.T. Werely, Fundamentals and Applications of Microfluidics Artech House, Norwood, MA (2002)

PAGE 211

194 Appendices

PAGE 212

195 Appendix A. Excel Spreadsheet for Theoretical Film Thickness The excel spreadsheet below is only a small fractio n of the total spreadsheet used for predicting the film thickness distribution acro ss a four inch wafer. The target erosion profile was used to determine the how the sputterin g yield varies across the target. By assuming a cosine distribution for the sputtering y ield and using a target to substrate distance of 5 cm the film thickness was predicted. d = 5 offset SY degradtancosx-posSy_0 -90-1.570796-1.63246E+166.12574E-17-8.16228E+166.12574E-17 -8.16228E+16 -89-1.553343-57.289961630.017452406-286.44980820.017452406 -288.2498082 -88-1.53589-28.636253280.034899497-143.18126640.034899497 -144.9812664 -87-1.518436-19.081136690.052335956-95.405683440.052335956 -97.20568344 -86-1.500983-14.300666260.069756474-71.503331280.069756474 -73.30333128 -85-1.48353-11.43005230.087155743-57.150261510.087155743 -58.95026151 -84-1.466077-9.5143644540.104528463-47.571822270.104528463 -49.37182227 -83-1.448623-8.1443464280.121869343-40.721732140.121869343 -42.52173214 -82-1.43117-7.1153697220.139173101-35.576848610.139173101 -37.37684861 -81-1.413717-6.3137515150.156434465-31.568757570.156434465 -33.36875757 -80-1.396263-5.671281820.173648178-28.35640910.173648178 -30.1564091 -79-1.37881-5.1445540160.190808995-25.722770080.190808995 -27.52277008 -78-1.361357-4.7046301090.207911691-23.523150550.207911691 -25.32315055 -77-1.343904-4.3314758740.224951054-21.657379370.224951054 -23.45737937 -76-1.32645-4.0107809340.241921896-20.053904670.241921896 -21.85390467 -75-1.308997-3.7320508080.258819045-18.660254040.258819045 -20.46025404 -74-1.291544-3.4874144440.275637356-17.437072220.275637356 -19.23707222 -73-1.27409-3.2708526180.292371705-16.354263090.292371705 -18.15426309 -72-1.256637-3.0776835370.309016994-15.388417690.309016994 -17.18841769 -71-1.239184-2.9042108780.325568154-14.521054390.325568154 -16.32105439 -70-1.22173-2.7474774190.342020143-13.73738710.342020143 -15.5373871 -69-1.204277-2.6050890650.35836795-13.025445320.35836795 -14.82544532 -68-1.186824-2.4750868530.374606593-12.375434270.374606593 -14.17543427 -67-1.169371-2.3558523660.390731128-11.779261830.390731128 -13.57926183 -66-1.151917-2.2460367740.406736643-11.230183870.406736643 -13.03018387 -65-1.134464-2.1445069210.422618262-10.72253460.422618262 -12.5225346 -64-1.117011-2.0503038420.438371147-10.251519210.438371147 -12.05151921 -63-1.099557-1.9626105060.4539905-9.8130525280.4539905 -11.61305253 -62-1.082104-1.8807264650.469471563-9.4036323270.469471563 -11.20363233 -61-1.064651-1.8040477550.48480962-9.0202387760.48480962 -10.82023878 -60-1.047198-1.7320508080.5-8.6602540380.5 -10.46025404 -59-1.029744-1.6642794820.515038075-8.3213974120.515038075 -10.12139741 -58-1.012291-1.6003345290.529919264-8.0016726450.529919264 -9.801672645 -57-0.994838-1.5398649640.544639035-7.6993248190.544639035 -9.499324819 -56-0.977384-1.4825609690.559192903-7.4128048430.559192903 -9.212804843 -55-0.959931-1.4281480070.573576436-7.1407400340.573576436 -8.940740034 -54-0.942478-1.376381920.587785252-6.8819096020.587785252 -8.681909602 -53-0.925025-1.3270448220.601815023-6.6352241080.601815023 -8.435224108 -52-0.907571-1.2799416320.615661475-6.3997081610.615661475 -8.199708161 -51-0.890118-1.2348971570.629320391-6.1744857830.629320391 -7.974485783 -50 -0.872665 -1.191753593 0.64278761 -5.958767963 0.64278761 -7.758767963 0.6 0.7 0.8 0.9 1 1.1 -5.5 -3.5 -1.5 0.5 2.5 Position (cm)Normalized Thickness Figure 108. Excel spreadsheet for predicting film t hickness.

PAGE 213

196 Appendix B. Sample of Mathcad Calculation for Film Stress An excel file containing the wafer profile before and after film deposition was first imported into Mathcad. From there it was bro ken down into smaller segments with a unique curvature and film thickness for each segmen t. The Stoney equation was then applied to each segment. Figure 109. Sample of Mathcad program used for calc ulating residual stress.

PAGE 214

About the Author Patrick Waters has received all of his degrees in Mechanical Engineering from the University of South Florida. His primary area of r esearch is in thin films and materials characterization. He was employed by Harris in Mel bourne Florida immediately following graduation.