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Thin Continuous Films

  • Y.-L. Shen
Chapter

Abstract

One of the simplest types of physical confinement is a thin continuous film (or blanket film) attached to a thick substrate material. Frequently this is a beginning form for creating micro- and nano-scale systems such as the semiconductor devices. Here the focus is on the constraint imposed by the substrate on the thin film. A numerical example is given below as an introductory illustration.

Keywords

Indentation Depth Metal Film Equivalent Plastic Strain Kinematic Hardening Model Initial Yield Strength 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    I. S. Sokolnikoff (1956) Mathematical theory of elasticity, 2nd ed., McGraw-Hill, New York.MATHGoogle Scholar
  2. 2.
    S. P. Timosheko and J. N. Goodier (1970) Theory of elasticity, 3rd ed., McGraw-Hill, New York.Google Scholar
  3. 3.
    T. P. Weihs, S. Hong, J. C. Bravman and W. D. Nix (1988) “Mechanical deflection of cantilever microbeams: A new technique for testing the mechanical properties of thin films,” Journal of Materials Research, vol. 3, pp. 931–942.CrossRefGoogle Scholar
  4. 4.
    S. P. Baker and W. D. Nix (1994) “Mechanical properties of compositionally modulated Au-Ni thin films – nanoindentation and microcantilever deflection experiments,” Journal of Materials Research, vol. 9, pp. 3131–3145.CrossRefGoogle Scholar
  5. 5.
    R. Schwaiger, G. Dehm and O. Kraft (2003) “Cyclic deformation of polycrystalline Cu films,” Philosophical Magazine, vol. 83, pp. 693–710.CrossRefGoogle Scholar
  6. 6.
    G. G. Stoney (1909) “The tension of metallic films deposited by electrolysis,” Proceedings of Royal Society (London), vol. A82, pp. 172–175.CrossRefGoogle Scholar
  7. 7.
    T. F. Retajczyk and A. K. Sinha (1980) “Elastic stiffness and thermal expansion coefficient of BN films,” Applied Physics Letters, vol. 36, pp. 161–163.CrossRefGoogle Scholar
  8. 8.
    J. T. Pan and I. A. Blech (1984) “In situ measurement of refractory silicides during sintering,” Journal of Applied Physics, vol. 55, pp. 2874–2880.CrossRefGoogle Scholar
  9. 9.
    P. A. Flinn, D. S. Gardner and W. D. Nix (1987) “Measurement and interpretation of stress in aluminum-based metallization as a function of thermal history,” IEEE Transactions on Electron Devices, vol. ED34, pp. 689–699.CrossRefGoogle Scholar
  10. 10.
    C. A. Volker (1991) “Stress and plastic flow in silicon during amorphization by ion-bombardment,” Journal of Applied Physics, vol. 70, pp. 3521–3527.CrossRefGoogle Scholar
  11. 11.
    A. L. Shull and F. Spaepen (1996) “Measurements of stress during vapor deposition of copper and silver thin films and multilayers,” Journal of Applied Physics, vol. 80, pp. 6243–6256.CrossRefGoogle Scholar
  12. 12.
    J. A. Floro and E. Chason (1996) “Measuring Ge segregation by real-time stress monitoring during Si1 − xGex molecular beam epitaxy,” Applied Physics Letters, vol. 69, pp. 3830–3832.CrossRefGoogle Scholar
  13. 13.
    A. J. Rosakis, R. B. Singh, Y. Tsuji, E. Kolawa and N. R. Moore (1998) “Full field measurements of curvature using coherent gradient sensing – application to thin-film characterization,” Thin Solid Films, vol. 325, pp. 42–54.CrossRefGoogle Scholar
  14. 14.
    A. E. Giannakopoulos, I. A. Blech and S. Suresh (2001) “Large deformation of layered thin films and flat panels: effects of gravity,” Acta Materialia, vol. 49, pp. 3671–3688.CrossRefGoogle Scholar
  15. 15.
    M. F. Doerner, D. S. Gardner and W. D. Nix (1986) “Plastic properties of thin films on substrates as measured by submicron indentation hardness and substrate curvature techniques,” Journal of Materials Research, vol. 1, pp. 845–851.CrossRefGoogle Scholar
  16. 16.
    W. D. Nix (1989) “Mechanical properties of thin films,” Metallurgical Transactions A, vol. 20A, pp. 2217–2245.CrossRefGoogle Scholar
  17. 17.
    A. K. Sinha and T. T. Sheng (1978) “The temperature dependence of stresses in aluminum films on oxidized silicon substrates,” Thin Solid Films, vol. 48, pp. 117–126.CrossRefGoogle Scholar
  18. 18.
    M. Hershkovitz, I. A. Blech and Y. Komem (1985) “Stress relaxation in thin aluminum films,” Thin Solid Films, vol. 130, pp. 87–93.CrossRefGoogle Scholar
  19. 19.
    V. M. Koleshko, V. F. Belitsky and I. V. Kiryushin (1986) “Stress relaxation in thin aluminum films,” Thin Solid Films, vol. 142, pp. 199–212.CrossRefGoogle Scholar
  20. 20.
    S. T. Chen, C. H. Yang, F. Faupel and P. S. Ho (1988) “Stress relaxation during thermal cycling in metal/polyimide layered films,” Journal of Applied Physics, vol. 64, pp. 6690–6698.CrossRefGoogle Scholar
  21. 21.
    D. S. Gardner and P. A. Flinn (1988) “Mechanical stress as a function of temperature in aluminum films,” IEEE Transactions on Electron Devices, vol. 35, pp. 2160–2169.CrossRefGoogle Scholar
  22. 22.
    D. S. Gardner and P. A. Flinn (1990) “Mechanical stress as a function of temperature for aluminum alloy films,” Journal of Applied Physics, vol. 67, pp. 1831–1844.CrossRefGoogle Scholar
  23. 23.
    R. Venkatraman, J. C. Bravman, W. D. Nix, P. W. Davis, P. A. Flinn and D. B. Fraser (1990) “Mechanical properties and microstructural characterization of Al-0.5%Cu thin films,” Journal of Electronic Materials, vol. 19, pp. 1231–1237.CrossRefGoogle Scholar
  24. 24.
    P. A. Flinn (1991) “Measurement and interpretation of stress in copper films as a function of thermal history,” Journal of Materials Research, vol. 6, pp. 1498–1501.CrossRefGoogle Scholar
  25. 25.
    R. Venkatraman and J. C. Bravman (1992) “Separation of film thickness and grain boundary strengthening effects in Al thin films on Si,” Journal of Materials Research, vol. 7, pp. 2040–2048.CrossRefGoogle Scholar
  26. 26.
    M. D. Thouless, J. Gupta and J. M. E. Harper (1993) “Stress development and relaxation in copper films during thermal cycling,” Journal of Materials Research, vol. 8, pp. 1845–1852.CrossRefGoogle Scholar
  27. 27.
    C. A. Volkert, C. F. Alofs and J. R. Liefting (1994) “Deformation mechanisms of Al films on oxidized Si wafers,” Journal of Materials Research, vol. 9, pp. 1147–1155.CrossRefGoogle Scholar
  28. 28.
    S. Bader, E. M. Kalaugher and E. Arzt (1995) “Comparison of mechanical properties and microstructgure of Al(1 wt.%Si) and Al(1 wt.%Si, 0.5 wt.%Cu) thin films,” Thin Solid Films, vol. 263, pp. 175–184.CrossRefGoogle Scholar
  29. 29.
    R. P. Vinci, E. M. Zielinski and J. C. Bravman (1995) “Thermal strain and stress in copper thin-films,” Thin Solid Films, vol. 262, pp. 142–153.CrossRefGoogle Scholar
  30. 30.
    Y.-L. Shen and S. Suresh (1995) “Thermal cycling and stress relaxation response of Si-Al and Si-Al-SiO2 layered thin films,” Acta Metallurgica et. Materialia, vol. 43, pp. 3915–3926.CrossRefGoogle Scholar
  31. 31.
    M. D. Thouless, K. P. Rodbell and C. Cabral, Jr. (1996) “Effect of a surface layer on the stress relaxation of thin films,” Journal of Vacuum Science and Technology A, vol. 14, pp. 2454–2461.CrossRefGoogle Scholar
  32. 32.
    R. P. Vinci and J. J. Vlassak (1996) “Mechanical behavior of thin films,” Annual Review of Materials Science, vol. 26, pp. 431–462.CrossRefGoogle Scholar
  33. 33.
    I.-S. Yeo, S. G. H. Anderson, D. Jawarani, P. S. Ho, A. P. Clark, S. Saimoto, S. Ramaswami and R. Cheung (1996) “Effects of oxide overlayer on thermal stress and yield behavior of Al alloy films,” Journal of Vacuum Science and Technology B, vol. 14, pp. 2636–2644.CrossRefGoogle Scholar
  34. 34.
    J. Proost, A. Witvrouw, P. Cosemans, Ph. Roussel and K. Maex (1997) “Stress relaxation in Al(Cu) thin films,” Microelectronic Engineering, vol. 33, pp. 137–147.CrossRefGoogle Scholar
  35. 35.
    R.-M. Keller, S. P. Baker and E. Arzt (1998) “Quantitative analysis of strengthening mechanisms in thin Cu films: Effects of film thickness, grain size, and passivation,” Journal of Materials Research, vol. 13, pp. 1307–1317.CrossRefGoogle Scholar
  36. 36.
    Y.-L. Shen, S. Suresh, M. Y. He, A. Bagchi, O. Kienzle, M. Ruhle and A. G. Evans (1998) “Stress evolution in passivated thin films of Cu on silica substrates,” Journal of Materials Research, vol. 13, pp. 1928–1937.CrossRefGoogle Scholar
  37. 37.
    J. Koike, S. Utsunomiya, Y. Shimoyama, K. Maruyama and H. Oikawa (1998) “Thermal cycling fatigue and deformation mechanism in aluminum alloy thin films on silicon,” Journal of Materials Research, vol. 13, pp. 3256–3264.CrossRefGoogle Scholar
  38. 38.
    R.-M. Keller, S. P. Baker and E. Arzt (1999) “Stress-temperature behavior of unpassivated thin copper films,” Acta Materialia, vol. 47, pp. 415–426.CrossRefGoogle Scholar
  39. 39.
    A. Witvrouw, J. Proost, Ph. Roussel, P. Cosemans and K. Maex (1999) “Stress relaxation in Al-Cu and Al-Si-Cu thin films,” Journal of Materials Research, vol. 14, pp. 1246–1254.CrossRefGoogle Scholar
  40. 40.
    M. J. Kobrinsky and C. V. Thompson (2000) “Activation volume for inelastic deformation in polycrystalline Ag thin films,” Acta Materialia, vol. 48, pp. 625–633.CrossRefGoogle Scholar
  41. 41.
    D. Weiss, H. Gao and E. Arzt (2001) “Constrained diffusional creep in UHV-produced copper thin films,” Acta Materialia, vol. 49, pp. 2395–2403.CrossRefGoogle Scholar
  42. 42.
    R. P. Vinci, S. A. Forrest and J. C. Bravman (2002) “Effect of interface conditions on yield behavior of passivated copper thin films,” Journal of Materials Research, vol. 17, pp. 1863–1870.CrossRefGoogle Scholar
  43. 43.
    G. Dehm, T. Wagner, T. J. Balk and E. Arzt (2002) “Plasticity and interfacial dislocation mechanisms in epitaxial and polycrystalline Al films constrained by substrates,” Journal of Materials Science and Technology, vol. 18, pp. 113–117.Google Scholar
  44. 44.
    G. Dehm, T. J. Balk, H. Edongue and E. Arzt (2003) “Small-scale plasticity in thin Cu and Al films,” Microelectronic Engineering, vol. 70, pp. 412–424.CrossRefGoogle Scholar
  45. 45.
    S. P. Baker, R.-M. Keller-Flaig and J. B. Shu (2003) “Bauschinger effect and anomalous thermomechanical deformation induced by oxygen in passivated thin Cu films on substrates,” Acta Materialia, vol. 51, pp. 3019–3036.CrossRefGoogle Scholar
  46. 46.
    T. J. Balk, G. Dehm and E. Arzt (2003) “Parallel glide: unexpected dislocation motion parallel to the substrate in ultrathin copper films,” Acta Materialia, vol. 51, pp. 4471–4485.CrossRefGoogle Scholar
  47. 47.
    Y.-L. Shen and U. Ramamurty (2003) “Constitutive response of passivated copper films to thermal cycling,” Journal of Applied Physics, vol. 93, pp. 1806–1812.CrossRefGoogle Scholar
  48. 48.
    T. K. Schmidt, T. J. Balk, G. Dehm and E. Arzt (2004) “Influence of tantalum and silver interlayers on thermal stress evolution in copper thin films on silicon substrates,” Scripta Materialia, vol. 50, pp. 733–737.CrossRefGoogle Scholar
  49. 49.
    S. Hyun, O. Kraft and R. P. Vinci (2004) “Mechanical behavior of Pt and Pt-Ru solid solution alloy thin films,” Acta Materialia, vol. 52, pp. 4199–4211.CrossRefGoogle Scholar
  50. 50.
    P. Wellner, G. Dehm, O. Kraft and E. Arzt (2004) “Size effect in the plastic deformation of NiAl thin films,” Zeitschrift für Metallkunde, vol. 95, pp. 769–778.Google Scholar
  51. 51.
    Y. Sun, J. Ye, Z. Shan, A. M. Minor and T. J. Balk (2007) “The mechanical behavior of nanoporous gold thin films,” JOM, vol. 59(9), pp. 54–58.CrossRefGoogle Scholar
  52. 52.
    P. A. Flinn and G. A. Waychunas (1988) “A new x-ray diffraction design for thin-film texture, strain, and phase characterization,” Journal of Vacuum Science and Technology B, vol. 6, pp. 1749–1755.CrossRefGoogle Scholar
  53. 53.
    M. F. Doerner and S. Brennan (1988) “Strain distribution in thin aluminum films using x-ray depth profiling,” Journal of Applied Physics, vol. 63, pp. 126–131.CrossRefGoogle Scholar
  54. 54.
    M. A. Korhonen, C. A. Paszkiet, R. D. Black and C.-Y. Li (1990) “Stress relaxation of continuous film and narrow line metallizations of aluminum on silicon substrates,” Scripta Metallurgica et. Materialia, vol. 24, pp. 2297–2302.CrossRefGoogle Scholar
  55. 55.
    P. A. Flinn and C. Chiang (1990) “X-ray diffraction determination of the effect of various passivations on stress in metal films and patterned lines,” Journal of Applied Physics, vol. 67, pp. 2927–2931.CrossRefGoogle Scholar
  56. 56.
    I. C. Noyan, J. Jordan-Sweet, E. G. Liniger and S. K. Kaldor (1998) “Characterization of substrate/thin-film interfaces with x-ray microdiffraction,” Applied Physics Letters, vol. 72, pp. 3338–3340.CrossRefGoogle Scholar
  57. 57.
    O. Kraft, M. Hommel and E. Arzt (2000) “X-ray diffraction as a tool to study the mechanical behavior of thin films,” Materials Science and Engineering A, vol. 288, pp. 209–216.CrossRefGoogle Scholar
  58. 58.
    S. P. Baker, A. Kretschmann and E. Arzt (2001) “Thermomechanical behavior of different texture components in Cu thin films,” Acta Materialia, vol. 49, pp. 2145–2160.CrossRefGoogle Scholar
  59. 59.
    T. Hanabusa, K. Kusaka and O. Sakata (2004) “Residual stress and thermal stress observation in thin copper films,” Thin Solid Films, vol. 459, pp. 245–248.CrossRefGoogle Scholar
  60. 60.
    E. Eiper, J. Keckes, K. J. Martinschitz, I. Zizak, M. Cabie and G. Dehm (2007) “Size independent stresses in Al thin films thermally strained down to −100°C,” Acta Materialia, vol. 55, pp. 1941–1946.CrossRefGoogle Scholar
  61. 61.
    A. Mendelson (1968) Plasticity: theory and application, MacMillan, New York.Google Scholar
  62. 62.
    R. Hill (1950) The mathematical theory of plasticity, Oxford University Press, Oxford.MATHGoogle Scholar
  63. 63.
    J. Lubliner (1990) Plasticity theory, Macmillan, New York.MATHGoogle Scholar
  64. 64.
    S. Suresh (1998) Fatigue of Materials, 2nd ed., Cambridge University Press, Cambridge.CrossRefGoogle Scholar
  65. 65.
    T. J. Chung (2007) General continuum mechanics, Cambridge University Press, Cambridge.MATHGoogle Scholar
  66. 66.
    J. P. Hirth and J. Lothe (1982) Theory of dislocations, 2nd ed., Wiley-Interscience, New York.Google Scholar
  67. 67.
    J. W. Christian and S. Mahajan (1995) “Deformation twinning,” Progress in Materials Science, vol. 39, pp. 1–157.CrossRefGoogle Scholar
  68. 68.
    A. J. Cao, Y. G. Wei and S. X. Mao (2007) “Deformation mechanisms of face-centered-cubic metal nanowires with twin boundaries,” Applied Physics Letters, vol. 90, 151909.CrossRefGoogle Scholar
  69. 69.
    T. Zhu, J. Li, A. Samanta, H. G. Kim and S. Suresh (2007) “Interfacial plasticity governs strain rate sensitivity and ductility in nanostructured metals,” Proceedings of the National Academy of Sciences of the United States of America, vol. 104, pp. 3031–3036.CrossRefGoogle Scholar
  70. 70.
    M. Dao, L. Lu, Y. F. Shen and S. Suresh (2006) “Strength, strain-rate sensitivity and ductility of copper with nanoscale twins,” Acta Materialia, vol. 54, pp. 5421–5432.CrossRefGoogle Scholar
  71. 71.
    L. Lu, R. Schwaiger, Z. W. Shan, M. Dao, K. Lu and S. Suresh (2005) “Nano-sized twins induce high rate sensitivity of flow stress in pure copper,” Acta Materialia, vol. 53, pp. 2169–2179.CrossRefGoogle Scholar
  72. 72.
    Z. H. Jin, P. Gumbsch, E. Ma, K. Albe, K. Lu, H. Hahn and H. Gleiter (2006) “The interaction mechanism of screw dislocations with coherent twin boundaries in different face-centered cubic metals,” Scripta Materialia, vol. 54, pp. 1163–1168.CrossRefGoogle Scholar
  73. 73.
    M. Dao, L. Lu, R. J. Asaro, J. T. M. De Hosson and E. Ma (2007) “Toward a quantitative understanding of mechanical behavior of nanocrystalline metals,” Acta Materialia, vol. 55, pp. 4041–4065.CrossRefGoogle Scholar
  74. 74.
    Y. Xiang, T. Y. Tsui and J. J. Vlassak (2006) “The mechanical properties of freestanding electroplated Cu thin films,” Journal of Materials Research, vol. 21, pp. 1607–1618.CrossRefGoogle Scholar
  75. 75.
    L. Lu, Y. Shen, X. Chen, L. Qian and K. Lu (2004) “Ultrahigh strength and high electrical conductivity in copper,” Science, vol. 304, pp. 422–426.CrossRefGoogle Scholar
  76. 76.
    O. Kraft, L. B. Freund, R. Phillips and E. Arzt (2002) “Dislocation plasticity in thin metal films,” MRS Bulletin, vol. 27(1), pp. 30–37.CrossRefGoogle Scholar
  77. 77.
    J. M. Jungk, W. M. Mook, M. J. Cordill, M. D. Chambers, W. W. Gerberich, D. F. Bahr, N. R. Moody and J. W. Hoehn (2004) “Length scale based hardening model for ultra-small volumes,” Journal of Materials Research, vol. 19, pp. 2812–2821.CrossRefGoogle Scholar
  78. 78.
    Y. Xiang and J. J. Vlassak (2005) “Bauschinger effect in thin metal films,” Scripta Materialia, vol. 53, pp. 177–182.CrossRefGoogle Scholar
  79. 79.
    C. J. Bayley, W. A. M. Brekelmans and M. G. D. Geers (2007) “A three-dimensional dislocation field crystal plasticity approach applied to miniaturized structures,” Philosophical Magazine, vol. 87, pp. 1361–1378.CrossRefGoogle Scholar
  80. 80.
    Y. Xiang and J. J. Vlassak (2006) “Bauschinger and size effects in thin-film plasticity,” Acta Materialia, vol. 54, pp. 5449–5460.CrossRefGoogle Scholar
  81. 81.
    M. Hommel, O. Kraft and E. Arzt (1999) “A new method to study cyclic deformation of thin films in tension and compression,” Journal of Materials Research, vol. 14, pp. 2373–2376.CrossRefGoogle Scholar
  82. 82.
    H. Huang and F. Spaepen (2000) “Tensile testing of free-standing Cu, Ag and Al thin films and Ag/Cu multilayers,” Acta Materialia, vol. 48, pp. 3261–3269.CrossRefGoogle Scholar
  83. 83.
    J. A. Ruud, D. Josell, F. Spaepen and A. L. Green (1993) “A new method for tensile testing of thin films,” Journal of Materials Research, vol. 8, pp. 112–117.CrossRefGoogle Scholar
  84. 84.
    J. A. Rogers, Z. Bao, K. Baldwin, A. Dodabalapur, B. Crone, V. R. Raju, V. Kuck, H. Katz, K. Amundson, J. Ewing and P. Drzaic (2001) “Paper-like electronic displays: large-area rubber-stamped plastic sheets of electronics and microencapsulated electrophoretic inks,” Proceedings of the National Academy of Sciences, vol. 98, pp. 4835–4840.CrossRefGoogle Scholar
  85. 85.
    S. R. Forrest (2004) “The path to ubiquitous and low-cost organic electronic appliances on plastic,” Nature, vol. 428, pp. 911–918.CrossRefGoogle Scholar
  86. 86.
    R. H. Reuss, D. G. Hopper and J.-G. Park (2006) “Macroelectronics,” MRS Bulletin, vol. 31(6), pp. 447–450.CrossRefGoogle Scholar
  87. 87.
    T. Li, Z. Suo, S. P. Lacour and S. Wagner (2005) “Compliant thin film patterns of stiff materials as platforms for stretchable electronics,” Journal of Materials Research, vol. 20, pp. 3274–3277.CrossRefGoogle Scholar
  88. 88.
    F. Faupel, C. H. Yang, S. T. Chen and P. S. Ho (1989) “Adhesion and deformation of metal/polyimide layered structures,” Journal of Applied Physics, vol. 65, pp. 1911–1917.CrossRefGoogle Scholar
  89. 89.
    Y. S. Kang and P. S. Ho (1997) “Thickness dependent mechanical behavior of submicron aluminum films,” Journal of Electronic Materials, vol. 26, pp. 805–813.CrossRefGoogle Scholar
  90. 90.
    F. Macionczyk and W. Bruckner (1999) “Tensile testing of AlCu thin films on polyimide foils,” Journal of Applied Physics, vol. 86, pp. 4922–4929.CrossRefGoogle Scholar
  91. 91.
    M. Hommel and O. Kraft (2001) “Deformation behavior of thin copper films on deformable substrates,” Acta Materialia, vol. 49, pp. 3935–3947.CrossRefGoogle Scholar
  92. 92.
    D. Y. W. Yu and F. Spaepen (2004) “The yield strength of thin copper films on Kapton,” Journal of Applied Physics, vol. 95, pp. 2991–2997.CrossRefGoogle Scholar
  93. 93.
    J. Bohm, P. Gruber, R. Spolenak, A. Stierle, A. Wanner and E. Arzt, (2004) “Tensile testing of ultrathin polycrystalline films: a synchrotron-based technique,” Review of Scientific Instruments, vol. 75, pp. 1110–1119.CrossRefGoogle Scholar
  94. 94.
    G. P. Zhang, C. A. Volkert, R. Schwaiger, P. Wellner, E. Arzt and O. Kraft (2006) “Length-scale-controlled fatigue mechanisms in thin copper films,” Acta Materialia, vol. 54, pp. 3127–3139.CrossRefGoogle Scholar
  95. 95.
    S. H. Oh, M. Legros, D. Kiener, P. Gruber and G. Dehm (2007) “In situ TEM straining of single crystal Au films on polyimide: change of deformation mechanisms at the nanoscale,” Acta Materialia, vol. 55, pp. 5558–5571.CrossRefGoogle Scholar
  96. 96.
    J. N. Florando and W. D. Nix (2005) “A microbeam bending method for studying stress-strain relations for metal thin films on silicon substrates,” Journal of the Mechanics and Physics of Solids, vol. 53, pp. 619–638.MATHCrossRefGoogle Scholar
  97. 97.
    Y.-L. Shen and S. Suresh (1995) “Elastoplastic deformation of multilayered materials during thermal cycling,” Journal of Materials Research, vol. 10, pp. 1200–1215.CrossRefGoogle Scholar
  98. 98.
    M. Ataka, A. Omodaka, N. Takeshima and H. Fujita (1993) “Fabrication and operation of polyimide bimorph actuators for a ciliary motion system,” Journal of Microelectromechanical Systems, vol. 2, pp. 146–150.CrossRefGoogle Scholar
  99. 99.
    R. B. Darling, J. W. Suh and T. A. Kovacs (1998) “Ciliary microactuator array for scanning electron microscope positioning stage,” Journal of Vacuum Science and Technology A, vol. 16, pp. 1998–2002.CrossRefGoogle Scholar
  100. 100.
    M. H. Mohebbi, M. L. Terry, K. F. Bohringer, G. T. Kovacs and J. W. Suh (2001) “Omnidirectional walking microrobot realized by thermal microactuator arrays,” in Proceedings of the 2001 ASME International Mechanical Engineering Congress and Exposition, American Society of Mechanical Engineers, New York, paper no. 23824.Google Scholar
  101. 101.
    E. Arzt, G. Dehm, P. Gumbsch, O. Kraft and D. Weiss (2001) “Interface controlled plasticity in metals: dispersion hardening and thin film deformation,” Progress in Materials Science, vol. 46, pp. 283–307.CrossRefGoogle Scholar
  102. 102.
    H. J. Frost and M. F. Ashby (1982) Deformation mechanism maps, Pergamon Press, Oxford.Google Scholar
  103. 103.
    Y.-L. Shen and S. Suresh (1996) “Steady-state creep of metal-ceramic multilayered materials,” Acta Materialia, vol. 44, pp. 1337–1348.CrossRefGoogle Scholar
  104. 104.
    G. B. Gibbs (1966) “Diffusion creep of a thin foil,” Philosophical Magazine, vol. 13, pp. 589–593.CrossRefGoogle Scholar
  105. 105.
    M. D. Thouless (1993) “Effect of surface diffusion on the creep of thin films and sintered arrays of particles,” Acta Metallurgica et. Materialia, vol. 41, pp. 1057–1064.CrossRefGoogle Scholar
  106. 106.
    H. Gao, L. Zhang, W. D. Nix, C. V. Thompson and E. Arzt (1999) “Crack-like grain boundary diffusion wedges in thin metal films,” Acta Materialia, vol. 47, pp. 2865–2878.CrossRefGoogle Scholar
  107. 107.
    A. Gangulee (1974) “Strain-relaxation in thin films on substrates,” Acta Metallurgica, vol. 22, pp. 177–183.CrossRefGoogle Scholar
  108. 108.
    M. Murakami (1978) “Thermal strain in lead thin films II: strain relaxation mechanisms,” Thin Solid Films, vol. 55, pp. 101–111.CrossRefGoogle Scholar
  109. 109.
    D. Josell, T. P. Weihs and H. Gao (2002) “Diffusional creep: stresses and strain rates in thin films and multilayers,” MRS Bulletin, vol. 27(1), pp. 39–44.CrossRefGoogle Scholar
  110. 110.
    Y. H. Zhang and M. L. Dunn (2004) “Geometric and material nonlinearity during the deformation of micron-scale thin-film bilayers subject to thermal loading,” Journal of the Mechanics and Physics of Solids, vol. 52, pp. 2101–2126.CrossRefGoogle Scholar
  111. 111.
    A. Fisher-Cripps (2002) Nanoindentation, Springer, New York.Google Scholar
  112. 112.
    W. C. Oliver and G. M. Pharr (1992) “An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments,” Journal of Materials Research, vol. 7, pp. 1564–1538.CrossRefGoogle Scholar
  113. 113.
    W. C. Oliver and G. M. Pharr (2004) “Measurement of hardness and elastic modulus by instrumented indentation: Advances in understanding and refinements to methodology,” Journal of Materials Research, vol. 19, pp. 3–20.CrossRefGoogle Scholar
  114. 114.
    A. Gouldstone, N. Challacoop, M. Dao, J. Ki, A. M. Minor and Y.-L. Shen (2007) “Indentation across size scales and disciplines: recent developments in experimentation and modeling,” Acta Materialia, vol. 55, pp. 4015–4039.CrossRefGoogle Scholar
  115. 115.
    C. A. Schuh (2006) “Nanoindentation studies of materials,” Materials Today, vol. 9(5), pp. 32–40.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Y.-L. Shen
    • 1
  1. 1.Dept. Mechanical EngineeringUniversity of New MexicoAlbuquerqueUSA

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