## 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

Fatigue Quartz SiO2 Dioxide Chromium### References

- 1.I. S. Sokolnikoff (1956) Mathematical theory of elasticity, 2nd ed., McGraw-Hill, New York.MATHGoogle Scholar
- 2.S. P. Timosheko and J. N. Goodier (1970) Theory of elasticity, 3rd ed., McGraw-Hill, New York.Google Scholar
- 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.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.R. Schwaiger, G. Dehm and O. Kraft (2003) “Cyclic deformation of polycrystalline Cu films,” Philosophical Magazine, vol. 83, pp. 693–710.CrossRefGoogle Scholar
- 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.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.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.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.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.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.J. A. Floro and E. Chason (1996) “Measuring Ge segregation by real-time stress monitoring during Si
_{1 − x}Ge_{x}molecular beam epitaxy,” Applied Physics Letters, vol. 69, pp. 3830–3832.CrossRefGoogle Scholar - 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.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.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.W. D. Nix (1989) “Mechanical properties of thin films,” Metallurgical Transactions A, vol. 20A, pp. 2217–2245.CrossRefGoogle Scholar
- 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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.A. Mendelson (1968) Plasticity: theory and application, MacMillan, New York.Google Scholar
- 62.R. Hill (1950) The mathematical theory of plasticity, Oxford University Press, Oxford.MATHGoogle Scholar
- 63.J. Lubliner (1990) Plasticity theory, Macmillan, New York.MATHGoogle Scholar
- 64.S. Suresh (1998) Fatigue of Materials, 2nd ed., Cambridge University Press, Cambridge.CrossRefGoogle Scholar
- 65.T. J. Chung (2007) General continuum mechanics, Cambridge University Press, Cambridge.MATHGoogle Scholar
- 66.J. P. Hirth and J. Lothe (1982) Theory of dislocations, 2nd ed., Wiley-Interscience, New York.Google Scholar
- 67.J. W. Christian and S. Mahajan (1995) “Deformation twinning,” Progress in Materials Science, vol. 39, pp. 1–157.CrossRefGoogle Scholar
- 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.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.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.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.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.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.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.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.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.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.Y. Xiang and J. J. Vlassak (2005) “Bauschinger effect in thin metal films,” Scripta Materialia, vol. 53, pp. 177–182.CrossRefGoogle Scholar
- 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.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.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.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.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.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.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.R. H. Reuss, D. G. Hopper and J.-G. Park (2006) “Macroelectronics,” MRS Bulletin, vol. 31(6), pp. 447–450.CrossRefGoogle Scholar
- 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.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.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.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.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.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.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.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.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.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.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.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.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.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.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.H. J. Frost and M. F. Ashby (1982) Deformation mechanism maps, Pergamon Press, Oxford.Google Scholar
- 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.G. B. Gibbs (1966) “Diffusion creep of a thin foil,” Philosophical Magazine, vol. 13, pp. 589–593.CrossRefGoogle Scholar
- 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.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.A. Gangulee (1974) “Strain-relaxation in thin films on substrates,” Acta Metallurgica, vol. 22, pp. 177–183.CrossRefGoogle Scholar
- 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.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.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.A. Fisher-Cripps (2002) Nanoindentation, Springer, New York.Google Scholar
- 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.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.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.C. A. Schuh (2006) “Nanoindentation studies of materials,” Materials Today, vol. 9(5), pp. 32–40.CrossRefGoogle Scholar

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