Simulation of dislocations and strength in thin films: A review

Progress in Materials Science

Volumn 54, Issue 6, 2009, Pages 874-908

  Fertig, Ray S ^a   Baker, Shefford P ^a  

^a Cornell University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ANALYTICAL TECHNIQUES; CRYSTALLINE THIN FILMS; DISCRETE DISLOCATION DYNAMICS; DISLOCATION DYNAMICS SIMULATION; LEVEL SET METHOD; MODELING AND SIMULATION; PHASE FIELD MODELS; STRAIN HARDENING MODEL;

DYNAMICS; LEVEL MEASUREMENT; MECHANICAL PROPERTIES; MECHANISMS; SIMULATORS; STRAIN HARDENING; THIN FILMS;

THREE DIMENSIONAL;

EID: 67349269225     PISSN: 00796425     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.pmatsci.2009.03.004     Document Type: Review

References (131)

1. Keller R., Baker S.P., and Arzt E. Quantitative analysis of strengthening mechanisms in thin Cu films: effects of film thickness, grain size, and passivation. J Mater Res 13 (1998) 1307
2. Vinci R.P., Zielinski E.M., and Bravman J.C. Thermal strain and stress in copper thin films. Thin Solid Films 262 (1995) 142
3. Baker S.P., Kretschmann A., and Arzt E. Thermomechanical behavior of different texture components in Cu thin films. Acta Mater 49 (2001) 2145
4. Baker S.P. Plastic deformation and strength of materials in small dimensions. Mater Sci Eng A 319-321 (2001) 16
5. Nix W.D. Mechanical properties of thin films. Metal Trans A 20 (1989) 2217
6. Freund L.B., and Suresh S. Thin film materials: stress, defect formation and surface evolution (2003), Cambridge University Press, Cambridge (United Kingdom)
7. Arzt E. Overview no. 130 - size effects in materials due to microstructural and dimensional constraints: a comparative review. Acta Mater 46 (1998) 5611
8. Kraft O., Freund L.B., Phillips R., and Arzt E. Dislocation plasticity in thin metal films. MRS Bull 27 (2002) 30
9. Vinci R.P., and Vlassak J.J. Mechanical behavior of thin films. Annu Rev Mater Sci 26 (1996) 431
10. Freund L.B. Dislocation mechanisms of relaxation in strained epitaxial-films. MRS Bull 17 (1992) 52
11. Dehm G., Balk T.J., von Blanckenhagen B., Gumbsch P., and Arzt E. Dislocation dynamics in sub-micron confinement: recent progress in Cu thin film plasticity. Z Metallkd 93 (2002) 383
12. Frost H.J., and Ashby M.F. Deformation-mechanism maps: the plasticity and creep of metals and ceramics (1982), Pergamon Press, Oxford
13. Keller R.-M., Baker S.P., and Arzt E. Stress-temperature behavior of unpassivated thin copper films. Acta Mater 47 (1999) 415
14. Koleshko V.M., Belitsky V.F., and Kiryushin I.V. Stress relaxation in thin aluminum films. Thin Solid Films 142 (1986) 199
15. Venkatraman R., Chen S., and Bravman J.C. The effect of laser reflow on the variation of stress with thermal cycling in aluminum thin-films. J Vac Sci Technol - Vac Surf Films 9 (1991) 2536
16. Volkert C.A., Alofs C.F., and Liefting J.R. Deformation mechanisms of Al films on oxidized Si wafers. J Mater Res 9 (1994) 1147
17. Shen Y.L., Suresh S., He M.Y., Bagchi A., Kienzle O., Ruhle M., and Evans A.G. Stress evolution in passivated thin films of Cu on silica substrates. J Mater Res 13 (1998) 1928
18. Weiss D., Gao H., and Arzt E. Constrained diffusional creep in UHV-produced copper thin films. Acta Mater 49 (2001) 2395
19. Vinci R.P., Forrest S.A., and Bravman J.C. Effect of interface conditions on yield behavior of passivated copper thin films. J Mater Res 17 (2002) 1863
20. Shu J.B., Clyburn S.B., Mates T.E., and Baker S.P. Effect of oxygen on the thermomechanical behavior of passivated Cu thin films. J Mater Res 18 (2003) 2122
21. Keller-Flaig R.M., Legros M., Sigle W., Gouldstone A., Hemker K.J., Suresh S., et al. In situ transmission electron microscopy investigation of threading dislocation motion in passivated thin aluminum films. J Mater Res 14 (1999) 4673
22. Thompson C.V. The yield stress of polycrystalline thin-films. J Mater Res 8 (1993) 237
23. Venkatraman R., and Bravman J.C. Separation of film thickness and grain-boundary strengthening effects in Al thin-films on Si. J Mater Res 7 (1992) 2040
24. Matthews J.W. Defects associated with the accommodation of misfit between crystals. J Vac Sci Technol 12 (1975) 126
25. Freund L.B. The stability of a dislocation threading a strained layer on a substrate. J Appl Mech 54 (1987) 553
26. Nix W.D. Yielding and strain hardening of thin metal films on substrates. Scr Mater 39 (1998) 545
27. Freund L.B. A criterion for arrest of a threading dislocation in a strained epitaxial layer due to an interface misfit dislocation in its path. J Appl Phys 68 (1990) 2073
28. Schwarz K.W., and Tersoff J. Interaction of threading and misfit dislocations in a strained epitaxial layer. Appl Phys Lett 69 (1996) 1220
29. Pant P., Schwarz K.W., and Baker S.P. Dislocation interactions in thin FCC metal films. Acta Mater 51 (2003) 3243
30. de Koning M., Miller R., Bulatov V.V., and Abraham F.F. Modelling grain-boundary resistance in intergranular dislocation slip transmission. Philos Mag A 82 (2002) 2511
31. de Koning M., Kurtz R.J., Bulatov V.V., Henager C.H., Hoagland R.G., Cai W., et al. Modeling of dislocation-grain boundary interactions in FCC metals. J Nucl Mater 323 (2003) 281
32. Lee T.C., Robertson I.M., and Birnbaum H.K. Prediction of slip transfer mechanisms across grain-boundaries. Scr Metal 23 (1989) 799
33. Robertson I.M., Lee T.C., Rozenak P., Bond G.M., and Birnbaum H.K. Dynamic observations of the transfer of slip across a grain-boundary. Ultramicroscopy 30 (1989) 70
34. Lee T.C., Robertson I.M., and Birnbaum H.K. TEM in situ deformation study of the interaction of lattice dislocations with grain-boundaries in metals. Philos Mag A 62 (1990) 131
35. Clark W.A.T., Wagoner R.H., Shen Z.Y., Lee T.C., Robertson I.M., and Birnbaum H.K. On the criteria for slip transmission across interfaces in polycrystals. Scr Metal Mater 26 (1992) 203
36. von Blanckenhagen B., Gumbsch P., and Arzt E. Dislocation sources in discrete dislocation simulations of thin-film plasticity and the Hall-Petch relation. Model Simul Mater Sci Eng 9 (2001) 157
37. von Blanckenhagen B., Arzt E., and Gumbsch P. Discrete dislocation simulation of plastic deformation in metal thin films. Acta Mater 52 (2004) 773
38. Espinosa H.D., Panico M., Berbenni S., and Schwarz K.W. Discrete dislocation dynamics simulations to interpret plasticity size and surface effects in freestanding FCC thin films. Int J Plasticity 22 (2006) 2091
39. Gao H., Zhang L., Nix W.D., Thompson C.V., and Arzt E. Crack-like grain-boundary diffusion wedges in thin metal films. Acta Mater 47 (1999) 2865
40. Baker S.P., Keller-Flaig R.M., and Shu J.B. Bauschinger effect and anomalous thermomechanical deformation induced by oxygen in passivated thin Cu films on substrates. Acta Mater 51 (2003) 3019
41. Shu J.B. Plastic deformation and thermomechancial behavior of passivated copper thin films on silicon substrates. Mater Sci Eng (2003), Cornell University, Ithaca (NY) p. 196
42. Shen Y.L., and Ramamurty U. Constitutive response of passivated copper films to thermal cycling. J Appl Phys 93 (2003) 1806
43. Xiang Y., and Vlassak J.J. Bauschinger effect in thin metal films. Scr Mater 53 (2005) 177
44. Gruber P.A., Böhm J., Onuseit F., Wanner A., Spolenak R., and Arzt E. Size effects on yield strength and strain hardening for ultra-thin Cu films with and without passivation: a study by synchrotron and bulge test techniques. Acta Mater 56 (2008) 2318
45. Eiper E., Keckes J., Martinschitz K.J., Zizak I., Cabie M., and Dehm G. Size-independent stresses in Al thin films thermally strained down to -100 °C. Acta Mater 55 (2007) 1941
46. Fitzgerald E.A. Gesi/Si nanostructures. Annu Rev Mater Sci 25 (1995) 417
47. Schwarz K.W., Liu X.H., and Chidambarrao D. Dislocation modeling for the silicon world. Mater Sci Eng A 309-310 (2001) 229
48. Schwarz K.W., and Chidambarrao D. Dislocation modeling for the microelectronics industry. Mater Sci Eng A - Struct Mater Prop Microstruct Process 400 (2005) 435
49. Freund L.B. The driving force for glide of a threading dislocation in a strained epitaxial layer on a substrate. J Mech Phys Solids 38 (1990) 657
50. Douin J., Pettinari-Sturmel F., and Coujou A. Dissociated dislocations in confined plasticity. Acta Mater 55 (2007) 6453
51. Schwarz K.W. Simulation of dislocations on the mesoscopic scale. I. Methods and examples. J Appl Phys 85 (1999) 108
52. Schwarz K.W. Discrete dislocation dynamics study of strained-layer relaxation. Phys Rev Lett 91 (2003) 145503
53. Pant P, Schwarz KW, Baker SP. Dislocation dynamics simulations of plastic deformation in thin films, in preparation.
54. Fertig RS, Pant P, Schwarz KW, Baker SP. Dislocation dynamics simulations of dislocation interactions and stresses in thin films; in preparation.
55. Rodney D., Deby J.B., and Verdier M. Atomic-scale modelling of plasticity at a metal film/amorphous substrate interface. Model Simul Mater Sci Eng 13 (2005) 427
56. Sedlacek R., Kratochvil J., and Werner E. The importance of being curved: bowing dislocations in a continuum description. Philos Mag 83 (2003) 3735
57. Sedlacek R., and Werner E. Constrained shearing of a thin crystalline strip: application of a continuum dislocation-based model. Phys Rev B 69 (2004) 134114
58. Schwarz C., Sedlacek R., and Werner E. Application of a continuum dislocation-based model to a tensile test on a thin film. Mater Sci Eng A 400-401 (2005) 443
59. Hirth J.P., and Lothe J. Theory of dislocations (1982), John Wiley and Sons, Inc., New York
60. Freund L.B. The mechanics of dislocations in strained-layer semiconductor materials. Adv Appl Mech 30 (1994) 1
61. Friedman L.H., and Chrzan D.C. Scaling theory of the Hall-Petch relation for multilayers. Phys Rev Lett 81 (1998) 2715
62. Friedman L.H. Towards a full analytic treatment of the Hall-Petch behavior in multilayers: putting the pieces together. Scr Mater 50 (2004) 763
63. Frank F.C., and van der Merwe J.H. One-dimensional dislocations. I. Static theory. Proc Royal Soc London. Series A, Math Phys Sci 198 (1949) 205
64. Frank F.C., and van der Merwe J.H. One-dimensional dislocations. II. Misfitting monolayers and oriented overgrowth. Proc Royal Soc London. Series A, Math Phys Sci 198 (1949) 216
65. Matthews J.W., Mader S., and Light T.B. Accommodation of misfit across the interface between crystals of semiconducting elements or compounds. J Appl Phys 41 (1970) 3800
66. Matthews J.W., and Blakeslee A.E. Defects in epitaxial multilayers. I. Misfit dislocations. J Cryst Growth 27 (1974) 118
67. Baker S.P., Zhang L., and Gao H.J. Effect of dislocation core spreading at interfaces on strength of thin-films. J Mater Res 17 (2002) 1808
68. Gao H.J., Zhang L., and Baker S.P. Dislocation core spreading at interfaces between metal films and amorphous substrates. J Mech Phys Solids 50 (2002) 2169
69. Kuan T.S., and Murakami M. Low-temperature strain behavior of Pb thin-films on a substrate. Metal Trans A 13 (1982) 383
70. Schwarz K.W. Interaction of dislocations on crossed glide planes in a strained epitaxial layer. Phys Rev Lett 78 (1997) 4785
71. Schwarz K.W. Simulation of dislocations on the mesoscopic scale. II. Application to strained-layer relaxation. J Appl Phys 85 (1999) 120
72. Stach E.A., Schwarz K.W., Hull R., Ross F.M., and Tromp R.M. New mechanism for dislocation blocking in strained layer epitaxial growth. Phys Rev Lett 84 (2000) 947
73. Dehm G., Balk T.J., Edongue H., and Arzt E. Small-scale plasticity in thin Cu and Al films. Microelectron Eng 70 (2003) 412
74. Schwarz K.W., and LeGoues F.K. Dislocation patterns in strained layers from sources on parallel glide planes. Phys Rev Lett 79 (1997) 1877
75. Quek S.S., Wu Z., Zhang Y.-W., Xiang Y., and Srolovitz D.J. Dislocation junctions as barriers to threading dislocation migration. Appl Phys Lett 90 (2007) 011905
76. Akasheh F., Zbib H.M., Hirth J.P., Hoagland R.G., and Misra A. Dislocation dynamics analysis of dislocation intersections in nanoscale metallic multilayered composites. J Appl Phys 101 (2007) 084314
77. Kukta R.V., and Freund L.B. Three-dimensional numerical simulation of interacting dislocations in a strained epitaxial surface layer. In: Bulatov V. (Ed). Multiscale modeling of materials vol. 538 (1999), Materials Research Society Proceedings, Pittsburgh (PA) 99
78. Freund L.B. Dislocation interactions in relaxation of a strained epitaxial layer. Scr Metal Mater 27 (1992) 669
79. Weihnacht V., and Bruckner W. Dislocation accumulation and strengthening in Cu thin films. Acta Mater 49 (2001) 2365
80. Wolf D., Yamakov V., Phillpot S.R., Mukherjee A., and Gleiter H. Deformation of nanocrystalline materials by molecular-dynamics simulation: relationship to experiments?. Acta Mater 53 (2005) 1
81. Lynch C., Chason E., Beresford R., Freund L.B., Tetz K., and Schwarz K.W. Limits of strain relaxation in InGaAs/GaAs probed in real time by in situ wafer curvature measurement. J Appl Phys 98 (2005) 073532
82. Van der Giessen E., and Needleman A. Discrete dislocation plasticity - a simple planar model. Model Simul Mater Sci Eng 3 (1995) 689
83. Nicola L., Van der Giessen E., and Needleman A. 2D dislocation dynamics in thin metal layers. Mater Sci Eng A - Struct Mater Prop Microstruct Process 309 (2001) 274
84. Nicola L., Van der Giessen E., and Needleman A. Discrete dislocation analysis of size effects in thin films. J Appl Phys 93 (2003) 5920
85. Nicola L., Van der Giessen E., and Needleman A. Two hardening mechanisms in single crystal thin films studied by discrete dislocation plasticity. Philos Mag 85 (2005) 1507
86. Nicola L., Xiang Y., Vlassak J.J., Van der Giessen E., and Needleman A. Plastic deformation of freestanding thin films: experiments and modeling. J Mech Phys Solids 54 (2006) 2089
87. Nicola L., Van der Giessen E., and Needleman A. Size effects in polycrystalline thin films analyzed by discrete dislocation plasticity. Thin Solid Films 479 (2005) 329
88. Hartmaier A., Buehler M.J., and Gao H.J. Multiscale modeling of deformation in polycrystalline thin metal films on substrates. Adv Eng Mater 7 (2005) 165
89. Hartmaier A., Buehler M.J., and Gao H. A discrete dislocation plasticity model of creep in polycrystalline thin films. Defects Diffus Metals: Annu Retrospective Vi 224-2 (2003) 107
90. Shen Y.-L., and Leger R.W. Parametric atomistic analysis of dislocation-interface interactions in thin metallic films. Mater Sci Eng: Mech Behav Micro- Nano-scale Syst 423 (2006) 102
91. Kubin L.P., Canova G., Condat M., Devincre B., Pontikis V., and Brechet Y. Dislocation microstructures and plastic flow: a 3D simulation. Solid State Phenom 23-24 (1992) 455
92. Devincre B., and Kubin L.P. Simulations of forest interactions and strain-hardening in Fcc crystals. Model Simul Mater Sci Eng 2 (1994) 559
93. Hirth J.P., Rhee M., and Zbib H. Modeling of deformation by a 3D simulation of multiple, curved dislocations. J Comput-Aided Mater Des 3 (1996) 164
94. Shenoy V.B., Kukta R.V., and Phillips R. Mesoscopic analysis of structure and strength of dislocation junctions in fcc metals. Phys Rev Lett 84 (2000) 1491 LP
95. Weygand D., Friedman L.H., van der Giessen E., and Needleman A. Discrete dislocation modeling in three-dimensional confined volumes. Mater Sci Eng A - Struct Mater Prop Microstruct Process 309 (2001) 420
96. Rhee M., Stolken J.S., Bulatov V.V., de la Rubia T.D., Zbib H.M., and Hirth J.P. Dislocation stress fields for dynamic codes using anisotropic elasticity: methodology and analysis. Mater Sci Eng A - Struct Mater Prop Microstruct Process 309 (2001) 288
97. von Blanckenhagen B., Gumbsch P., and Arzt E. Dislocation sources and the flow stress of polycrystalline thin metal films. Philos Mag Lett 83 (2003) 1
98. Zbib H.M., de la Rubia T.D., and Bulatov V. A multiscale model of plasticity based on discrete dislocation dynamics. J Eng Mater Technol - Trans ASME 124 (2002) 78
99. Bulatov V.V., and Cai W. Computer simulations of dislocations (2006), Oxford University Press, New York
100. Arsenlis A., Cai W., Tang M., Rhee M., Oppelstrup T., Hommes G., et al. Enabling strain hardening simulations with dislocation dynamics. Model Simul Mater Sci Eng 15 (2007) 553
101. Tsao J.Y., and Dodson B.W. Excess stress and the stability of strained heterostructures. Appl Phys Lett 53 (1988) 848
102. Brown L.M. The self-stress of dislocations and the shape of extended nodes. Philos Mag 10 (1964) 441
103. Zbib H.M., Rhee M., and Hirth J.P. On plastic deformation and the dynamics of 3D dislocations. Int J Mech Sci 40 (1998) 113
104. Cai W., Arsenlis A., Weinberger C.R., and Bulatov V.V. A non-singular continuum theory of dislocations. J Mech Phys Solids 54 (2006) 561
105. Liu X.H., and Schwarz K.W. Modelling of dislocations intersecting a free surface. Model Simul Mater Sci Eng (2005) 1233
106. Hartmaier A., Fivel M.C., Canova G.R., and Gumbsch P. Image stresses in a free-standing thin film. Model Simul Mater Sci Eng 7 (1999) 781
107. Gomez-Garcia D., Devincre B., and Kubin L. Dislocation dynamics in confined geometry. J Comput-Aided Mater Des 6 (1999) 157
108. Groh S., Devincre B., Kubin L.P., Roos A., Feyel F., and Chaboche J.L. Dislocations and elastic anisotropy in heteroepitaxial metallic thin films. Philos Mag Lett 83 (2003) 303
109. Akasheh F., Zbib H.M., Hirth J.P., Hoagland R.G., and Misra A. Interactions between glide dislocations and parallel interfacial dislocations in nanoscale strained layers. J Appl Phys (2007) 102
110. Bulatov V.V., Hsiung L.L., Tang M., Arsenlis A., Bartelt M.C., Cai W., et al. Dislocation multi-junctions and strain hardening. Nature 440 (2006) 1174
111. Schwarz K.W., Cai J., and Mooney P.M. Comparison of large-scale layer-relaxation simulations with experiment. Appl Phys Lett 85 (2004) 2238
112. Fertig RS, Baker SP. Threading dislocation interactions in an inhomogeneous stress field: a statistical model; in preparation.
113. Fertig R.S., and Baker S.P. Relationship between film stress and dislocation microstructure evolution in thin films. In: LaVan D., Spearing M., Vengallatore S., and Silva M.d. (Eds). Microelectromechanical systems - materials and devices vol. 1052 (2007), Mater. Res. Soc., Boston (MA) DD07
114. Espinosa H.D., Berbenni S., Panico M., and Schwarz K.W. An interpretation of size-scale plasticity in geometrically confined systems. Proc Natl Acad Sci USA 102 (2005) 16933
115. Friedman L.H., and Chrzan D.C. Continuum analysis of dislocation pile-ups: influence of sources. Philos Mag A 77 (1998) 1185
116. Wang Y.U., Jin Y.M., and Khachaturyan A.G. Phase field microelasticity modeling of dislocation dynamics near free surface and in heteroepitaxial thin films. Acta Mater 51 (2003) 4209
117. Xiang Y., Cheng L.-T., Srolovitz D.J., and Weinan E. A level set method for dislocation dynamics. Acta Mater 51 (2003) 5499
118. Quek S.S., Xiang Y., Zhang Y.W., Srolovitz D.J., and Lu C. Level set simulation of dislocation dynamics in thin films. Acta Mater 54 (2006) 2371
119. Thompson C.V., Floro J., and Smith H.I. Epitaxial grain-growth in thin metal-films. J Appl Phys 67 (1990) 4099
120. Owusu-Boahen K., and King A.H. The early stages of plastic yielding in polycrystalline gold thin films. Acta Mater 49 (2001) 237
121. Dehm G., Weiss D., and Arzt E. In situ transmission electron microscopy study of thermal-stress-induced dislocations in a thin Cu film constrained by a Si substrate. Mater Sci Eng A 309-310 (2001) 468
122. Dehm G., and Arzt E. In situ transmission electron microscopy study of dislocations in a polycrystalline Cu thin film constrained by a substrate. Appl Phys Lett 77 (2000) 1126
123. Martínez E., Marian J., Arsenlis A., Victoria M., and Perlado J.M. Atomistically informed dislocation dynamics in fcc crystals. Acta Mater 56 (2008) 869
124. Vodnick AM, Nowak DE, Labat S, Thomas O, Baker SP. Out-of-plane stresses arising from grain interactions in textured thin films. Acta Mater, submitted for publication.
125. Balk T.J., Dehm G., and Arzt E. Parallel glide: unexpected dislocation motion parallel to the substrate in ultrathin copper films. Acta Mater 51 (2003) 4471
126. Schwarz K.W. Local rules for approximating strong dislocation interactions in discrete dislocation dynamics. Model Simul Mater Sci Eng (2003) 609
127. Kukta RV. Observations on the kinetics of relaxations in epitaxial films grown on conventional and compliant substrates: a continuum simulation of dislocation glide near an interface. PhD Dissertation. Division of Engineering. Providence (RI): Brown University; 1998.
128. Weygand D., Friedman L.H., Giessen E., and Needleman A. Aspects of boundary-value problem solutions with three-dimensional dislocation dynamics. Model Simul Mater Sci Eng 10 (2002) 437
129. Zbib H.M., and de la Rubia T.D. A multiscale model of plasticity. Int J Plasticity 18 (2002) 1133
130. Bulatov V, Cai W, Fier J, Hiratani M, Hommes G, Pierce T, et al. Scalable line dynamics in ParaDiS. In: Proceedings of the IEEE/ACM. Conference on High Performance Networking and Computing (SC'04). New York: Institute of Electrical and Electronics Engineers Inc.; 2004. p.19.
131. Tang M., Cai W., Xu G., and Bulatov V.V. A hybrid method for computing forces on curved dislocations intersecting free surfaces in three-dimensional dislocation dynamics. Model Simul Mater Sci Eng 14 (2006) 1139