A phase field study of morphological instabilities in multilayer thin films

Acta Materialia

Volumn 57, Issue 4, 2009, Pages 1060-1067

  Chirranjeevi, B G ^a   Abinandanan, T A ^b   Gururajan, M P ^c  

^a INDIAN INSTITUTE OF TECHNOLOGY MADRAS   (India)

^b INDIAN INSTITUTE OF SCIENCE   (India)

^c Northwestern University   (United States)

Author keywords

Asaro Tiller Grinfeld instability; Elastically stressed solids; Microstructural evolution; Phase field modelling; Thin films

Indexed keywords

FILM PREPARATION; LATTICE MISMATCH; MICROSTRUCTURAL EVOLUTION; MULTILAYER FILMS; MULTILAYERS; SUPERALLOYS; THIN FILMS; TITRATION;

A STABILITIES; ANISOTROPIC SYSTEMS; ANTI-SYMMETRIC; ASARO-TILLER-GRINFELD INSTABILITY; BREAK-UP; DRIVING FORCES; ELASTIC INTERACTIONS; ELASTIC MODULUS MISMATCHES; ELASTIC STRESS; ELASTICALLY STRESSED SOLIDS; IN-PHASE; LATTICE PARAMETERS; MATRIX PHASIS; MATRIXES; MODE OF INSTABILITIES; MORPHOLOGICAL INSTABILITIES; MULTI-LAYER THIN FILMS; MULTIPLE LAYERS; OUT-OF-PHASE; PHASE FIELD MODELLING; PHASE FIELD MODELS; PHASE FIELDS;

PHASE INTERFACES;

EID: 59349090574     PISSN: 13596454     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.actamat.2008.10.051     Document Type: Article

References (43)

1. Asaro R.J., and Tiller W.A. Interface development during stress corrosion cracking. Metall Trans A 3 (1972) 1789-1796
2. Grinfeld M.A. Instability of interface between non-hydrostatically stressed elastic body and melts. Sov Phys Doklady 290 (1986) 1358-1363
3. Srolovitz D.J. On the stability of surfaces of stressed solids. Acta Metall 37 (1989) 621-625
4. Grinfeld M.A. The stress driven instability in elastic crystals: mathematical models and physical manifestations. J Nonlinear Sci 3 (1993) 35-83
5. Godrèche C. Solids far from equilibrium (1992), Cambridge University Press, Cambridge, UK
6. Pimpinelli A., and Villain J. Physics of crystal growth (1998), Cambridge University Press, Cambridge, UK
7. Freund L.B., and Suresh S. Thin film materials: stress, defect formation and surface evolution (2004), Cambridge University Press, Cambridge, UK
8. Shchukin V.A., and Bimberg D. Spontaneous ordering of nanostructures on crystal surfaces. Rev Modern Phys 71 (1999) 1125-1171
9. Gao H., and Nix W.D. Surface roughening of heteroepitaxial thin films. Ann Rev Mater Sci 29 (1999) 173-209
10. Stangl J., Holý V., and Bauer G. Structural properties of self-organized semi-conductor nanostructures. Rev Modern Phys 76 (2004) 725-783
11. Voorhees P.W., and Johnson W.C. The thermodynamics of elastically stressed crystals. Solid state physics: advances in research and applications vol. 59 (2004), Elsevier Academic Press 1-201
12. Balibar S., Alles H., and Parshin A.Y. The surface of helium crystals. Rev Modern Phys 77 (2005) 317-370
13. Sridhar N., Rickman J.M., and Srolovitz D.J. Multilayer film stability. J Appl Phys 82 (1997) 4582-4589
14. Sridhar N., Rickman J.M., and Srolovitz D.J. Microstructural stability of stressed lamellar and fiber composites. Acta Metall 45 (1997) 2715-2733
15. Müller J., and Grant M. Model of surface instabilities induced by stress. Phys Rev Lett 82 (1999) 1736-1739
16. Kassner K., and Misbah C. A phase-field approach for stress-induced instabilities. Europhys Lett 46 2 (1999) 217-223
17. Kassner K., Misbah C., Müller J., Kappey J., and Kohlert P. Phase-field modeling of stress-induced instabilities. Phys Rev E 63:036117 (2001) 1-27
18. Haataja M., Müller J., Rutenberg A.D., and Grant M. Dynamics of dislocations and surface instabilities in misfitting heteroepitaxial films. Phys Rev B 65:035401 (2001) 1-5
19. Eggleston J.J., and Voorhees P.W. Ordered growth of nanocrystals via a morphological instability. Appl Phys Lett 80 (2002) 306-308
20. Haataja M., Müller J., Rutenberg A.D., and Grant M. Dislocations and morphological instabilities: continuum modeling of misfitting heteroepitaxial films. Phys Rev B 65:165414 (2002) 1-20
21. Wang Y.U., Jin Y.M., and Khachaturyan A.G. Phase field microelasticity modeling of surface instability of heteroepitaxial thin films. Acta Mater 52 (2004) 81-92
22. Paret J. Long-time dynamics of the three-dimensional biaxial Grinfeld instability. Phys Rev E 72:011105 (2005) 1-5
23. Seol D.J., Hu S.Y., Liu Z.K., Chen L.Q., Kim S.G., and Oh K.H. Phase-field modeling of stress-induced surface instabilities in heteroepitaxial thin films. J Appl Phys 98:044910 (2005) 1-5
24. Ni Y., He L.H., and Soh A.K. Three-dimensional phase field simulation for surface roughening of heteroepitaxial films with elastic anisotropy. J Cryst Growth 284 (2005) 281-292
25. Wise S.M., Lowengrub J.S., Kim J.S., Thornton K., Voorhees P.W., and Johnson W.C. Quantum dot formation on a strain-patterned epitaxial thin film. Appl Phys Lett 87 (2005) 1-3
26. Yeon D.-H., Cha P.-R., and Grant M. Phase field model of stress-induced surface instabilities: surface diffusion. Acta Mater 54 (2006) 1623-1630
27. Rätz A., Ribalta A., and Voigt A. Surface evolution of elastically stressed films under deposition by a diffuse interface model. J Comput Phys 214 (2006) 187-208
28. Elder K.R., and Grant M. Modeling elastic and plastic deformations in nonequilibrium processing using phase field crystals. Phys Rev E 70:051605 (2004) 1-18
29. Elder K.R., Provatas N., Berry J., Stefanovic P., and Grant M. Phase-field crystal modeling and classical density functional theory of freezing. Phys Rev B 75:064107 (2007) 1-14
30. Zhang Y.W. Self-organization, shape transition, and stability of epitaxially strained islands. Phys Rev B 61 15 (2000) 10388-10392
31. Zhang Y.W., and Bower A.F. Three-dimensional analysis of shape transitions in strained-heteroepitaxial islands. Appl Phys Lett 78 18 (2001) 2706-2708
32. Liu P., Zhang Y.W., and Lu C. Coarsening kinetics of heteroepitaxial islands in nucleationless Stranski-Krastanov growth. Phys Rev B 68 (2003) 1-8
33. Ramasubramaniam A., and Shenoy V.B. Three-dimensional simulations of self-assembly of hut-shaped Si-Ge quantum dots. J Appl Phys 95 12 (2004) 7813-7824
34. Dong L., Schnitker J., Smith R.W., and Srolovitz D.J. Stress relaxation and misfit dislocation nucleation in the growth of misfitting films: a molecular dynamics simulation study. J Appl Phys 83 1 (1998) 217-227
35. Lam C.H., Lee C.K., and Sander L.M. Competing roughening mechanisms in strained heteroepitaxy: a fast kinetic Monte Carlo study. Phys Rev Lett 89:216102 21 (2002) 1-4
36. Cahn J.W., and Hilliard J.E. Free energy of a nonuniform system I. Interfacial free energy. J Chem Phys 28 (1958) 258-267
37. Gururajan MP, Abinandanan TA. A phase field study of microstructural evolution in elastically inhomogeneous systems. In: Howe JM, Laughlin DE, Lee JK, Dahmen U, Soffa WA, editors. Proceedings of solid-solid phase transformations in inorganic materials. TMS (The minerals, Metals & Materials Society); 5005.
38. Gururajan M.P., and Abinandanan T.A. Phase field study of precipitate rafting under a uniaxial stress. Acta Mater 55 (2007) 5015-5026
39. Hu Y., and Chen L.Q. A phase field model for evolving microstructures with strong elastic inhomogeneity. Acta Mater 49 (2001) 1879-1890
40. Frigo M., and Johnson S.G. The design and implementation of FFTW3. Proc IEEE 93 (2005) 216-231
41. Schmidt I., and Gross D. Directional coarsening in Ni-base superalloys: analytical results for an elasticity based model. Proc R Soc (London) 455 (1999) 3016-3085
42. Gururajan MP, Abinandanan TA. A linear stability analysis of ATG-instabilities in thin film assemblies under volume diffusion control. Unpublished notes. Available from: http://www.imechanica.org/node/2703.
43. Riley K.F., Hobson M.P., and Bence S.J. Mathematical methods for physics and engineering. 2nd ed. (2002), Cambridge University Press, Cambridge, UK