An energy localization principle and its application to fast kinetic Monte Carlo simulation of heteroepitaxial growth

Journal of the Mechanics and Physics of Solids

Volumn 57, Issue 3, 2009, Pages 521-538

  Schulze, Tim P ^a   Smereka, Peter ^b  

^a UNIVERSITY OF TENNESSEE   (United States)

^b UNIVERSITY OF MICHIGAN   (United States)

Author keywords

Heteroepitaxy; Kinetic Monte Carlo; Strained thin films

Indexed keywords

EPITAXIAL GROWTH; GROWTH (MATERIALS); RADIATION DAMAGE; THIN FILMS;

CONVERGENCE CRITERION; DISCRETE MODELS; ELASTIC ENERGIES; ELASTIC FIELDS; ELASTIC INTERACTIONS; ENERGY DIFFERENCES; ENERGY LOCALIZATIONS; ERROR ESTIMATES; HETERO-EPITAXIAL GROWTHS; HETEROEPITAXY; HOPPING RATES; KINETIC MONTE CARLO; LOCAL APPROXIMATIONS; LONG RANGES; MONTE CARLO; MONTE CARLO SIMULATIONS; REJECTION ALGORITHMS; STRAINED THIN FILMS;

MONTE CARLO METHODS;

EID: 59649101037     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmps.2008.11.007     Document Type: Article

References (40)

1. Asaro R.J., and Tiller W.A. Interface morphology development during stress-corrosion cracking. 1. Via surface diffusion. Metall. Trans. 3 (1972) 1789-&
2. Biehl M., Ahr M., Kinzel W., and Much F. Kinetic Monte Carlo simulations of heteroepitaxial growth. Thin Solid Films 428 (2003) 52-55
3. Blue, J.L., Beichl, I., Sullivan, F., 1995. Faster Monte Carlo simulations. Phys. Rev. E 867-868.
4. Caflsich R.E., Lee Y.J., Shu S., Xiao Y.X., and Xu J. An application of multigrid methods for a discrete elastic model for epitaxial systems. J. Comput. Phys. 219 (2006) 697-714
5. Diaz J.B., and Payne L.E. Mean value theorems in the theory of elasticity. Proceedings of the Third U.S. National Congress on Applied Mechanics (1958), ASME, New York 293-303
6. Fratzl P., Penrose O., and Lebowitz J.L. Modeling of phase separation in alloys with coherent elastic misfit. J. Stat. Phys. 95 (1999) 1429-1503
7. Freund L.B., and Jonsdottir F. Instability of a biaxially stressed thin-film on a substrate due to material diffusion over its free-surface. J. Mech. Phys. Solids 41 (1993) 1245-1264
8. Freund L.B., and Suresh S. Thin Film Materials (2003), Cambridge University Press, Cambridge
9. Gao, H., 1991a. In: Wu, J.J., Ting, T.C.T., Barnett, D.M. (Eds.), Modern Theory of Anisotropic Elasticity and Applications. SIAM, Philadelphia, p. 139.
10. Gao H. Stress concentration at slightly undulating surfaces. J. Mech. Phys. Solids 39 (1991) 443-458
11. Gao H. Surface roughening of heteroepitaxial thin films. Annu. Rev. Mater. Sci. 29 (1999) 173-209
12. Grinfeld M.A. Instability of interface between nonhydrostatically stressed elastic body and melts. Dokl. Akad. Nauk SSSR 290 (1986) 1358-1363
13. Guo, W., Schulze, T.P., W.E., 2007. Simulation of impurity diffusion in a strained nanowire using off-lattice KMC. Commun. Comput. Phys. 2, 164-176.
14. Gurtin M.E. The linear theory of elasticity. Handbook der Physik VIa/2 (1972), Springer, Berlin
15. 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 1-4 (2002) 16102
16. Lam C.H., Lung M.T., and Sander L.M. Fast kinetic Monte Carlo simulation of strained heteroepitaxy in three dimensions. J. Sci. Comput. 37 (2008) 73-88
17. Landau L.D., and Lifshitz E.M. Theory of Elasticity (1986), Pergamon Press, Oxford
18. Lee S., Caflsich R.E., and Lee Y.J. Exact artificial boundary conditions for continuum and discrete elasticity. SIAM J. Appl. Math. 66 (2006) 1749-1775
19. Love A.E.H. A Treatise on the Mathematical Theory of Elasticity (1927), Cambridge University Press, Cambridge
20. Lung, M.T., Lam, C.H., Sander, L.M., 2005. Island, pit, and groove formation in strained heteroepitaxy. Phys. Rev. Lett. 95, Art. No. 086102.
21. Much F., and Biehl M. Simulation of wetting-layer and island formation in heteroepitaxial growth. Europhys. Lett. 63 (2003) 14-20
22. Much F., Ahr M., Biehl M., and Kinzel W. A kinetic Monte Carlo method for the simulation of heteroepitaxial growth. Comput. Phys. Commun. 147 (2002) 226-229
23. Orr B.G., Kessler D.A., Snyder C.W., and Sander L.M. A model for strain-induced roughening and coherent island growth. Europhys. Lett. 19 (1992) 33-38
24. Politi P., Grenet G., Marty A., Ponchet A., and Villain J. Instabilities in crystal growth by atomic or molecular beams. Phys. Rep. 324 (2000) 271
25. Ratsch C., and Zangwill A. Equilibrium theory of the Stranski-Krastanov epitaxial morphology. Surf. Sci. 293 (1993) 123-131
26. Ratsch C., Šmilauer P., Vvedensky D.D., and Zangwill A. Mechanism for coherent island formation during heteroepitaxy. J. Phys. I France 6 (1996) 575-581
27. Rickman J.M., and Srolovitz D.J. Defect interactions on solid surfaces. Surf. Sci. 284 (1993) 211-221
28. Russo G., and Smereka P. Kinetic Monte Carlo simulation of strained epitaxial growth in three dimensions. J Comput. Phys. 214 (2006) 809-828
29. Russo G., and Smereka P. A multigrid-Fourier method for the computation of elastic fields with application to heteroepitaxy. Multiscale Model. Simulation 5 (2006) 130-148
30. Saint-Venant A.J.C.B. Memoire sur la Torsion des Prismes. Mem. Divers Savants 14 (1855) 233-560
31. Shchukin V.A., and Bimberg D. Spontaneous ordering of nanostructure on crystal surfaces. Rev. Mod. Phys. 71 (1999) 1125
32. Spencer B.J., Voorhees P.W., and Davis S.H. Morphological instability in epitaxially strained dislocation free solid films. Phys. Rev. Lett. 67 (1991) 3696-3699
33. Spencer B.J., Voorhees P.W., and Davis S.H. Morphological instability in epitaxially strained dislocation-free solid films: Linear stability theory. J. Appl. Phys. 73 (1993) 4955-4970
34. Spencer, B.J., Voorhees, P.W., Tersoff, J., 2001. Morphological instability theory for strained alloy film growth: the effect of compositional stresses and species-dependent surface mobilities on ripple formation during epitaxial film deposition. Phys. Rev. B 64, Art. No. 235318.
35. Srolovitz D.J. On the stability of surfaces of stressed solids. Acta Metall. 37 (1989) 621-625
36. Tu, Y.H., Tersoff, J., 2004. Origin of apparent critical thickness for island formation in heteroepitaxy. Phys. Rev. Lett. 93, Art. No. 216101.
37. Tu, Y.H., Tersoff, J., 2007. Coarsening, mixing, and motion: the complex evolution of epitaxial islands. Phys. Rev. Lett. 98, Art. No. 096103.
38. Von Mises R. On Saint Venant's principle. Bull. Amer. Math. Soc. 51 (1945) 555-562
39. Wise S.M., Lowengrub J.S., Kim J.S., and Johnson W.C. Efficient phase-field simulation of quantum dot formation in a strained heteroepitaxial film. Superlattice and Microstructures 36 (2004) 293-304
40. Wise, S.M., Lowengrub, J.S., Kim, J.S., Thornton, K., Voorhees, P.W., Johnson, W.C., 2005. Quantum dot formation on a strain-patterned epitaxial thin film. Appl. Phys. Lett. 87, Art. No. 133102.