Journal of Scientific Computing

, Volume 37, Issue 1, pp 73–88 | Cite as

Fast Kinetic Monte Carlo Simulation of Strained Heteroepitaxy in Three Dimensions

Article

Abstract

Accelerated algorithms for simulating the morphological evolution of strained heteroepitaxy based on a ball and spring lattice model in three dimensions are explained. We derive exact Green’s function formalisms for boundary values in the associated lattice elasticity problems. The computational efficiency is further enhanced by using a superparticle surface coarsening approximation. Atomic hoppings simulating surface diffusion are sampled using a multi-step acceptance-rejection algorithm. It utilizes quick estimates of the atomic elastic energies from extensively tabulated values modulated by the local strain. A parameter controls the compromise between accuracy and efficiency of the acceptance-rejection algorithm.

Keywords

Heteroepitaxy Monte Carlo simulation Surfaces Thin films 

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References

  1. 1.
    Shchukin, V.A., Bimberg, D.: Rev. Mod. Phys. 71, 1125 (1999) CrossRefGoogle Scholar
  2. 2.
    Politi, P., Grenet, G., Marty, A., Ponchet, A., Villain, J.: Phys. Rep. 324, 271 (2000) CrossRefGoogle Scholar
  3. 3.
    Freund, L.B., Suresh, S.: Thin Film Materials, Stress, Defect Formation and Surface Evolution. Cambridge University Press, Cambridge (2003) Google Scholar
  4. 4.
    Stangl, J., Holy, V., Bauer, G.: Rev. Mod. Phys. 76, 725 (2004) CrossRefGoogle Scholar
  5. 5.
    Mo, Y.-W., Savage, D.E., Swartzentruber, B.S., Lagally, M.G.: Phys. Rev. Lett. 65, 1020 (1990) CrossRefGoogle Scholar
  6. 6.
    Ross, F.M., Tromp, R.M., Reuter, M.C.: Science 286, 1931 (1999) CrossRefGoogle Scholar
  7. 7.
    Vailionis, A., Cho, B., Glass, G., Desjardins, P., Cahill, D.G., Greene, J.E.: Phys. Rev. Lett. 85, 3672 (2000) CrossRefGoogle Scholar
  8. 8.
    Floro, J.A., Chason, E., Freund, L.B., Twesten, R.D., Hwang, R.Q., Lucadamo, G.A.: Phys. Rev. B 59, 1990 (1999) CrossRefGoogle Scholar
  9. 9.
    Tromp, R.M., Ross, F.M., Reuter, M.C.: Phys. Rev. Lett. 84, 4641 (2000) CrossRefGoogle Scholar
  10. 10.
    Sutter, P., Lagally, M.G.: Phys. Rev. Lett. 84, 4637 (2000) CrossRefGoogle Scholar
  11. 11.
    Tersoff, J., LeGoues, F.K.: Phys. Rev. Lett. 72, 3570 (1994) CrossRefGoogle Scholar
  12. 12.
    Asaro, R.J., Tiller, W.A.: Metall. Trans. 3, 1789 (1972) CrossRefGoogle Scholar
  13. 13.
    Grinfeld, M.A.: J. Nonlinear Sci. 3, 35 (1993) MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Srolovitz, D.J.: Acta Metall. 37, 621 (1989) CrossRefGoogle Scholar
  15. 15.
    Spencer, B.J., Voorhees, P.W., Davis, S.H.: J. Appl. Phys. 73, 4955 (1993) CrossRefGoogle Scholar
  16. 16.
    Tersoff, J., Spencer, B.J., Rastelli, A., Von Känel, H.: Phys. Rev. Lett. 89, 196104 (2002) CrossRefGoogle Scholar
  17. 17.
    Rastelli, A., Von Känel, H., Spencer, B.J., Tersoff, J.: Phys. Rev. B 68, 115301 (2003) CrossRefGoogle Scholar
  18. 18.
    Orr, B.G., Kessler, D.A., Snyder, C.W., Sander, L.M.: Eur. Phys. Lett. 19, 33 (1992) CrossRefGoogle Scholar
  19. 19.
    Barabási, A.-L.: Appl. Phys. Lett. 70, 2565 (1997) CrossRefGoogle Scholar
  20. 20.
    Khor, K.E., Das Sarma, S.: Phys. Rev. B 62, 16657 (2000) CrossRefGoogle Scholar
  21. 21.
    Lam, C.H., Lee, C.K., Sander, L.M.: Phys. Rev. Lett. 89, 216102 (2002) CrossRefGoogle Scholar
  22. 22.
    Gray, J.L., Hull, R., Lam, C.H., Sutter, P., Means, J., Floro, J.A.: Phys. Rev. B 72, 155323 (2005) CrossRefGoogle Scholar
  23. 23.
    Lung, M.T., Lam, C.H., Sander, L.M.: Phys. Rev. Lett. 95, 086102 (2005) CrossRefGoogle Scholar
  24. 24.
    Lam, C.H., Lung, M.T.: Int. J. Mod. Phys. B 21, 4219 (2007) CrossRefGoogle Scholar
  25. 25.
    Russo, G., Smereka, P.: J. Comput. Phys. 214, 809 (2006) MATHCrossRefMathSciNetGoogle Scholar
  26. 26.
    Russo, G., Smereka, P.: SIAM MMS 5, 130 (2006) MATHMathSciNetGoogle Scholar
  27. 27.
    Meixner, M., Schöll, E., Shchukin, V.A., Bimberg, D.: Phys. Rev. Lett. 87, 236101 (2001) CrossRefGoogle Scholar
  28. 28.
    Zhu, R., Pan, E., Chung, P.W.: Phys. Rev. B 75, 205339 (2007) CrossRefGoogle Scholar
  29. 29.
    Yang, W.H., Srolovitz, D.J.: Phys. Rev. Lett. 71, 1593 (1993) CrossRefGoogle Scholar
  30. 30.
    Zhang, Y.W., Bower, A.F., Liu, P.: Thin Solid Films 424, 9 (2003) CrossRefGoogle Scholar
  31. 31.
    Liu, P., Zhang, Y.W., Lu, C.: Phys. Rev. B 68, 035402 (2003) CrossRefGoogle Scholar
  32. 32.
    Tu, Y., Tersoff, J.: Phys. Rev. Lett. 93, 216101 (2004) CrossRefGoogle Scholar
  33. 33.
    Tu, Y., Tersoff, J.: Phys. Rev. Lett. 98, 096103 (2007) CrossRefGoogle Scholar
  34. 34.
    Huang, Z., Zhou, T., Chiu, C.-H.: Phys. Rev. Lett. 98, 196102 (2007) CrossRefGoogle Scholar
  35. 35.
    Much, F., Ahr, M., Biehl, M., Kinzel, W.: Europhys. Lett. 56, 791 (2001) CrossRefGoogle Scholar
  36. 36.
    Much, F., Biehl, M.: Europhys. Lett. 63, 14 (2003) CrossRefGoogle Scholar
  37. 37.
    Makeev, M.A., Yu, W., Madhukar, A.: Phys. Rev. B 68, 195301 (2003) CrossRefGoogle Scholar
  38. 38.
    Retford, C.M., Asta, M., Miksis, M.J., Voorhees, P.W., Webb, E.B.: Phys. Rev. B 75, 075311 (2007) CrossRefGoogle Scholar
  39. 39.
    Fujikawa, Y., Akiyama, K., Nagao, T., Sakurai, T., Lagally, M.G., Hashimoto, T., Morikawa, Y., Terakura, K.: Phys. Rev. Lett. 88, 176101 (2002) CrossRefGoogle Scholar
  40. 40.
    Shklyaev, O.E., Beck, M.J., Asta, M., Miksis, M.J., Voorhees, P.W.: Phys. Rev. Lett. 94, 176102 (2005) CrossRefGoogle Scholar
  41. 41.
    Lu, G.H., Cuma, M., Liu, F.: Phys. Rev. B 72, 125415 (2005) CrossRefGoogle Scholar
  42. 42.
    Savage, D.E., et al.: In: Hull, R., Bean, J.C. (eds.) Semiconductors and Semimetals, vol. 56. Academic Press, San Diego (1999) Google Scholar
  43. 43.
    Paris, F., Canas, J.: Boundary Element Method, Fundamentals and Applications. Oxford University Press, Oxford (1997) MATHGoogle Scholar
  44. 44.
    Tewary, V.K.: Adv. Phys. 22, 757 (1973) CrossRefGoogle Scholar
  45. 45.
    Tewary, V.K.: Phys. Rev. B 69, 094109 (2004) CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Department of Applied PhysicsHong Kong Polytechnic UniversityHong KongChina
  2. 2.Michigan Center for Theoretical Physics, Department of Physics, Randall LaboratoryUniversity of MichiganAnn ArborUSA

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