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Simulation of Three-Dimensional Strained Heteroepitaxial Growth Using Kinetic Monte Carlo

Published online by Cambridge University Press:  20 August 2015

Tim P. Schulze  and
Peter Smereka
Tim P. Schulze*
Affiliation:
Department of Mathematics, University of Tennessee, Knoxville, TN 37996, USA
Peter Smereka*
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA
*
Corresponding author.Email:schulze@math.utk.edu
Email:psmereka@umich.edu
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Abstract

Efficient algorithms for the simulation of strained heteroepitaxial growth with intermixing in 2+1 dimensions are presented. The first of these algorithms is an extension of the energy localization method [T. P. Schulze and P. Smereka, An energy localization principle and its application to fast kinetic Monte Carlo simulation of heteroepitaxial growth, J. Mech. Phys. Sol., 3 (2009), 521-538] from 1+1 to 2+1 dimensions. Two approximations of this basic algorithm are then introduced, one of which treats adatoms in a more efficient manner, while the other makes use of an approximation of the change in elastic energy in terms of local elastic energy density. In both cases, it is demonstrated that a reasonable level of fidelity is achieved. Results are presented showing how the film morphology is affected by misfit and deposition rate. In addition, simulations of stacked quantum dots are also presented.

Keywords

82B8082B2182D2565C05Heteroepitaxystrained thin filmkinetic Monte Carlo
Type
Research Article
Information
Communications in Computational Physics , Volume 10 , Issue 5 , November 2011 , pp. 1089 - 1112
Copyright
Copyright © Global Science Press Limited 2011

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References

[1]Baskaran, A., Devita, J., and Smereka, P., Kinetic Monte Carlo simulation of strained heteropi-taxy griwth with intermixing, Cont. Mech. Thermo., 22 (2010), 1–26.Google Scholar
[2]Biehl, M., Ahr, M., Kinzel, W., and Much, F., Kinetic Monte Carlo simulations of heteroepitaxial growth, Thin Solid Films, 428 (2003), 52–55.Google Scholar
[3]Blue, J. L., Biechl, I., and Sullivan, F., Faster Monte Carlo simulations, Phys. Rev. E, 51 (1995), 876.Google Scholar
[4]Devita, J. P., Sander, L. M., and Smereka, P., Multiscale kinetic Monte Carlo for simulating epitaxial growth, Phys. Rev. B, 72 (2005), 205421.Google Scholar
[5]Eshelby, J. D., The determination of the elastic field of an ellipsoidal inclusion, and related problems, Proc. Roy. Soc. Lond. A, 241 (1957), 376–396.Google Scholar
[6]Guo, W., Schulze, T. P., and W. E, , Simulation of impurity diffusion in a strained nanowire using off-lattice KMC, Commun. Comput. Phys., 2 (2007), 164–176.Google Scholar
[7]Henkelman, G., Uberuaga, B. P., and Jonsson, H., A climbing image nudged elastic band method for finding saddle points and minimum energy paths, J. Chem. Phys., 113 (2000), 9901–9904.Google Scholar
[8]Kachanov, M., Shafiro, B., and Tsukrov, I., Handbook of Elasticity Solutions, Kluwer Academic Publishers, Dordrecht, 2003.CrossRefGoogle Scholar
[9]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 (2002), 16102.Google Scholar
[10]Lee, J. Y., Noordhoek, M. J., Smereka, P., McKay, H., and Millunchick, J. M., Filling of hole arrays with InAs quantum dots, Nanotechnology, 20 (2009), 285305.Google Scholar
[11]Lita, B., Goldman, R. S., Phillips, J. D., and Bhattacharya, P. K., Nanometer-scale studies of vertical organization and evolution of stacked self-assembled InAs/GaAs quantum dots, Appl. Phys. Lett., 74 (1999), 2824–2826.Google Scholar
[12]Lung, M. T., Lam, C. H., and Sander, L. M., Island, pit, and groove formation in strained heteroepitaxy, Phys. Rev. Lett., 95 (2005), 086102.Google Scholar
[13]Medeiros-Ribeiro, G., Bratkovski, M., Kamins, T. I., Ohlberg, D. A. A., and Williams, R. S., Shape transition of germanium nanocrystals on a silicon (001) surface from pyramids to domes, Science, 279 (1998), 353–355.Google Scholar
[14]Millunchick, J. M., Twesten, R. D., Follstaedt, D. M., Lee, S. R., Jones, E. D., Zhang, Y., Ahrenkiel, S. P., and Mascarenhas, A., Lateral composition modulation in AlAs/InAs short period superlattices grown on InP (001), Appl. Phys. Lett., 70 (1997), 1402–1404.Google Scholar
[15]Niu, X. B., Lee, Y. J., Caflisch, R. E, and Ratsch, C., Optimal capping layer thickness for stacked quantum dots, Phys. Rev. Lett., (2008), 086103.CrossRefGoogle ScholarPubMed
[16]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.Google Scholar
[17]Pan, E. and Yuan, F. G., Three dimension Green’s functions in anisotropic bimaterials, Int. J. Solids Struct., 37 (2000), 5329–5351.Google Scholar
[18]Plapp, M. and Karma, A., Multiscale finite-difference-diffusion-Monte-Carlomethod for simulating dendritic solidification, J. Comput. Phys., 165 (2000), 592–619.Google Scholar
[19]Russo, G. and Smereka, P., Kinetic Monte Carlo simulation of strained epitaxial growth in three dimensions, J. Comput. Phys., 214 (2006), 809–828.Google Scholar
[20]Russo, G. and Smereka, P., A multigrid-Fourier method for the computation of elastic fields with application to heteroepitaxy, Multiscale Model. Simu., 5 (2006), 130–148.Google Scholar
[21]Srensen, M. R. and Voter, A. F., Temperature-accelerated dynamics for simulation of infrequent events, J. Chem. Phys., 112 (2000), 9599–9606.Google Scholar
[22]Schulze, T. P. and Smereka, P., An energy localization principle and its application to fast kinetic Monte Carlo simulation of heteroepitaxial growth, J. Mech. Phys. Sol., 3 (2009), 521–538.Google Scholar
[23]Tersoff, J., Teichert, C., and Lagally, M. G., Self-organization in growth of quantum dot super-lattices, Phys. Rev. Lett., 76 (1996), 1675–1678.CrossRefGoogle Scholar
[24]Voter, A. F., Montalenti, F., and Germann, T. C., Extending the time scale in atomistic simulation of materials, Annu. Rev. Mater. Res., 32 (2002), 321–346.Google Scholar