Hostname: page-component-76fb5796d-vfjqv Total loading time: 0 Render date: 2024-04-28T02:49:52.723Z Has data issue: false hasContentIssue false
  • English
  • Français

Epitaxial Growth and Recovery: an Analytic Approach

Published online by Cambridge University Press:  21 February 2011

A. Zangwillt ,
C. N. Luset ,
D. D. Vvedensky  and
M. R. Wilby
A. Zangwillt
Affiliation:
school of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332
C. N. Luset
Affiliation:
school of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332
D. D. Vvedensky
Affiliation:
The Blackett Laboratory, Imperial College, London SW7 2BZ, UK
M. R. Wilby
Affiliation:
The Blackett Laboratory, Imperial College, London SW7 2BZ, UK
Get access

Abstract

Most detailed studies of morphological evolution during epitaxial growth and recovery make use of computer-based simulation techniques. In this paper, we discuss an alternative, analytic approach to this problem which takes explicit account of the atomistically random processes of deposition and surface diffusion. Beginning with a master equation representation of the dynamics of a solid-on-solid model of epitaxial growth, we derive a discrete, stochastic equation of motion for the surface profile. This Langevin equation is appropriate for growth studies. In particular, we are able to provide a microscopic justification for a non-linear continuum equation of motion proposed for this problem by others on the basis of heuristic arguments. During recovery, the deposition flux and its associated shot noise are absent. We analyze this process with a completely deterministic equation of motion obtained by performing a statistical average of the original stochastic equation. Results using the latter compare favorably with full Monte Carlo simulations of the original model for the case of the decay of sinusoidally modulated initial surfaces.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 237: Symposium Ca – Interface Dynamics and Growth , 1991 , 189
Copyright
Copyright © Materials Research Society 1992

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1. Bauer, E.G., Dodson, B.W., Ehrlich, D.J., Feldman, L.C., Flynn, C.P., Geis, M.W., Harbison, J.P., Matyi, R.J., Peercy, P.S., Petroff, P.M., Phillips, J.M., Stringfellow, G.B. and Zangwill, A., J. Mater. Res. 5, 852 (1990).CrossRefGoogle Scholar
2. See, for example, the various contributions to Reflection High Energy Electron Diffraction and Reflection Electron Imaging of Surfaces, edited by Larsen, P.K. and Dobson, P.J. (Plenum, New York, 1988).CrossRefGoogle Scholar
3. Eaglesham, D.J., Gossmann, H.-J. and Cernilo, M., Phys. Rev. Lett. 65, 1227 (1990);CrossRefGoogle Scholar
Eaglesham, D.J., Pfeiffer, L.N., West, K.W. and Dykaar, R.R., Appl. Phys. Lett. 58, 65 (1991).CrossRefGoogle Scholar
4. Venables, J.A., Spiller, G.D.T., and Hanbücken, M., Rep. Prog. Phys. 47, 399 (1984).CrossRefGoogle Scholar
5. Kariotis, R. and Lagally, M.G., Surf. Sci. 216, 557 (1989).CrossRefGoogle Scholar
6. Dodson, B.W., CRC Crit. Rev. Sol. State and Mat. Sci. 16, 115 (1990).CrossRefGoogle Scholar
7. Luedtke, W.D. and Landman, U., Phys. Rev. B44, 5970 (1991).CrossRefGoogle Scholar
8. Weeks, J.D. and Gilmer, G.H., Adv. Chem. Phys. 40, 157 (1979);CrossRefGoogle Scholar
Madhukar, A. and Ghaisas, S.V., CRC Crit. Rev. Solid State Mater. Sci. 13, 1434 (1987);Google Scholar
Vvedensky, D.D., Clarke, S., Hugill, K.J., Myers-Beaghton, A.K., and Wilby, M.R., in Kinetics of Ordering and Growth at Surfaces, edited by Lagally, M.G. (Plenum, New York, 1990), pp. 297–311.CrossRefGoogle Scholar
9. Shitara, T., Vvedensky, D.D., Wilby, M.R., Neave, J.H., Zhang, J. and Joyce, B.A. (to be published).Google Scholar
10. For a review, see, e.g., Family, F., Physica A168, 561 (1990).CrossRefGoogle Scholar
11. Villain, J., J. Phys. I (France) 1 19, (1991).CrossRefGoogle Scholar
12. Lai, Z.-W. and Das, S. Sarma, Phys. Rev. Lett. 66, 2348 (1991).CrossRefGoogle Scholar
13. Tan, L.-H. and Nattermann, T., Phys. Rev. Lett. 66, 2899 (1991).CrossRefGoogle Scholar
14. Wolf, D., Phys. Rev. Lett. 67, 1783 (1991).CrossRefGoogle Scholar
15. Mullins, W.W., J. Appl. Phys. 28, 333 (1957).CrossRefGoogle Scholar
16. Gardiner, C.W., Handbook of Stochastic Methods (Springer, Berlin, 1985);Google Scholar
van Kampen, N.G., Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam, 1981).Google Scholar
An earlier application of master equation methods to the SOS model can be found in Saito, Y. and Muller-Krumbhaar, H., J. Chem. Phys. 70, 1078 (1979).CrossRefGoogle Scholar
17. Fox, R.F. and Keizer, J., Phys. Rev. A43, 1709 (1991).CrossRefGoogle Scholar
See also Keizer, J., Statistical Thermodynamics of Nonequilibrium Processes (Springer-Verlag, New York, 1987).CrossRefGoogle Scholar
18. See, e.g., Zangwill, A., Physics at Surfaces (Cambridge University Press, Cambridge, 1988), Chapter 14.CrossRefGoogle Scholar
19. Kardar, M., Parisi, G. and Zhang, Y.-C., Phys. Rev. Lett. 56, 889 (1986).CrossRefGoogle Scholar
20. One readily verifies that a4Vτå = γ(1 — γ) and a4λτå = γ2 although, of course, the numerical values of the critical exponents do not depend on the magnitudes of these coefficients.Google Scholar
21. Sun, T., Guo, H. and Grant, M., Phys. Rev. A40, 6763 (1989).CrossRefGoogle Scholar
22. Burton, W.K., Cabrera, N. and Frank, F.C., Philos. Trans. Roy. Soc. A243, 299 (1951).Google Scholar
23. van Beijeren, H. and Nolden, I., in Structure and Dynamics of Surfaces II, edited by Schommers, W. and von Blanckenhagen, P. (Springer- Verlag, Berlin, 1987), pp. 259–300.CrossRefGoogle Scholar
24. See the contribution of Keefe, Umbach and Blakely to this volume.Google Scholar
25. Vvedensky, D.D. and Clarke, S., Surf. Sci. 225, 373 (1990) and references therein.CrossRefGoogle Scholar
26. Reichl, L.E., A Modern Course in Statistical Physics (University of Texas, Austin, 1980).Google Scholar