Phys. Rev. Lett. Phys. Rev. A Phys. Rev. B Phys. Rev. C Phys. Rev. D Phys. Rev. E Phys. Rev. ST AB Rev. Mod. Phys. Phys. Rev. (Series I) Phys. Rev. Volume: Page/Article:

Phys. Rev. E 50, 3370–3382 (1994)

[Issue 5 – November 1994 ]

[ Previous article | Next article | Issue 5 contents ]

Dynamics of interfaces in a model for molecular-beam epitaxy

Tao Sun and Michael Plischke

Department of Physics, Simon Fraser University, Burnaby, British Columbia, Canada V5A||1S6

The dynamics of driven interfaces in a continuum model of growth by molecular-beam epitaxy has been studied by means of the Nozières-Gallet dynamic renormalization group technique. Relaxation of the growing film is due to both surface tension and surface diffusion. In 1+1 dimensions, three growth regimes have been found. The first is a linearly stable state with a positive surface tension, which can be described by the Edwards-Wilkinson equation. The second is a purely diffusive state with a dynamic exponent z, different from that given by the Wolf-Villain linear theory. The last is a linearly unstable growth state in which the creation of large slopes in the interface configuration is expected. In 2+1 dimensions, which is the critical dimension of the model, the purely diffusive regime is absent at the one loop order. However, the other two growth regimes are still present. The scaling properties of the growth states are discussed in detail.

©1994 The American Physical Society

URL: http://link.aps.org/abstract/PRE/v50/p3370
DOI: 10.1103/PhysRevE.50.3370
PACS: 05.40.+j, 68.55.Bd, 68.35.Fx

[ Previous article | Next article | Issue 5 contents ]

References

1. K. L. Chopra, Thin Film Phenomena (McGraw Hill, New York, 1969).
2. D. Henderson, M. H. Brodsky and P. Chaudhari, Appl. Phys. Lett. 25, 641 (1974) [ INSPEC].
3. H. J. Leamy and A. G. Dirks, J. Appl. Phys. 49, 3430 (1978) [ SPIN][ INSPEC].
4. H. J. Leamy, G. H. Gilmer, and A. G. Dirks, in Current Topics in Materials Science, edited by E. Kaldis (North Holland, Amsterdam, 1980), Vol. 6.
5. T. Vicsek, Fractal Growth Phenomena (World Scientific, Singapore, 1989).
6. F. Family and T. Vicsek, Dynamics of Fractal Surfaces (World Scientific, Singapore, 1991).
7. F. Family, Physica A 168, 561 (1990) [ INSPEC].
8. Molecular Beam Epitaxy 1990, edited by C. W. Tu and J. S. Harris, Jr. (North Holland, Amsterdam, 1991).
9. Solids Far From Equilibrium, edited by C. Godréche (Cambridge University Press, Cambridge, 1991).
10. Surface Disordering: Growth, Roughening and Phase Transitions, edited by R. Jullien, J. Kertész, P. Meakin, and D. E. Wolf (Nova Science, Commack, NY, 1992).
11. M. Kardar, G. Parisi and Y. C. Zhang, Phys. Rev. Lett. 56, 889 (1986) [SPIRES]; E. Medina, T. Hwa, M. Kardar and Y. C. Zhang, Phys. Rev. A 39, 3053 (1989).
12. T. Sun, H. Guo and M. Grant, Phys. Rev. A 40, 6763 (1989); A. Chakrabarti, J. Phys. A 23, L919 (1990) [ INSPEC]; Z. Ràcz, M. Siegert, D. Liu and M. Plischke, Phys. Rev. A 43, 5275 (1991).
13. Z. W. Lai and S. Das Sarma, Phys. Rev. Lett. 66, 2348 (1991).
14. J. Villain, J. Phys. I (France) 1, 19 (1991) [ INSPEC].
15. S. Das Sarma and P. Tamborenea, Phys. Rev. Lett. 66, 325 (1991).
16. A. Mazor, D. J. Srolovitz, P. S. Hagan and B. G. Bukiet, Phys. Rev. Lett. 60, 424 (1988).
17. S. Das Sarma and S. V. Ghaisas, Phys. Rev. Lett. 69, 3762 (1992).
18. L. Golubovic and R. P. U. Karunasiri, Phys. Rev. Lett. 66, 3156 (1991).
19. M. Siegert and M. Plischke, Phys. Rev. Lett. 68, 2035 (1992); J. Phys. I (France) 3, 1371 (1993) [ INSPEC].
20. J. Krug, M. Plischke and M. Siegert, Phys. Rev. Lett. 70, 3271 (1993).
21. M. Plischke, J. D. Shore, M. Schroeder, M. Siegert and D. E. Wolf, Phys. Rev. Lett. 71, 2509 (1993).
22. M. Siegert and M. Plischke, Phys. Rev. E 50, 917 (1994).
23. W. W. Mullins, J. Appl. Phys. 28, 333 (1957).
24. S. F. Edwards and D. R. Wilkinson, Proc. R. Soc. London, Ser. A 381, 17 (1982) [ INSPEC].
25. D. E. Wolf and J. Villain, Europhys. Lett. 13, 389 (1990) [ INSPEC].
26. T. Sun and M. Plischke, Phys. Rev. Lett. 71, 3174 (1993).
27. M. Grant, Phys. Rev. B 37, 5705 (1988).
28. A. Maritan, F. Toigo, J. Koplik and J. R. Banavar, Phys. Rev. Lett. 69, 3193 (1992).
29. P. Nozières and F. Gallet, J. Phys. (Paris) 48, 353 (1987) [ INSPEC].
30. F. Gallet, S. Balibar and E. Rolley, J. Phys. (Paris) 48, 369 (1987) [ INSPEC].
31. S. K. Ma, Modern Theory of Critical Phenomena (Addison Wesley, Reading, MA, 1976).
32. B. I. Halperin, P. C. Hohenberg and S. K. Ma, Phys. Rev. Lett. 29, 1548 (1972).
33. In some cases where the one loop calculation is not adequate, one must use field theory renormalization group method. The KPZ equation in 2+1 dimensions is an example, see T. Sun and M. Plischke, Phys. Rev. E 49, 5046 (1994).
34. P. C. Martin, E. D. Siggia and H. A. Rose, Phys. Rev. A 8, 423 (1973).
35. D. Forster, D. R. Nelson and M. J. Stephen, Phys. Rev. A 16, 732 (1977).
36. T. Hwa, M. Kardar and M. Paczuski, Phys. Rev. Lett. 66, 441 (1991).
37. Y. C. Tsai and Y. Shapir, Phys. Rev. Lett. 69, 1773 (1992) [SPIRES].
38. We have discussed the dynamic roughening using the generalized NG method, see T. Sun, B. Morin, H. Guo, and M. Grant, in Surface Disordering: Growth, Roughening and Phase Transitions ( Ref. 10), p. 45; and (to be published).
39. In some cases one needs a smooth cutoff, see, Modern Theory of Critical Phenomena ( Ref. 31), p. 215; and also see Ref. 38.
40. If we do include these terms in the calculation (even though this complicates the algebra substantially, it still can be done in the 1+1 case, but appears to be barely feasible in the 2+1 case), we find that the physics is not changed. That is, no new stable fixed point is found.
41. A negative kappa corresponds to a locally unstable situation, which would be unphysical.
42. M. Siegert and M. Plischke, Phys. Rev. Lett. 73, 1517 (1994). .

[ Previous article | Next article | Issue 5 contents ]