Nonuniversality in models of epitaxial growth

Physical Review B - Condensed Matter and Materials Physics

Volumn 53, Issue 20, 1996, Pages 13777-13792

  Kotrla, Miroslav ^a   Šmilauer, Pavel ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000584211     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.53.13777     Document Type: Article

References (65)

1. J. Krug, Adv. Phys. (to be published).
2. T. Halpin-Healy and Y.-C. Zhang, Phys. Rep. 254, 216 (1995).
3. F. Family and T. Vicsek, J. Phys. A 18, L75 (1985).
4. M. Kardar, G. Parisi and Y.-C. Zhang, Phys. Rev. Lett. 56, 889 (1986).
5. J. Villain, J. Phys. (France) I 1, 19 (1991).
6. D.E. Wolf and J. Villain, Europhys. Lett. 13, 389 (1990).
7. S. Das Sarma and P. Tamborenea, Phys. Rev. Lett. 66, 325 (1991).
8. Z.-W. Lai and S. Das Sarma, Phys. Rev. Lett. 66, 2348 (1991).
9. H. Park, A. Provata and S. Redner, J. Phys. A 24, L1391 (1991).
10. M. Kotrla, A.C. Levi and P. Smilauer, Europhys. Lett. 20, 25 (1992).
11. S. Das Sarma and S.V. Ghaisas, Phys. Rev. Lett. 69, 3762 (1992).
12. See, also, M. Plischke, J.D. Shore, M. Schroeder, M. Siegert and D.E. Wolf, Phys. Rev. Lett. 71, 2509 (1993).
13. S. Das Sarma and S.V. Ghaisas, Phys. Rev. Lett. 71, 2510 (1993).
14. J. Krug, M. Plischke and M. Siegert, Phys. Rev. Lett. 70, 3271 (1993).
15. J. Krug, M. Plischke and M. Siegert, Phys. Rev. Lett. 71, 949(E) (1993).
16. M. Schroeder, M. Siegert, D.E. Wolf, J.D. Shore and M. Plischke, Europhys. Lett. 24, 563 (1993).
17. P. Smilauer and M. Kotrla, Phys. Rev. B 49, 5769 (1994).
18. P. Smilauer and M. Kotrla, Europhys. Lett. 27, 261 (1994).
19. M.R. Wilby, D.D. Vvedensky and A. Zangwill, Phys. Rev. B 46, 12t896 (1992).
20. R. Wilby, D.D. Vvedensky and A. Zangwill, Phys. Rev. B 47, 16t068(E) (1993).
21. M. Siegert and M. Plischke, Phys. Rev. Lett. 68, 2035 (1992).
22. M. Siegert and M. Plischke, Phys. Rev. E 50, 917 (1994).
23. M. Kotrla and P. Smilauer, Acta Phys. Slovaca 44, 237 (1994).
24. D.D. Vvedensky, S. Clarke, K.J. Hugill, A.K. Myers-Beaghton, and M.R. Wilby, in Kinetics of Ordering and Growth at Surfaces, edited by M.G. Lagally (Plenum Press, New York, 1990), p. 297.
25. L.-H. Tang and T. Nattermann, Phys. Rev. Lett. 66, 2899 (1991).
26. S.F. Edwards and D.R. Wilkinson, Proc. R. Soc. London Ser. A 381, 17 (1982).
27. J.W. Evans, Phys. Rev. B 43, 3897 (1991).
28. D.D. Vvedensky, A. Zangwill, C.N. Luse, and M.R. Wilby, Phys. Rev. E 48, 852 (1993).
29. G. Ehrlich and F.G. Hudda, J. Chem. Phys. 44, 1039 (1966).
30. R.L. Schwoebel and E.J. Shipsey, J. Appl. Phys. 37, 3682 (1966).
31. W.W. Mullins, J. Appl. Phys. 28, 333 (1957).
32. A direct integration of Eq. (1), with the nonlinear terms ∇(∇h(Formula presented) and (Formula presented)(∇h(Formula presented), gives the EW exponent Β≈1/4 [J.M. Kim and S. Das, Sarma, Phys. Rev. E 51, 1889 (1995)], in agreement with renormalization-group analysis of S. Das Sarma and R. Kotlyar, ibid. 50, R4275 (1994), according to which a Laplacian term appears upon renormalization (cf. also the discussion in Ref. 1).
33. G.H. Gilmer and P. Bennema, J. Appl. Phys. 43, 1347 (1972).
34. J.D. Weeks and G.H. Gilmer, Adv. Chem. Phys. 40, 157 (1979).
35. S. Das Sarma, S.V. Ghaisas and J.M. Kim, Phys. Rev. E 49, 122 (1994).
36. J. Krug, Phys. Rev. Lett. 72, 2907 (1994).
37. Note that unusual scaling of G(r, t), which occurs if ζ>1, was first noted by J.G. Amar, P.-M. Lam and F. Family, Phys. Rev. E 47, 3242 (1993) and H. Leschhorn and L.-H. Tang, Phys. Rev. Lett. 70, 2973 (1993). However, this type of anomalous scaling that appears, e.g., for the linear equation (cf. the paper by Amar et. al), does not lead to anomalous scaling of the structure factor and is thus rather different from the anomalous scaling considered in Refs. 13 and 29 (cf. the discussion in Ref. 1).
38. We used the algorithm for the relaxation of incoming particles that is similar to the one employed earlier in simulations of the FD model, cf. S. Clarke, M.R. Wilby and D.D. Vvedensky, Surf. Sci. 255, 91 (1991). We stress that, in the present paper (Sec. IV), a FD model with random deposition of incoming particles (without any incorporation search) is used.
39. K. Park, B. Kahng and S.S. Kim, Physica A 210, 146 (1994).
40. M. Siegert, Phys. Rev. E (to be published).
41. P. Smilauer, M.R. Wilby and D.D. Vvedensky, Phys. Rev. B 47, 4119 (1993).
42. P. Smilauer, M.R. Wilby and D.D. Vvedensky, Surf. Sci. Lett. 291, L733 (1993).
43. P. Smilauer, M.R. Wilby and D.D. Vvedensky, Phys. Rev. B 48, 4968 (1993).
44. H. Yan, Phys. Rev. Lett. 68, 3048 (1992).
45. D. Kessler, H. Levine and L.M. Sander, Phys. Rev. Lett. 69, 100 (1992).
46. S. Das Sarma, C.J. Lanczycki, S.V. Ghaisas and J.M. Kim, Phys. Rev. B 49, 10t963 (1994).
47. M. Schimschak and J. Krug, Phys. Rev. B 52, 8550 (1995).
48. Y. Kim, D.K. Park and J.M. Kim, J. Phys. A 27, L533 (1994).
49. D. E. Wolf, in Scale Invariance, Interfaces, and Non-Equilibrium Dynamics, edited by A. McKane, M. Droz, J. Vannimenus, and D. Wolf (Plenum, New York, 1995), p. 215.
50. P. Tamborenea and S. Das Sarma, Phys. Rev. E 48, 2575 (1993).
51. T. Shitara, D.D. Vvedensky, M.R. Wilby, J. Zhang, J.H. Neave and B.A. Joyce, Phys. Rev. B 46, 6815 (1992).
52. T. Shitara, D.D. Vvedensky, M.R. Wilby, J. Zhang, J.H. Neave and B.A. Joyce, Phys. Rev. B 46, 6825 (1992).
53. Note that the dependence G(1, t)∝logt has been observed in an experimental study of Si/Si(111) growth [H.-N. Yang, G.-C. Wang, and T.-M. Lu, Phys. Rev. Lett. 73, 2348 (1994)].
54. Z. Rácz, M. Siegert, D. Liu and M. Plischke, Phys. Rev. A 43, 5275 (1991).
55. R. Phillips and D.C. Chrzan, Phys. Rev. Lett. 67, 220 (1991).
56. see, also, M. Plischke and M. Siegert, Phys. Rev. Lett. 68, 2854 (1992).
57. C.J. Lanczycki and S. Das Sarma, Phys. Rev. E 50, 213 (1994).
58. S. Pal and D.P. Landau, Phys. Rev. B 49, 10t597 (1994).
59. For recent reviews of experiments on kinetic roughening see, e.g., the review paper G. Palasantzas and J. Krim, Int. J. Mod. Phys. B 9, 599 (1995), the work of Krug (Ref. 1), or the book of Barabási and Stanley (Ref. 2).
60. G. Ehrlich, Surf. Sci. 331-333, 865 (1995).
61. See, for example, J. Chevrier, V. Le Thanh, R. Buys and J. Derrien, Europhys. Lett. 16, 737 (1991).
62. Y.-L. He, H.-N. Yang, T.-M. Lu and G.-C. Wang, Phys. Rev. Lett. 69, 3770 (1992).
63. G. Palasantzas and J. Krim, Phys. Rev. Lett. 73, 3564 (1994).
64. P. Smilauer and D.D. Vvedensky, Phys. Rev. B 52, 14t263 (1995).
65. M. Siegert and M. Plischke, Phys. Rev. E 53, 307 (1996).