Unified view of step-edge kinetics and fluctuations

Physical Review B - Condensed Matter and Materials Physics

Volumn 57, Issue 8, 1998, Pages 4782-4797

  Khare, S ^a   Einstein, T ^b  

^a OHIO STATE UNIVERSITY   (United States)

^b University of Maryland   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001232154     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.57.4782     Document Type: Article

References (61)

1. L. Kuipers, M. S. Hoogeman, and J. W. M. Frenken, Phys. Rev. Lett. 71, 3517 (1993).
2. L. Kuipers, M. S. Hoogeman, J. W. M. Frenken, and H. van Beijeren, Phys. Rev. B 52, 11 387 (1995).
3. N. C. Bartelt, J. L. Goldberg, T. L. Einstein, E. D. Williams, J. C. Heyraud, and J. J. Métois, Phys. Rev. B 48, 15 453 (1993).
4. C. Alfonso, J. M. Bermond, J. C. Heyraud, and J. J. Métois, Surf. Sci. 262, 37 (1992).
5. N. C. Bartelt, R. M. Tromp, and E. D. Williams, Phys. Rev. Lett. 73, 1656 (1994).
6. N. C. Bartelt and R. M. Tromp, Phys. Rev. B 54, 11 731 (1996).
7. Phys. Rev. BN. C. Bartelt, W. Theis, and R. M. Tromp, 54, 11 741 (1996).
8. S. Tanaka, N. C. Bartelt, C. C. Umbach, R. M. Tromp, and J. M. Blakely, Phys. Rev. Lett. 78, 3342 (1997).
9. M. Poensgen, J. F. Wolf, J. Frohn, M. Giesen, and H. Ibach, Surf. Sci. 274, 430 (1992).
10. M. Giesen-Seibert, R. Jentjens, M. Poensgen, and H. Ibach, Phys. Rev. Lett. 71, 3521 (1993).
11. Phys. Rev. Lett.M. Giesen-SeibertR. JentjensM. PoensgenH. Ibach73, E911 (1994).
12. M. Giesen-Seibert and H. Ibach, Surf. Sci. 316, 205 (1994).
13. Surf. Sci.M. Giesen-Seibert, F. Schmitz, R. Jentjens, and H. Ibach, 329, 47 (1995).
14. M. Giesen, G. S. Icking-Konert, D. Stapel, and H. Ibach, Surf. Sci. 366, 229 (1996).
15. L. Barbier, L. Masson, J. Cousty, and B. Salanon, Surf. Sci. 354, 197 (1996).
16. L. Masson, L. Barbier, J. Cousty, and B. Salanon, Surf. Sci. 317, L1115 (1994).
17. Surf. Sci.L. MassonL. BarbierJ. CoustyB. Salanon324, L378 (1995).
18. W. W. Pai, N. C. Bartelt, and J. E. Reutt-Robey, Phys. Rev. B 53, 15 991 (1996).
19. Phys. Rev. BW. W. Pai and J. E. Reutt-Robey, 53, 15 997 (1996).
20. P. Wang, H. Pfnür, S. V. Khare, T. L. Einstein, E. D. Williams, W. W. Pai, and J. Reutt-Robey, Bull. Am. Phys. Soc. 41, 189 (1996); (unpublished).
21. C. Pearson, B. Borovsky, M. Krueger, R. Curtis, and E. Ganz, Phys. Rev. Lett. 74, 2710 (1995).
22. B. S. Swartzentruber and M. Schacht, Surf. Sci. 322, 83 (1995).
23. W. W. Mullins, in Metal Surfaces: Structure, Energetics and Kinetics, edited by N. A. Gjostein and R. W. Roberts (American Society of Metals, Metals Park, Ohio, 1963), p. 17.
24. W. W. Mullins, J. Appl. Phys. 28, 333 (1957).
25. J. Appl. Phys.W. W. Mullins36, 77 (1959).
26. N. C. Bartelt, J. L. Goldberg, T. L. Einstein, and E. D. Williams, Surf. Sci. 273, 252 (1992).
27. N. C. Bartelt, T. L. Einstein, and E. D. Williams, Surf. Sci. 312, 411 (1994).
28. A. Pimpinelli, J. Villain, D. E. Wolf, J. J. Métois, J. C. Heyraud, I. Elkinani, and G. Uimin, Surf. Sci. 295, 143 (1993).
29. J. W. Cahn and J. E. Taylor. Acta Metall. Mater. 42, 1045 (1994).
30. H. P. Bonzel and W. W. Mullins, Surf. Sci. 350, 285 (1996).
31. F. Liu and H. Metiu, Phys. Rev. E 49, 2601 (1994).
32. C. Herring, in The Physics of Powder Metallurgy, edited by W. Kingston (McGraw-Hill, New York, 1951).
33. C. Herring, J. Appl. Phys. 21, 437 (1950).
34. C. Herring, in Structure and Properties of Solid Surfaces, edited by R. Gomer and C. S. Smith (University of Chicago Press, Chicago, 1952).
35. P. Nozières, in Solids Far From Equilibrium, edited by C. Godrèche (Cambridge University Press, Cambridge, 1992), p. 1.
36. G. S. Bales and A. Zangwill, Phys. Rev. B 41, 5500 (1990).
37. A. A. Chernov, Modern Crystallography III (Springer-Verlag, Berlin, 1984).
38. A. M. Meirmanov, The Stefan Problem (W. de Gruyter, Berlin, 1992).
39. L. I. Rubenstein, The Stefan Problem (American Mathematical Society, Providence, Rhode Island, 1971).
40. O. Pierre-Louis, Ph.D. thesis, Université J. Fourier-Grenoble 1, 1997 (unpublished);O. Pierre-Louis and C. Misbah (unpublished).
41. S. V. Khare, N. C. Bartelt, and T. L. Einstein, Phys. Rev. Lett. 75, 2148 (1995).
42. S. V. Khare and T. L. Einstein, Phys. Rev. B 54, 11 752 (1996). See also Appendix D for comments on the notation used in this paper.
43. M. Kardar, J. Phys. I 18, 221 (1994).
44. J. Villain, J. Phys. I 1, 19 (1991).
45. R. L. Schwoebel and E. J. Shipsey, J. Appl. Phys. 37, 3682 (1966).
46. G. Ehrlich and F. Hudda, J. Chem. Phys. 44, 1039 (1966).
47. R. L. Schwoebel, J. Appl. Phys. 40, 614 (1969).
48. D. Kandel, Phys. Rev. Lett. 78, 499 (1997) and private communication. Specifically, from his Eq. (6-i) it follows that our kinetic coefficient (Formula presented), where (Formula presented) is the attachment/detachment factor from the step edge and (Formula presented) is the extra barrier (above the normal diffusion barrier on the terrace) associated with the appropriate side of the step edge. (The prefactor of (Formula presented) is assumed to be the same as that of (Formula presented).) Then it quickly follows that (Formula presented). For (Formula presented), (Formula presented), where (Formula presented) but in general there is no simple connection between (Formula presented) and (Formula presented). In fact, in the limit of high temperature, (Formula presented) In Fig. 5 of Ref. 23, (Formula presented) and (Formula presented) are labeled (Formula presented) and (Formula presented) respectively.
49. P. C. Hohenberg and B. I. Halperin, Rev. Mod. Phys. 49, 435 (1977).
50. W. W. Pai, A. K. Swan, Z. Zhang, and J. F. Wendelken, Phys. Rev. Lett. 79, 3210 (1997). In these systems there is evidence that the dominant transport mechanism is step-edge diffusion. In our perspective, the experiment would seem to lie in the crossover region at the bottom of Fig. 3 of Ref. 33 between EC and PD behavior.
51. K. Morgenstern, G. Rosenfeld, B. Poelsema, and G. Comsa, Phys. Rev. Lett. 74, 2058 (1995).
52. U. Kürpick, P. Kürpick, and T. S. Rahman, Surf. Sci. 383, L713 (1997).
53. P. M. Duxbury (private communication);B. Blagojević and P. M. Duxbury (unpublished).
54. Handbook of Mathematical Functions, edited by M. Abramowitz and I. A. Stegun (Dover Publications Inc., New York, 1972).
55. W. Feller, An Introduction to Probability Theory and Its Applications (Wiley, New York, 1968), Vol. 1, pp. 446-448.
56. J. B. Hannon, C. Klünker, M. Giesen, H. Ibach, N. C. Bartelt, and J. C. Hamilton, Phys. Rev. Lett. 79, 2506 (1997).
57. M. Ozdemir and A. Zangwill, Phys. Rev. B 45, 3718 (1992).
58. E. S. Fu, D.-J. Liu, M. D. Johnson, J. D. Weeks, and E. D. Williams, Surf. Sci. 385, 259 (1997).
59. O. Pierre-Louis and C. Misbah, Phys. Rev. Lett. 76, 4761 (1996).
60. D. Kandel and J. D. Weeks, Phys. Rev. B 52, 2154 (1995).
61. T. L. Einstein and S. V. Khare, in Dynamics of Crystal Surface and Interfaces, edited by P. M. Duxbury and T. Pence (Plenum, New York, 1997), p. 83.