Ab initio calculations of energies and self-diffusion on flat and stepped surfaces of Al and their implications on crystal growth

Physical Review B - Condensed Matter and Materials Physics

Volumn 53, Issue 8, 1996, Pages 4958-4973

  Stumpf, Roland ^a   Scheffler, Matthias ^a  

^a FRITZ HABER INSTITUT DER MAX PLANCK GESELLSCHAFT   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000684679     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.53.4958     Document Type: Article

References (85)

1. G. Vineyard, J. Phys. Chem. Solids 3, 121 (1957).
2. R. Gomer, Rep. Prog. Phys. 53, 917 (1990).
3. J.tA. Venables, G.tD.tT. Spiller and M. Hanbücken, Rep.tProg. Phys. 47, 815 (1984).
4. J. Villain, J. Phys. (France) I 1, 19 (1991).
5. Z.-W. Lai and S. Das Sarma, Phys.tRev.tLett. 66, 2348 (1991).
6. Z.-W. Lai and S. Das Sarma Hong Yan, Phys.tRev.tLett. 68, 3048 (1992).
7. S. Kenny, M.tR. Wilby, A.tK. Myers-Beaghton and D.tD. Vvedensky, Phys. Rev. B 46, 10t345 (1992).
8. P. Smilauer, M.tR. Wilby and D.tD. Vvedensky, Phys. Rev. B 47, 4119 (1993).
9. K. D. Hammonds and R. M. Lynden-Bell, Surf. Sci. 278, 437 (1992).
10. C.tL. Liu, J.tM. Cohen, J.tB. Adams and A.tF. Voter, Surf. Sci. 253, 334 (1991).
11. C.-L. Liu and J. B. Adams, Surf. Sci. 265, 262 (1992).
12. R.tC. Nelson, T.tL. Einstein, S.tV. Khare and P.tJ. Rous, Surf. Sci. 295, 462 (1993).
13. L.tB. Hansen, P. Stoltze, K.tW. Jacobsen and J.tK. Nørskov, Phys. Rev. B 44, 6523 (1991).
14. L.tB. Hansen, P. Stoltze, K.tW. Jacobsen and J.tK. Nørskov, Surf. Sci. 289, 68 (1993).
15. S. Liu, Z. Zhang, J.tK. Nørskov and H. Metiu, Phys.tRev.tLett. 71, 2967 (1993).
16. M. Villarba and H. Jonsson, Phys. Rev. B 49, 2208 (1994).
17. M. Villarba and H. Jonsson, Surf. Sci. 317, 15 (1994).
18. R.tSmoluchowski, Phys.tRev.t 60, 661 (1941).
19. A. Zangwill, Physics at Surfaces (Cambridge University Press, Cambridge, 1988).
20. W.tE. Pickett, Comput.tPhys.tRep. 9, 117 (1989).
21. M. Scheffler, J. Neugebauer and R. Stumpf, J. Phys. Condens. Matter 5, A91 (1993).
22. R. Stumpf and M. Scheffler, Surf. Sci. 307-309, 501 (1994).
23. R. Stumpf and M. Scheffler, Phys.tRev.tLett.t 72, 254 (1994).
24. M. Klaua and H. Bethge, Ultramicroscopy 17, 73 (1995).
25. H. Bethge, in Kinetics of Ordering and Growth at Surfaces, edited by M. Lagally (Plenum, New York, 1990), p. 125.
26. B. Lang, R. W. Joyner and G. A. Somorjai, Surf. Sci. 30, 440 (1972).
27. M. A. van Hove and G. A. Somorjai, Surf. Sci. 92, 489 (1980).
28. D. R. Eisner and T. L. Einstein, Surf. Sci. 286, L559 (1993).
29. T. Michely and G. Comsa, Surf. Sci. 256, 217 (1991).
30. T. Michely, T. Land, U. Littmark and G. Comsa, Surf. Sci. 272, 204 (1992).
31. M. Bott, T. Michely and G. Comsa, Surf. Sci. 272, 161 (1992).
32. C.-L. Chen and T. T. Tsong, Phys.tRev.tB 47, 15t852 (1993).
33. T. Michely, M. Hohage, M. Bott and G. Comsa, Phys. Rev. Lett. 70, 3943 (1993).
34. S.tC. Wang and G. Ehrlich, Surf. Sci. 239, 301 (1990).
35. S. C. Wang and G. Ehrlich, Phys. Rev. Lett. 67, 2509 (1991).
36. K. Besocke, B. Krahl-Urban and H. Wagner, Surf. Sci. 68, 39 (1977).
37. R. Kunkel, B. Poelsema, L. K. Verheij and G. Comsa, Phys. Rev. Lett. 65, 733 (1990).
38. W.tF. Egelhoff, Jr., and I. Jacob, Phys. Rev. Lett. 62, 921 (1989).
39. B.tJ. Hinch, R.tB. Doak and L.tH. Dubois, Surf. Sci. 286, 261 (1993).
40. S. Oppo, V. Fiorentini and M. Scheffler, Phys. Rev. Lett. 71, 2437 (1993).
41. R. Stumpf and M. Scheffler, Comput. Phys. Commun. 79, 447 (1994).
42. W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965).
43. D.tM. Ceperley and B.tJ. Alder, Phys. Rev. Lett. 45, 566 (1980) as parametrized by J.tP. Perdew and A. Zunger, Phys. Rev. B 23, 5048 (1981).
44. R. Car and M. Parrinello, Phys. Rev. Lett. 55, 2471 (1985).
45. A. Williams and J. Soler, Bull. Am. Phys. Soc. 32, 562 (1987).
46. R. Stumpf, X. Gonze, and M. Scheffler (unpublished).
47. X. Gonze, R. Stumpf and M. Scheffler, Phys. Rev. B 44, 8503 (1991).
48. H.tJ. Monkhorst and J.tD. Pack, Phys. Rev. B 13, 5188 (1976).
49. AIP Handbook, 3rd ed., edited by D. E. Gray (McGraw-Hill, New York, 1987).
50. J. Neugebauer and M. Scheffler, Phys. Rev. B 46, 16t067 (1992).
51. Y.-M. Juan and E. Kaxiras, Phys. Rev. B 48, 14t944 (1993)]. It is widely accepted that adsorption energy differences for different sites are only weakly affected by this problem.
52. J.tS. Nelson and P.tJ. Feibelman, Phys.tRev.tLett. 68, 2188 (1992).
53. P.tJ. Feibelman, Phys. Rev. Lett. 69, 1568 (1992). The adsorption energies given in this paper are not directly comparable to ours (see Ref. 42) because of the reference energy of the isolated atom. Apparently there is an inconsistency of this reference energy caused by Feibelman's Green's-function technique; energy differences are comparable, however, and for these the main (but small) differences to our results arise because Feibelman did not include the adsorbate-induced relaxation of the Alt(331) substrate.
54. S.C. Wang and G. Ehrlich, Phys. Rev. Lett. 70, 41 (1993).
55. "Simple bond-cutting" models assume that the energy per atom varies linearly with the atom's coordination number. An improved version that takes the bond saturation into account makes this approach very similar to the effective-medium and embedded-atom methods [see, for example, I. J Robertson et. al Europhys. Lett. 15, 301 (1991).
56. I. J Robertson et. al Phys. Rev. Lett. 70, 1944 (1993)
57. M. Methfessel et. al Appl. Phys. A 55, 442 (1992)].
58. J. K. Grepstad, P. O. Gartland and B. J. Slasvold, Surf. Sci. 57, 348 (1976).
59. H. Ishida and A. Liebsch, Phys. Rev. B 46, 7153 (1992).
60. A. P. Seitsonen and M. Scheffler (unpublished).
61. C. Stampfl, M. Scheffler and H. Over, Phys. Rev. Lett. 69, 1532 (1992).
62. M. S. Daw and M. I. Baskes, Phys. Rev. B 29, 12 (1984).
63. R. T. Tung and W. R. Graham, Surf. Sci. 97, 73 (1980).
64. G. Ayrault and G. Ehrlich, J. Chem. Phys. 60, 281 (1974).
65. G. L. Kellogg, Surf. Sci. 246, 31 (1991).
66. D. W. Basset and P. R. Webber, Surf. Sci. 70, 520 (1978).
67. S. C. Wang and G. Ehrlich, Phys. Rev. Lett. 62, 2297 (1989).
68. T. T. Tsong and C.-L. Chen, Phys. Rev. B 43, 2007 (1991).
69. T. T. Tsong, Atom-Probe Field Ion Microscopy (Cambridge University Press, Cambridge, 1990).
70. C. Kittel, Introduction to Solid State Physics, 6th ed. (Wiley, New York, 1986).
71. B. Hammer, K. W. Jacobsen, V. Milman and M. C. Payne, J. Phys. Condens. Matter 4, 10t453 (1992).
72. K. W. Jacobsen, J. K. Nørskov and M. J. Puska, Phys. Rev. B 35, 7423 (1987).
73. M. F. Crommie, C. P. Lutz and D. Eigler, Nature 363, 524 (1993).
74. Y. Hasegawa and P. Avouris, Phys. Rev. Lett. 71, 1071 (1993).
75. R. Q. Hwang et. al Phys. Rev. Lett. 67, 3279 (1991).
76. M.tJ. Gillan, J. Phys. Condens. Matter 1, 689 (1989).
77. A. de Vita and M.tJ. Gillan, J. Phys. C 3, 6225 (1991).
78. G. Kresse and J. Haffner, Phys. Rev. B 48, 13t115 (1993).
79. There exists a more elegant way to smear the occupation numbers around the Fermi energy introduced in M. Methfessel and A.tT. Paxton, Phys. Rev. B 40, 3616 (1989). There the total energy is minimized so that the energies and forces do not have to be corrected. We do not use this method in this paper, however.
80. M.tR. Pederson and K.tA. Jackson, Phys.tRev.tB 43, 7312 (1991).
81. K.-M. Ho, J. Ihm and J.tD. Joannopoulos, Phys.tRev. B 25, 4260 (1982).
82. and T.tA. Arias, M.tC. Payne and J.tD. Joannopoulos, Phys.tRev. B 45, 1538 (1992).
83. M.tW. Finnis, J. Phys. Condens. Matter 2, 331 (1990).
84. P.tJ.tFeibelman, Phys.tRev.tLett. 65, 729 (1990).
85. S. Debiaggi and A. Caro, J. Phys. Condens. Matter 4, 3905 (1992).