A Monte Carlo simulation method for {111} surfaces of silicon and other diamond-cubic materials

Surface Science

Volumn 374, Issue 1-3, 1997, Pages 319-332

  Woodraska, Donald L ^a   Jaszczak, John A ^a  

^a MICHIGAN TECHNOLOGICAL UNIVERSITY   (United States)

Author keywords

Computer simulations; Diamond; Etching; Growth; Silicon; Single crystal surfaces; Surface roughening; Surface structure, morphology, roughness and topography

Indexed keywords

COMPUTER SIMULATION; CRYSTAL GROWTH; DIAMONDS; ETCHING; MATHEMATICAL MODELS; MONTE CARLO METHODS; MORPHOLOGY; PHASE EQUILIBRIA; SILICON; SPECIFIC HEAT; SURFACE ROUGHNESS; SURFACE STRUCTURE;

DIAMOND LIKE MATERIALS; STEP ENERGY; SURFACE ROUGHENING;

SURFACES;

EID: 0031101405     PISSN: 00396028     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0039-6028(96)01201-0     Document Type: Article

References (67)

1. R.J. Schutz, in: VLSI Technology, 2nd ed., Ed. S.M. Sze (McGraw-Hill, New York, 1988).
2. R.B. Heimann, in: Silicon Chemical Etching, Ed. J. Grabmaier (Springer, Berlin, 1982); National Research Council, Plasma Processing of Materials: Scientific Opportunities and Technological Challenges (National Academy Press, Washington, 1991).
3. R.B. Heimann, in: Silicon Chemical Etching, Ed. J. Grabmaier (Springer, Berlin, 1982); National Research Council, Plasma Processing of Materials: Scientific Opportunities and Technological Challenges (National Academy Press, Washington, 1991).
4. J.L. Davidson, in: Synthetic Diamond: Emerging CVD Science and Technology, Eds. K.E. Spear and J.P. Dismukes (Wiley, New York, 1994) p. 355; M.W. Geis, J.A. Gregory and B.B. Pate, IEEE Trans. Electron Dev. 38 (1991) 619.
5. J.L. Davidson, in: Synthetic Diamond: Emerging CVD Science and Technology, Eds. K.E. Spear and J.P. Dismukes (Wiley, New York, 1994) p. 355; M.W. Geis, J.A. Gregory and B.B. Pate, IEEE Trans. Electron Dev. 38 (1991) 619.
6. P. Boguslawski, Q.-M. Zhang, Z. Zhang and J. Bernholc, Phys. Rev. Lett. 72 (1994) 3694; Q.-M. Zhang, C. Roland, P. Boguslawski and J. Bernholc, Phys. Rev. Lett. 75 (1995) 101.
7. P. Boguslawski, Q.-M. Zhang, Z. Zhang and J. Bernholc, Phys. Rev. Lett. 72 (1994) 3694; Q.-M. Zhang, C. Roland, P. Boguslawski and J. Bernholc, Phys. Rev. Lett. 75 (1995) 101.
8. M. Seel and P. Bagus, Phys. Rev. B 28 (1983) 2023.
9. P.C. Weakliem, C.J. Wu and E.A. Carter, Phys. Rev. Lett. 69 (1992) 200; L.E. Carter and E.A. Carter Surf. Sci. 323 (1995) 39.
10. P.C. Weakliem, C.J. Wu and E.A. Carter, Phys. Rev. Lett. 69 (1992) 200; L.E. Carter and E.A. Carter Surf. Sci. 323 (1995) 39.
11. M.E. Barone and D.B. Graves, J. Appl. Phys. 77 (1995) 1263; B.A. Helmer, D.B. Graves and M.E. Barone, in: Modeling and Simulation of Thin-Film Processing, Ed. D.J. Srolovitz, C.A. Volkert, M.J. Fluss and R.J. Kee, MRS Symp. Proc. 389 (Materials Research Society, Pittsburgh, 1995) p. 23.
12. M.E. Barone and D.B. Graves, J. Appl. Phys. 77 (1995) 1263; B.A. Helmer, D.B. Graves and M.E. Barone, in: Modeling and Simulation of Thin-Film Processing, Ed. D.J. Srolovitz, C.A. Volkert, M.J. Fluss and R.J. Kee, MRS Symp. Proc. 389 (Materials Research Society, Pittsburgh, 1995) p. 23.
13. S.D. Athavale and D.J. Economou, J. Vac. Sci. Technol. A 13 (1995) 966.
14. For reviews, see: H. Müller-Krumbhaar, in: Monte Carlo Methods in Statistical Physics, Ed. K. Binder (Springer, Berlin, 1986) p. 261; J.D. Weeks and G.H. Gilmer, Adv. Chem. Phys. 40 (1979) 157; J.P. van der Eerden and P. Bennema, Prog. Cryst. Growth Charact. 1 (1978) 219.
15. For reviews, see: H. Müller-Krumbhaar, in: Monte Carlo Methods in Statistical Physics, Ed. K. Binder (Springer, Berlin, 1986) p. 261; J.D. Weeks and G.H. Gilmer, Adv. Chem. Phys. 40 (1979) 157; J.P. van der Eerden and P. Bennema, Prog. Cryst. Growth Charact. 1 (1978) 219.
16. For reviews, see: H. Müller-Krumbhaar, in: Monte Carlo Methods in Statistical Physics, Ed. K. Binder (Springer, Berlin, 1986) p. 261; J.D. Weeks and G.H. Gilmer, Adv. Chem. Phys. 40 (1979) 157; J.P. van der Eerden and P. Bennema, Prog. Cryst. Growth Charact. 1 (1978) 219.
17. D.L. Woodraska, J. LaCosse and J.A. Jaszczak, in: Modeling and Simulation of Thin-Film Processing, Eds. D.J. Srolovitz, C.A. Volkert, M.J. Fluss and R.J. Kee, MRS Symp. Proc. 389 (Materials Research Society, Pittsburgh, 1995) p. 209.
18. S. Clarke and D.D. Vvedensky, Phys. Rev. B 37 (1988) 6559; S. Clarke, M.R. Wilby, D.D. Vvedensky and T. Kawamura, Thin Solid Films 183 (1989) 221; Phys. Rev. B 40 (1989) 1369; D.D. Vvedensky and S. Clarke, Surf. Sci. 225 (1990) 373; N. Haider, M. Wilby and D.D. Vvedensky J. Cryst. Growth 127 (1993) 922.
19. S. Clarke and D.D. Vvedensky, Phys. Rev. B 37 (1988) 6559; S. Clarke, M.R. Wilby, D.D. Vvedensky and T. Kawamura, Thin Solid Films 183 (1989) 221; Phys. Rev. B 40 (1989) 1369; D.D. Vvedensky and S. Clarke, Surf. Sci. 225 (1990) 373; N. Haider, M. Wilby and D.D. Vvedensky J. Cryst. Growth 127 (1993) 922.
20. S. Clarke and D.D. Vvedensky, Phys. Rev. B 37 (1988) 6559; S. Clarke, M.R. Wilby, D.D. Vvedensky and T. Kawamura, Thin Solid Films 183 (1989) 221; Phys. Rev. B 40 (1989) 1369; D.D. Vvedensky and S. Clarke, Surf. Sci. 225 (1990) 373; N. Haider, M. Wilby and D.D. Vvedensky J. Cryst. Growth 127 (1993) 922.
21. S. Clarke and D.D. Vvedensky, Phys. Rev. B 37 (1988) 6559; S. Clarke, M.R. Wilby, D.D. Vvedensky and T. Kawamura, Thin Solid Films 183 (1989) 221; Phys. Rev. B 40 (1989) 1369; D.D. Vvedensky and S. Clarke, Surf. Sci. 225 (1990) 373; N. Haider, M. Wilby and D.D. Vvedensky J. Cryst. Growth 127 (1993) 922.
22. S. Clarke and D.D. Vvedensky, Phys. Rev. B 37 (1988) 6559; S. Clarke, M.R. Wilby, D.D. Vvedensky and T. Kawamura, Thin Solid Films 183 (1989) 221; Phys. Rev. B 40 (1989) 1369; D.D. Vvedensky and S. Clarke, Surf. Sci. 225 (1990) 373; N. Haider, M. Wilby and D.D. Vvedensky J. Cryst. Growth 127 (1993) 922.
23. S.A. Barnett and A. Rockett, Surf. Sci. 198 (1988) 133.
24. M.I. Larsson and G.V. Hansson, Jpn. J. Appl. Phys. 33 (1994) 2282; M.I. Larsson, W.-X. Ni and G.V. Hansson, J. Appl. Phys. 78 (1995) 3792.
25. M.I. Larsson and G.V. Hansson, Jpn. J. Appl. Phys. 33 (1994) 2282; M.I. Larsson, W.-X. Ni and G.V. Hansson, J. Appl. Phys. 78 (1995) 3792.
26. T. Yokotsuka, M.R. Wilby, D.D. Vvedensky, T. Kawamura, K. Fukutani and S. Ino, Appl. Phys. Lett. 62 (1993) 1673.
27. W.J.P. van Enckevort and J.P. van der Eerden, J. Cryst. Growth 47 (1979) 501.
28. A.K. Tan, C.K. Ong and H.S. Tan, Semicon. Sci. Technol. 3 (1988) 1.
29. J.A. Jaszczak, W.F. Saam and B. Yang, Phys. Rev. B 39 (1989) 9289.
30. J.A. Jaszczak, W.F. Saam and B. Yang, Phys. Rev. B 41 (1990) 6864.
31. T.L. Hill, Statistical Mechanics (McGraw-Hill, New York 1956).
32. W.H. Press, S.A. Teukolsky, W.T. Vetterling and B.P. Flannery, in: Numerical Recipes in Fortran: The Art of Scientific Computing, 2nd ed. (Cambridge University Press, Cambridge, 1992) p. 271.
33. M.P. Allen and D.J. Tildesley, in: Computer Simulation of Liquids (Clarendon, Oxford, 1987) p. 192.
34. K. Rommelse and M. den Nijs, Phys. Rev. Lett. 59 (1987) 2578.
35. M. den Nijs and K. Rommelse, Phys. Rev. B 40 (1989) 4709.
36. M. den Nijs, Phys. Rev. Lett. 64 (1990) 435.
37. M. den Nijs, Phys. Rev. B 46 (1992) 10386.
38. P.J.M. Bastiaansen and H.J.F. Knops, Phys. Rev. B 53 (1996) 126.
39. G. Mazzeo, G. Jug, A.C. Levi and E. Tosatti, Phys. Rev. B 49 (1994) 7625.
40. S. Prestipino, G. Santoro and E. Tosatti, Phys. Rev. Lett. 75 (1995) 4468.
41. P.B. Weichman and A. Prasad, Phys. Rev. Lett. 76 (1996) 2322.
42. See, for example, M. Wortis, in: Chemistry and Physics of Solid Surfaces VII, Eds. R. Vanselow and R. Howe (Springer, Berlin, 1988) p. 367.
43. See, for example, P. Bak and M. Paczuski, in: The Chemical Physics of Solid Surfaces, Vol. 7, Eds. D.A. King and D.P. Woodruff (Elsevier, New York, 1994) p. 1.
44. E.H. Conrad, Prog. Surf. Sci. 39 (1992) 65; J.W. Frenken and H.M. van Pinxteren, in: The Chemical Physics of Solid Surfaces, Vol. 7, Eds. D.A. King and D.P. Woodruff (Elsevier, New York, 1994) p. 259.
45. E.H. Conrad, Prog. Surf. Sci. 39 (1992) 65; J.W. Frenken and H.M. van Pinxteren, in: The Chemical Physics of Solid Surfaces, Vol. 7, Eds. D.A. King and D.P. Woodruff (Elsevier, New York, 1994) p. 259.
46. H. van Beijeren, Phys. Rev. Lett. 38 (1977) 993.
47. R.H. Swendsen, Phys. Rev. B 17 (1978) 3710.
48. J.P. van der Eerden and H.J.F. Knops, Phys. Lett. 66A, 334 (1978)
49. W.J. Shugard, J.D. Weeks and G.H. Gilmer, Phys. Rev. Lett. 41 (1978) 1399.
50. R.H. Swendsen, Phys. Rev. B 15 (1977) 5421.
51. Such behavior, termed pseudoroughening, was anticipated in footnote 23 of Ref. [17].
52. H.E. Hessel, A. Feltz, M. Reiter, U. Memmert and R.J. Behm, Chem. Phys. Lett. 186 (1991) 275.
53. R.J. Pechman, X.-S. Wang and J.H. Weaver. Phys. Rev. B 52 (1995) 11412.
54. P. Nozières and F. Gallet, J. Phys. (Paris) 48 (1987) 353; J.W. Cahn, Acta Metall. 8 (1960) 554.
55. P. Nozières and F. Gallet, J. Phys. (Paris) 48 (1987) 353; J.W. Cahn, Acta Metall. 8 (1960) 554.
56. For a recent review see J.P. van der Eerden, in: Handbook of Crystal Growth 1: Fundamentals, Ed. D.T.J. Hurle (Elsevier, Amsterdam, 1993) p. 307.
57. E. Sirtl and A. Adler, Z. Metallic. 52 (1961) 529.
58. A.V. Pakhomov and E.M. Nadgorny, Bull. Am. Phys. Soc. 39(1) (1994) 930.
59. F.C. Frank, K.E. Puttick and E.M. Wilks, Phil. Mag. 3 (series 8) (1958) 1262; F.C. Frank and K.E. Puttick, Phil. Mag. 3 (series 8) (1958) 1273.
60. F.C. Frank, K.E. Puttick and E.M. Wilks, Phil. Mag. 3 (series 8) (1958) 1262; F.C. Frank and K.E. Puttick, Phil. Mag. 3 (series 8) (1958) 1273.
61. Y.L. Orlov, in: The Mineralogy of the Diamond (Wiley, New York, 1973) pp. 82-87.
62. D.N. Robinson, J.A. Scott, A. Van Niekerk and V.G. Anderson, in: Kimberlites and Related Rocks, Vol. 2, Eds. J. Ross et al., GSA Special Publication No. 14 (Blackwell Scientific, Cambridge, MA, 1989) p. 990.
63. See, for example, M.S. Duesbery and G.Y. Richardson, Solid State Mater. Sci. 17 (1991) 1.
64. A.S. Nandedkar and J. Narayan, Phil. Mag. A 61 (1990) 873.
65. G.H. Gilmer, J. Cryst. Growth 35 (1976) 15; 42 (1977) 3.
66. G.H. Gilmer, J. Cryst. Growth 35 (1976) 15; 42 (1977) 3.
67. R.H. Swendsen, P.J. Kortman, D.P. Landau and H. Müller-Krumbhaar, J. Cryst. Growth 35 (1976) 73.