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. B 47, 2289–2300 (1993)

[Issue 4 – 15 January 1993 ]

[ Previous article | Next article | Issue 4 contents ]

Influence of roughness distributions and correlations on x-ray diffraction from superlattices

A. P. Payne and B. M. Clemens

Department of Materials Science and Engineering, Stanford University, Stanford, California 94305-2205

Interfacial roughness in superlattices is currently a topic of significant interest as a result of its impact on device applications and its influence on thin-film phenomena. In this work we examine the effects of interfacial roughness on x-ray diffraction from superlattices. By means of a Taylor expansion of the amplitude reflection coefficient of the multilayer, we present general expressions for the specular, diffuse, and total diffracted intensity from a rough multilayer and examine how these quantities are influenced by roughness distributions and correlations among the interfaces. We present analytical solutions for exemplary structures including superlattices with no roughness, correlated roughness, uncorrelated roughness, and partially correlated roughness. We also present a model for cumulative roughening in multilayers and characterize its diffraction signature. We show how specific configurations of interfacial roughness give rise to a variety of additional features in diffraction spectra beyond the customary pseudo-Debye-Waller attenuation. Specifically, we illustrate how roughness distributions induce broadening of the diffraction features, and how modulations in the diffuse scattering result directly from interfacial roughness correlations. We also show that partial correlation of interfacial roughness constitutes a second important source of peak broadening.

©1993 The American Physical Society

URL: http://link.aps.org/abstract/PRB/v47/p2289
DOI: 10.1103/PhysRevB.47.2289
PACS: 68.35.Bs, 68.65.+g, 78.66.-w, 68.55.Jk

[ Previous article | Next article | Issue 4 contents ]

See Also:

Erratum: A. P. Payne and B. M. Clemens, Erratum: Influence of roughness distributions and correlations on x-ray diffraction from superlattices [Phys. Rev. B 47, 2289 (1993)], Phys. Rev. B 47, 16068 (1993).

References

1. Armin Segmuller, I. C. Noyan and V. S. Speriosu, Prog. Cryst. Growth Charact. 18, 21 (1989) [ INSPEC].
2. B. M. Clemens and J. A. Bain, MRS Bull. 17, 46 (1992) [ INSPEC].
3. H. Homma, K. Y. Yang and I. K. Schuller, Phys. Rev. B 36, 9435 (1987).
4. Chin-An Chang, J. Vac. Sci. Technol. A 9, 98 (1991) [ INSPEC].
5. J. R. Levine, J. B. Cohen, Y. W. Chung and P. Georgopoulos, J. Appl. Crystallogr. 22, 528 (1989) [ INSPEC].
6. E. Vlieg, A. W. Denier van der Gon, J. F. van der Veen, J. E. Macdonald and C. Norris, Phys. Rev. Lett. 61, 2241 (1988).
7. B. M. Clemens, J. Less Common Met. 140, 33 (1988).
8. M. A. Hollanders, B. J. Thijsse and E. J. Mittenmeijer, Phys. Rev. B 42, 5481 (1990).
9. M. B. Stearns, Phys. Rev. B 38, 8109 (1988).
10. W. P. Lowe, T. W. Barbee, Jr., T. H. Geballe and D. B. McWhan, Phys. Rev. B 24, 6193 (1981).
11. E. Spiller, in Physics, Fabrication and Applications of Multilayered Structures, edited by P. Dhez and C. Weisbuch (Plenum, New York, 1988).
12. Eric E. Fullerton, David M. Kelly, J. Guimpel, Ivan K. Schuller and Y. Bruynseraede, Phys. Rev. Lett. 68, 859 (1992).
13. B. M. Clemens and J. G. Gay, Phys. Rev. B 35, 9337 (1987).
14. W. Sevenhans, M. Gijs, Y. Bruynseraede, H. Homma and Ivan K. Schuller, Phys. Rev. B 34, 5955 (1986).
15. D. E. Savage, J. Kleiner, N. Schimke, Y. H. Phang, T. Jankowsky, J. Jacobs, R. Dariotis and M. G. Lagally, J. Appl. Phys. 69, 1411 (1991) [ INSPEC].
16. B. K. Tanner and J. M. Hudson, IEEE Trans. Magn. 28, 2736 (1992) [ INSPEC].
17. John M. Cowley, Diffraction Physics (North-Holland, Amsterdam, 1984).
18. F. J. Lamelas, H. David He and Roy Clarke, Phys. Rev. B 43, 12296 (1991).
19. J. P. Locquet, L. Neerinck, L. Stockman, Y. Bruynseraede and Ivan K. Schuller, Phys. Rev. B 39, 13338 (1989).
20. E. E. Fullerton, I. K. Schuller, H. Vanderstraeten and Y. Bruynseraede, Phys. Rev. B 45, 9292 (1991).
21. W. J. Bartels, J. Hornstra, and D. J. W. Lobeek, Acta Crystallogr. Sect. A 42, 539 (1986).
22. J. H. Underwood, Jr. and T. W. Barbee,, Appl. Opt. 20, 3027 (1981) [ SPIN][ INSPEC].
23. P. Croce, J. Opt. 14, 213 (1983) [ INSPEC].
24. G. V. Rozhnov, J. Opt. 69, 646 (1989).
25. J. M. Eastman, in Physics of Thin Films, Advances in Research and Development, edited by G. Hass and W. R. Hunter (Academic, New York, 1978), Vol. 10.
26. J. M. Elson, J. P. Rahn and J. M. Bennett, Appl. Opt. 19, 669 (1980) [ SPIN][ INSPEC].
27. B. Vidal and P. Vincent, Appl. Opt. 23, 1794 (1984) [ SPIN][ INSPEC].
28. M. Wormington, D. K. Bowen, and B. K. Tanner, in Structure and Properties of Interfaces in Materials, edited by W. A. T. Clark, C. L. Briant, and V. Dahmen, MRS Symposia Proceedings No. 238 (Materials Research Society, Pittsburgh, 1992), p. 119.
29. B. E. Warren, X-Ray Diffraction (Addison-Wesley, Reading, MA, 1969).
30. B. D. Cullity, Elements of X-Ray Diffraction (Addison-Wesley, Reading, MA, 1978).
31. Petr Beckmann and Andre Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (MacMillan, New York, 1963).
32. S. K. Sinha, E. B. Sirota, S. Garhoff and H. B. Stanley, Phys. Rev. B 38, 2297 (1988).
33. A. Bruson, C. Dufour, B. George, M. Vergnat, G. Marchal and Ph. Mangin, Solid State Commun. 71, 1045 (1989) [ INSPEC].
34. J. B. Kortright, J. Appl. Phys. 70, 3620 (1991) [ INSPEC].
35. D. Chrzan and P. Dutta, J. Appl. Phys. 59, 1504 (1985) [ SPIN][ INSPEC].
36. D. E. Savage, N. Schimke, Y. H. Phang and M. G. Lagally, J. Appl. Phys. 71, 3283 (1992) [ INSPEC].
37. Po-zen Wong and Alan J. Bray, J. Mod. Opt. 37, 7751 (1988).
38. D. G. Stearns, J. Appl. Phys. 65, 491 (1989) [ SPIN][ INSPEC].
39. M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics (Wiley, New York, 1991).
40. O. S. Heavens, Optical Properties of Thin Solid Films (University of Michigan, Ann Arbor, MI, 1989).
41. D. G. Stearns, R. S. Rosen and S. P. Vernon, Opt. Lett. 16, 1283 (1991) [ SPIN][ INSPEC].
42. E. Chason, T. M. Mayer, A. Payne and D. Wu, Appl. Phys. Lett. 60, 2353 (1990) [ INSPEC].
43. M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1983).
44. F. E. Christensen, Rev. Phys. Appl. 23, 1701 (1988) [ INSPEC].
45. M. B. Stearns, C. H. Chang and D. G. Stearns, J. Appl. Phys. 71, 187 (1992) [ INSPEC].
46. D. G. Stearns, R. S. Rosen and S. P. Vernon, J. Vac. Sci. Technol. A 9, 2662 (1991) [ INSPEC].

[ Previous article | Next article | Issue 4 contents ]