Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-16T01:19:15.183Z Has data issue: false hasContentIssue false
  • English
  • Français

Faceting of Stepped Silicon (113) Surfaces: Step Unbinding, Dynamic Scaling, and Nano-Scale Grooves

Published online by Cambridge University Press:  15 February 2011

S. G. J. Mochrie ,
S. Song  and
Mirang Yoon
S. G. J. Mochrie
Affiliation:
Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139
S. Song
Affiliation:
Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139
Mirang Yoon
Affiliation:
Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139
Get access

Abstract

X-ray scattering studies are reviewed of the faceting kinetics of stepped silicon (113) surfaces misoriented towards [001]. Following a quench from the one-phase region of the orientational phase diagram into the coexistence region, initially-uniformly-distributed steps rearrange to form a grooved superstructure. Our measurements reveal the behavior of the grooved surface morphology as a function of time. The surface is found to be self-similar in time, with a characteristic groove size (L) varying as a power-law versus time (t): L = L0tøwith a coarsening exponent of ø = 0.164 ± 0.021 ≃ 1/6, consistent with a theory for the kinetics of faceting which focuses on thermally fluctuating step bunches and their collisions. At later times, the groove size approaches a limiting value which depends on the stepped phase misorientation angle, as expected for faceted surfaces in the case that elastic effects are important.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 440: Symposia CA – Structure and Evolution of Surfaces , 1996 , 3
Copyright
Copyright © Materials Research Society 1997

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Herring, C., Phys. Rev. 82, 87 (1951).Google Scholar
[2] Andreev, A. F., Zh. Eksp. Teor. Fiz. 80, 2042 (1981), [Sov. Phys.–JETP 53, 1063 (1982)].Google Scholar
[3] Rottman, C. and Wortis, M., Phys. Rev. B 29, 328 (1984).Google Scholar
[4] Phaneuf, R. J. and Williams, E. D., Phys. Rev. Lett. 58, 2563 (1987).Google Scholar
[5] Williams, E. D. and Bartelt, N. C., Science 251, 393 (1991).Google Scholar
[6] Watson, G. M., Gibbs, D., Zehner, D. M., Yoon, M., and Mochrie, S. G. J., Phys. Rev. Lett. 71, 3166 (1993).Google Scholar
[7] Yoon, M., Mochrie, S. G. J., Zehner, D. M., Watson, G. M., and Gibbs, D., Phys. Rev. B 49, 16702 (1994).Google Scholar
[8] Song, S. and Mochrie, S. G. J., Phys. Rev. Lett. 73, 995 (1994).Google Scholar
[9] Song, S. and Mochrie, S. G. J., Phys. Rev. B 51, 10068 (1995).Google Scholar
[10] Watson, G., Gibbs, D., Zehner, D. M., Song, S., Sandy, A. R., and Mochrie, S. G. J., Phys. Rev. B 52, 12329 (1995).Google Scholar
[11] Ozcomert, J. S., Pai, W. W., Bartelt, N. C., and Reutt-Robey, J. E., Phys. Rev. Lett. 72, 258 (1994).Google Scholar
[12] Noh, D. Y, Blum, K. I., Ramstad, M. J., and Birgeneau, R. J., Phys. Rev. B 48, 1612 (1993).Google Scholar
[13] Song, S., Yoon, M., and Mochrie, S. G. J., Surf. Sci. 334, 153 (1995).Google Scholar
[14] Suzuki, T., Tanishiro, Y., Minoda, H., Yagi, K., and Suzuki, M., Surf. Sci. 298, 473 (1993).Google Scholar
[15] Baski, A. A., Erwin, S. C., and Whitman, L. J., Science 269, 1556 (1995).Google Scholar
[16] Kasu, M. and Kobayashi, N., Appl. Phys. Lett. 62, 1262 (1993).Google Scholar
[17] Ledentsov, N. N., Gur'yanov, G. M., Tsyrlin, G. E., Petrov, V. N., Samsonenko, Y. B., Golubok, A. O., and Tipisev, S. Y., Fiz. Tekh. Poluprovodn. 28, 903 (1994), semiconductors 28, 526 (1994).Google Scholar
[18] Koch, R., Borbonus, M., Haase, O., and Rieder, K. H., Phys. Rev. Lett. 67, 3416 (1991).Google Scholar
[19] Zuo, J., Warmack, R. J., Zehner, D. M., and Wendelken, J. F., Phys. Rev. B 47, 10743 (1993).Google Scholar
[20] Baski, A. A. and Whitman, L. J., Phys. Rev. Lett. 74, 956 (1995).Google Scholar
[21] Heffelfinger, J. R., Bench, M. W., and Carter, C. B., Surf. Sci. 343, L1161 (1995).Google Scholar
[22] Notzel, R., Ledentsov, N. N., Ploog, L. D. K., and Hohenstein, M., Phys. Rev. B 45, 3507 (1992).Google Scholar
[23] Jayaprakash, C. and Saam, W. F., Phys. Rev. B 30, 3916 (1984).Google Scholar
[24] Jayaprakash, C., Rottman, C., and Saam, W. F., Phys. Rev. B 30, 6549 (1984).Google Scholar
[25] Rottman, C. and Wortis, M., Phys. Repts. 103, 59 (1984).Google Scholar
[26] Lässig, M., Phys. Rev. Lett. 77, 526 (1996).Google Scholar
[27] Bhattacharjee, S. M., Phys. Rev. Lett. 76, 4568 (1996).Google Scholar
[28] Chui, S. T. and Weeks, J. D., Phys. Rev. B 23, 2438 (1981).Google Scholar
[29] Gunton, J. D., Miguel, M. San, and Sahni, P. S., in Phase Transitions and Critical Phenomena, edited by Domb, C. and Leibowitz, J. L. (Academic Press, London and Orlando, 1983), Vol.8.Google Scholar
[30] Furukawa, H., Advances in Physics 34, 703 (1985).Google Scholar
[31] Bray, A. J., Phys. Rev. Lett. 62, 2841 (1989).Google Scholar
[32] Bray, A. J., Physica A 194, 41 (1993).Google Scholar
[33] Stewart, J. and Goldenfeld, N., Phys. Rev. A 46, 6505 (1992).Google Scholar
[34] Liu, F. and Metiu, H., Phys. Rev. B 48, 5808 (1993).Google Scholar
[35] Papoular, M., Europhys. Lett. 33, 211 (1996).Google Scholar
[36] Phaneuf, R. J., Bartelt, N. C., Williams, E. D., Swiech, W., and Bauer, E., Phys. Rev. Lett. 67, 2986 (1991).Google Scholar
[37] Marchenko, V. I. and Parshin, A. Y., Zh. Eksp. Teor. Fiz. 79, 257 (1980), [Sov. Phys.-JETP 52, 129 (1980)].Google Scholar
[38] Marchenko, V. I., Zh. Eksp. Teor. Fiz. 81, 1141 (1981), [Sov. Phys.–JETP 54, 605 (1981)].Google Scholar
[39] Marchenko, V. I., Zh. Eksp. Teor. Fiz. 55, 72 (1992), [Sov. Phys.–JETP 55, 73 (1992)].Google Scholar
[40] This is the “downhill” current direction. Recently, it has been found that direct-current parallel to the surface can cause a step-bunching instability of certain stepped Si( 111) surfaces, which results in nonequilibrium faceting [45, 46]. The instability depends on the direction of the current [45, 46, 47, 48], and does not occur for downhill currents on stepped Si(113) surfaces.Google Scholar
[41] Song, S., Yoon, M., Mochrie, S. G. J., Stephenson, G. B., and Milner, S. T., Surf. Sci., in press.Google Scholar
[42] Khare, S. V., Einstein, T. L., and Bartelt, N. C., Surf. Sci. 339, 353 (1995).Google Scholar
[43] Bartelt, N. C., Goldberg, J. L., Einstein, T. L., Williams, E. D., Heyraud, J. C., and M~tois, J. J., Phys. Rev. B 48, 15453 (1993).Google Scholar
[44] Shchukin, V. A., Borovkov, A. I., Ledentsov, N. N., and Bimberg, D., Phys. Rev. B 51, 10104 (1995).Google Scholar
[45] Latyshev, A. V., Aseev, A. L., Krasilnikov, A. B., and Stenin, S. I., Surf. Sci. 213, 157 (1989).Google Scholar
[46] Ramstad, M. J., Birgeneau, R. J., Blum, K. I., Noh, D. Y., Wells, B. O., and Young, M. J., Europhys. Lett. 24, 653 (1993).Google Scholar
[47] Stoyanov, S., Jpn. J. Appl. Phys. 30, 1 (1991).Google Scholar
[48] Krug, J. and Dobbs, H. T., Phys. Rev. Lett. 73, 1947 (1994).Google Scholar