J. Phys. I France
Volume 2, Numéro 11, November 1992
Page(s) 2107 - 2121
DOI: 10.1051/jp1:1992271
J. Phys. I France 2 (1992) 2107-2121

Terrace sizes in molecular beam epitaxy

Jacques Villain1, Alberto Pimpinelli1, 2, 3, Leihan Tang4 and Dietrich Wolf1, 5

1  S.P.S.M.S./M.D.N., Département de Recherche Fondamentale M.C., C.E.N.G., 85X, F-38041 Grenoble Cedex, France
2  Laboratoire de spectrométrique physique, Université J. Fourier, Grenoble
3  Dipartimento di fisica, Università di Parma, I-43100 Parma, Italy
4  Institut für theoretische Physik, Universität Köln, Grmany
5  FB 10, Universität Duisburg, D-4100 Duisburg, Germany

(Received 18 July 1992, revised 17 July 1992, accepted 28 July 1992)

The order of magnitude of the typical distance $\ell$ between steps in MBE-grown crystal surfaces in calculated from simple scaling assumptions in the absence of evaporation. This distance is measurable by diffraction methods and yields access to the surface diffusion constant D. At the lowest non trivial temperatures the characteristic distance is of order (D/F)1/6 where F is the beam flux. At slightly higher temperature, $\ell$ is given by an algebraic formula which depends on the lifetime $\tau_2$ of a bound pair of adatoms at the surface, as well as of the diffusion constant D2 of these pairs. In certain ranges, $\ell$ varies as F-1/4 or F-1/5. At higher temperatures yet, $\ell$ is given by a formula which depends on a larger number of parameters. In special cases, our results are in agreement with the classical formulae of Stoyanov and Kashchiev, but disagree with certain recents works. $\ell$ is found to increase with temperature more rapidly than an Arrhenius exponential. Monte-Carlo simulations are reported and the discrepancy with certain other authors is clarified.

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