ELSEVIER Applied Surface Science 102 (1996) 6-11 :;.-:3.:~:~:~::: ::::x': ........................... ":':'::::-'.~:~i!!!~.,' applied surface science The physical origin of the two-dimensional towards three-dimensional coherent epitaxial Stranski-Krastanov transition P. Miiller *, R. Kern • . . 1 Centre de Recherche sur les Mdcanismes de la Crmssance Crtstalhne , Campus de Luminy, case 913, F-13288 Marseille Cedex 9, France Abstract Epitaxial two-dimensional layer growth (2D) relayed by three-dimensional (3D) growth, characterizes the Stranski- Krastanov growth mode. The physical origin of this transition is not well understood up to now. We show for a coherent epitaxy that three conditions are necessary and sufficient to rationalize the problem: (i) the perfect wetting condition of Bauer's criterion expressed in terms of long range forces (ii) an elastic misfit energy of the so produced layers (iii) an elastic striction energy induced in the substrate by appearing islands. The three associated energies may compete each other. A single layer island may spontaneously thicken when it grows over a number of A layers greater than a critical one z * provided it has reached a critical size Rz,. At this point striction opposes to wetting and spends the necessary energy for creating new edges. The kinetics of 2D --~ 3D transition is surface diffusion dependent and driven by the striction giving a very abrupt transition around Rz. which is of mesoscopic size. The Ge(lll)/Si(lll)7 × 7 system is treated numerically since most of the necessary data are known. 1. Introduction Bauer in his thesis [1] discovered on alkali-halide crystals three epitaxial growth modes: a three-dimen- sional (3D) one, a two-dimensional (2D) one where A grows layer by layer over B and finally but later, on metal/metal systems also a mixed mode (Stran- ski-Krastanov (SK) mode). In the latter case, after one or more 2D layers of A on B, 3D crystals start to develop on it. Bauer rationalized these growth modes in terms of surface energies o- i of the faces coming * Correspondingauthor. Tel.: +9-117-2851; fax: +9-141-8916; e-mail: muller @ crmc2.univ-mrs.fr. i Associ6 aux Universitrs Aix-Marseille II et III. in contact or alternatively with the adhesion energy /3: (/)c~ = O'A -- O'B + ~FAB = 20"A -- fi, q)~ < 0 for 2D, qL > 0 for 3D (1) For the intermediate SK mode there remains only the vague criterion ~ = 0. Bauer's criterion has shown to be very effective not only for alkali-halide sys- tems but also for metals, organics and semi-conduc- tors [2]. Much later Kern et al. [2,3] have added two important ingredients for the 45 < 0 case: (i) The misfit energy ~-c~=(EA//(1- VA))Vm2 where v is the volume per atom and m the natural misfit m = (b - a)/a; E and v Young modulus and Poisson ratio. (ii) The finite size effect (or long range effect) of 0169-4332/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved. PII S0169-4332(96)00009-8