Generic computer simulations using empiric interatomic potentials suggest a new, collective mechanism that could be responsible for mixing at heteroepitaxial interfaces. Even if single adsorbate atoms diffuse by hopping on the substrate surface and do not mix at the terraces, two-dimensional islands formed by nucleation may become unstable above a certain critical size and explode upwards forming clusters of several atomic layers. This process is accompanied by strong distortions of the underlying atomic layers, and on soft materials it can result in surface etching and incorporation of substrate atoms into the islands.

A way of understanding localization as a breakdown of extended states is presented by considering a three-dimensional disordered cluster of length Ll and finite cross section L&L3, which is repeated periodically along the Ll direction. The exact Green s function is calculated in the tightbinding scheme and the complex self-energy X(e}=A(e)+if'(e) is studied as a function of the cell length; this procedure of finding 1" guarantees that one is always looking at the properties coming from the eigenvalues. The singular spectrum of an infinite isolated cell is then obtained as a limit from the absolutely continuous spectrum of periodic systems with finite cell length. For the repeating cell the measure of the spectrum support approaches zero as L l increases and this is reflected by -I l/A, the law (I L (e) &,"-e ' for the ensemble average. Theoretical arguments allow us to show that l the loca1ization length A, of the eigenfunction of the isolated cells is the same as that calculated by previous authors from the exponential decay of the transmittance and by ourselves from convergence of self-energies in the realm of real numbers. A numerical calculation of the dependence of A, on cross section and disorder parameter 8' shows a behavior similar to that found by MacKinnon and Kramer.