Physical Review B 49, 5554-5564 (1994)

Theory of impurity-induced step bunching

Abstract

We study in detail the impurity mechanism suggested by Frank for step bunching instabilities on crystal surfaces during crystal growth and evaporation. A two-dimensional model in which the impurities are treated microscopically is proposed. We perform a numerical simulation of the model and show that it leads to step bunching. In this paper we examine the large line tension limit, where the step train remains effectively one dimensional. Using a mean-field theory, we express the velocity of a step in terms of the widths of adjacent terraces and the parameters of the microscopic model. It is shown that the theory is valid over a wide range of physical parameters, and only outside this range does one have to use a more complicated exposure time formalism. We compare the velocity function predicted by the theory with results from Monte Carlo simulations of the two-dimensional model and find remarkable agreement. Our theory predicts a logarithmic growth of the average terrace width with time for noninteracting impurities, in agreement with Monte Carlo simulations. Lastly, we suggest new physical realizations of the impurity mechanism. We illustrate the robustness of the idea by considering generalized impurities, which are created by the kinetic process itself without involving an external impurity source. In some of these cases a power-law coarsening of the terrace widths may arise.