### Physical Review B 49, 5554-5564 (1994)

### Theory of impurity-induced step bunching

Kandel, D.; Weeks, J.D.
### 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.

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