Formation of macroscopic steps at vicinal surfaces during crystal growth
Bar'yakhtar V. G., Borovik A. E., Kaganovskii Yu. S.
The evolution of the macroscopic relief of a vicinal surface of a growing (or evaporating) crystal is analyzed. An equation is derived to describe the formation and decay of macroscopic steps as a result of nonlinear effects of a diffusion interaction of moving elementary steps. Depending on the extent of supersaturation, this equation may reduce to either a Burgers equation or a Korteweg-de Vries equation. Some particular exact solutions of these equations which are of most interest for applications are analyzed.