Kinetic model for step flow growth of [100] steps

A kinetic model for the step flow growth of [100] steps is derived. This model extends the implicit close-to-equilibrium assumption in the classical Burton-Cabrera-Frank theory to out-of-equilibrium growth regimes common in molecular beam epitaxy. In equilibrium, the kink density coincides with Burton, Cabrera, and Frank [Philos. Trans. R. Soc. London, Ser. A 243, 299 (1951)] but in a planar steady state solution for a periodic sequence of steps the kink density derivates and we analyze its scaling behavior with the step Peclet number. Furthermore, we observe a discontinuity of adatoms on the steps that might give a new explaination for step bunching.