A 2 + 1-Dimensional Terrace-Step-Kink Model for Epitaxial Growth Far from Equilibrium

Abstract

We derive from kinetic arguments a discrete-continuum step flow model for epitaxial growth. Besides the usual adatom densities in such models we in addition account for step adatom densities and kink densities. The model extends the implicit close-to-equilibrium assumption in the classical Burton--Cabrera--Frank model to far-from-equilibrium growth regimes. Thepaper closely follows the derivation in [R. E. Caflisch et al., Appl. Math. Lett., 12 (1999), pp. 13-22] but extends the validity of the terrace-step-kink model to larger kink densities. Furthermore, the more detailed description of the exchange processes between adatoms, step adatoms, kinks, and the crystal itself leads to a new explanation for bunching.