We derive, in the form of coupled partial differential equations, the evolution equations for the epitaxial growth, via step flow, of a multispecies crystal on a stepped surface. Both adsorption–desorption on the terraces and attachment–detachment along the step edges are accompanied by chemical reactions and adatom diffusion. Moreover, we account for deposition from either a vacuum, e.g., in molecular beam epitaxy, or a gas, e.g., during vapour phase epitaxy (chemical or physical). Our theory (i) endows the steps with a
thermodynamic
structure whose main ingredients are a free-energy density and species edge chemical potentials, (ii) incorporates
anisotropy
into the terrace species diffusion as well as into the edge free energy, species mobilities, attachment–detachment and reaction-rate coefficients, (iii) allows for large departures from local equilibrium along the steps, and (iv) ensures the consistency of the constitutive relations for the terrace and edge chemical rates with the second law. In particular, a configurational force balance at each step yields a generalization of the classical Gibbs–Thomson relation. Finally, the special case of steady-state growth of a
binary compound
is discussed.
A vicinal surface model for epitaxial growth with logarithmic free energy
