Nonlinear equation for diffusion and adatom interactions during epitaxial growth on vicinal surfaces

We present a continuum model for growth on vicinal surfaces that incorporates an approximation to adatom interactions in the form of diatomic island formation. The resulting nonlinear-diffusion equation is then integrated numerically to obtain the adatom- and diatomic-island-concentration profiles along the terrace. It is shown that due to the inclusion of adatom interactions, the model is applicable to molecular-beam epitaxy (MBE) on vicinal surfaces over a wide range of growth temperatures, beam fluxes, and terrace-misorientation angles. Furthermore, a natural outcome of the model is the identification of the transition temperature ${\mathit{T}}_{\mathit{c}}$, at which island formation may be neglected and epitaxial growth proceeds predominantly by step propagation. The excellent agreement between the value of ${\mathit{T}}_{\mathit{c}}$ determined by the nonlinear model and those obtained from both Monte Carlo simulations and measurements on vicinal GaAs(001) surfaces for different Ga and ${\mathrm{As}}_2$ fluxes shows that the inclusion of adatom interactions is an essential ingredient of a realistic model of MBE growth on misoriented surfaces.