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 Tc, at which island formation may be neglected and epitaxial growth proceeds predominantly by step propagation. The excellent agreement between the value of Tc determined by the nonlinear model and those obtained from both Monte Carlo simulations and measurements on vicinal GaAs(001) surfaces for different Ga and As₂ fluxes shows that the inclusion of adatom interactions is an essential ingredient of a realistic model of MBE growth on misoriented surfaces.