New Nonlinear Evolution Equation for Steps during Molecular Beam Epitaxy on Vicinal Surfaces

Abstract

A nonlinear evolution equation for a vicinal surface growing in the step flow mode is derived in the limit of weak desorption. This limit turns out to be singular, and nonlinearities of arbitrary order need to be taken into account. The meandering instability caused by step edge barriers leads to a step morphology with a fixed meander wavelength, cusp singularities, and a step width increasing as $\sqrt{t}$ without bound. Full lattice gas simulations confirm this picture, and the observed step morphology is derived analytically from the evolution equation.