Monte carlo simulation of transitions related to growth on (001) faces of Si and Ge

Based on Monte Carlo simulations for molecular beam epitaxy, three types of growth related transitions on the Si(001) and Ge(001) surfaces have been studied. In the thermal roughening simulations on a Ge(001) surface, a different type of transition from the Kosterlitz and Thouless type is obtained. The simulated result is consistent with the experimental x-ray diffraction data, at least qualitatively. In the growth simulations, a transition in the shape of growing islands is shown at the very initial stage of the homoepitaxial growth on a Si(001)-2x1 flat surface. During the transition, the step density variations as a function time show different behaviors at various temperatures. In the homoepitaxial growth on Si(001)-2x1 vicinal surfaces, the growth mode transition from two-dimensional island formation to the step-flow mode is reproduced by increasing the system temperature, which agrees qualitatively with the observed results. At the intermediate temperature, a transient growth mode is obtained, in which the two-dimensional island formation and the step flow growth modes coexist on two types of terraces on the surface.