Molecular-beam epitaxial growth surface roughening kinetics of Ge (001): A theoretical study

Abstract

A stochastic model for the molecular-beam epitaxial (MBE) growth of Ge is developed based on the master equation approach with solid-on-solid restriction and quasichemical approximation. The surface kinetic processes included are adsorption, evaporation, and intralayer and interlayer surface migrations. The growth rate, the time averaged intensity of reflection high-energy electron diffraction (RHEED) (using kinematical theory of electron diffraction) were obtained for the MBE growth of Ge with the temperature in the range 423—698 K and a flux of 1 Å/s. The growth rate was observed to be 1 Å/s implying unity sticking coefficient. The time averaged surface roughness and isolated terrace adatom concentration which are good indicators of the average surface roughness, are found to be independent of the substrate temperature below 473 K and above 648 K. In the intermediate temperature range, the isolated terrace adatom concentration and the surface roughness decrease with increasing temperature. The kinetic roughening temperature above which a smooth surface remains smooth, is identified from the temperature dependence of the time averaged surface roughness, terrace adatom concentration, and the RHEED intensity, as 648 K. The temperature dependence of the time averaged RHEED intensity and the kinetic roughening temperature obtained from this study compare favorably with experimental results. The phenomenon of kinetic surface roughening is explained in terms of competition between the incorporation of Ge atoms on the surface, which is a surface roughening process and the migration of Ge atoms to energetically favorable island edge sites which is a surface smoothing process.