A study of the kinetic rate equation model for simulations of molecular beam epitaxy crystal growth: temperature dependence of surface kinetic processes
In this paper, we have studied the rate equation model of Kariotis and Lagally that can be used for a computer simulation of molecular beam epitaxial (MBE) growth. The advantage of such a model is the high speed of calculations so that results can be obtained in a very short time. The model is based on a solution of kinetic rate equations that govern the time dependence of the concentration of islands of varying sizes and differing heights on the top of the surface during MBE growth. One of the results of this model is an expression for the time dependence of the coverage of each layer . Within the present approach the MBE growth mode is evaluated by a calculation of the RHEED (reflection high-energy electron diffraction) intensity I(t). Similarly a calculation of the interface width IW(t), which determines the roughness of the growing surface, serves to confirm the growth mode of the MBE structure. In original model of Kariotis and Lagally the MBE growth has been affected by an appropriate choice of a set of the RE input parameters describing the probability of various kinetic processes appearing on the surface during the growth. In order to make the model applicable to simulations of MBE growth at `real' growth parameters (substrate temperature and deposition), we have included the substrate temperature dependence of all surface kinetic processes in the model. In this manner, and including processes described in the text, we have created a qualitatively new model that describes the MBE growth more accurately. This model has been used to simulate the MBE growth of GaAs at different substrate temperatures. The results have been compared with MC simulations and give an agreement in coverage profile