A STUDY OF A KINETIC RATE-EQUATION MODEL FOR SIMULATIONS OF MBE CRYSTAL-GROWTH - A COMPARISON WITH MONTE-CARLO SIMULATIONS

We present the simulations of molecular beam epitaxy (MBE) growth usin g a rate equation (RE) model and its comparison with Monte-Carlo (MC) simulations. The advantage of the RE model is the higher speed of calc ulations, so a much shorter time is required for obtaining results, Th e RE model is described by a set of differential equations that calcul ate at each time interval the change of the N-kj numbers of atoms and islands of each k size in each jth layer. This change is due to kineti c processes occurring on the surface during the growth. In the origina l model (R. Kariotis and H.G. Lagally, Surf Sci., 216 (1989) 557) the probabilities of these processes were described by parameters (input p arameters for equations) and the simulations of MBE growth were realiz ed by an appropriate choice of them. To make this model applicable to real simulations, we have included the substrate-temperature dependenc e of all input parameters using an Arrhenius form, This form is used i n MC simulations to calculate a migration of atoms on the surface with substrate-temperature dependence. Since the RE model is described by a set of differential equations it was important to first find the all owed temperature range for simulations. This range includes the substr ate temperature for the 3D growth mode (low temperatures) and also for the 2D growth mode (epitaxial temperatures). Using an Arrhenius form for temperature dependence of the parameters in the RE model we were a ble to compare the obtained results with MC calculations. We have made MC simulations (S, Nemeth, R. Harman and M. Vesely;, Correlation betw een the stochastic simulation of molecular beam epitaxy growth and exp eriment, 9th Int. Conf. of Thin Films, 6-10 September, 1993, Vienna, A ustria) using the same input parameters (T = 775 K, E(n) = 0.3 eV, E(s ) = 1.45 eV). Since the RE model is strongly substrate-size dependent (D. Papajova, W.E. Hagston and P. Harrison, Appl. Phys. A, 59 (1994) 2 15-222; D. Papajova, S. Nemeth, W.E Hagston, H. Sitter and M. Vesely, J.Appl. Phys. A, submitted) we have found very good agreement in 2D gr owth for smaller substrate sizes S (in the RE model) only, when this d ependence does not influence the results.