Stochastic growth theory of molecular beam epitaxy with atom correlation effects: A Monte-Carlo master equation method

Structural phase transition of epitaxial growing layer is quite important to understand the atomic scale mechanism of molecular beam epitaxy (MBE). GaAs and related alloy semiconductors are typical systems which show variety of such structural transitions during MBE. Structural evolution of surface reconstruction phases and an order-disorder transition in III–V alloy semiconductors are typical cases where such phase transitions appear during epitaxial processes. In this work, a stochastic theory and the Monte-Carlo simulation have been presented to describe the structural evolution of epitaxial growth in binary system. This method, known here as the ‘Monte-Carlo master equation (MCME) method’, couples a master equation for epitaxial growth kinetics with an Ising Hamiltonian of growing surface. The Monte-Carlo (MC) simulation of binary growing surface with atom-correlation effects has successfully revealed the evolution of atomic structure and the formation of short-range ordering (SRO) during epitaxy. This demonstrates the usefulness of the MCME method in describing the atomic-structural dynamics as compared with a conventional theory of epitaxy based on a diffusion equation and standard nucleation theory.