Role of lateral interaction in the homoepitaxy of GaAs on the (001)-$\beta(2\times 4)$ surface

The homoepitaxy of GaAs on the (001)-β(2 × 4) surface during molecular beam epitaxy is considered as a twodimensional first-order phase transition from the lattice gas of adsorbed growth components to the two-dimensional crystalline phase. In the context of the mean field theory of phase transitions, the parameters of lateral interaction between filled cells of the lattice gas are determined. The causes for the completion of the growth of a particular monolayer (self-ordering) before the beginning of growth of a new monolayer are clarified. The oscillations observed in the reflection high-energy electron diffraction experiments support the conclusions of the suggested theory of the phase transition for homoepitaxy.