Energetics of molecular-beam epitaxy models

Abstract

A Green’s function method is used to calculate the removal energies of constituent atoms from various unreconstructed semiconductor surfaces. An efficient difference equation approach within the second-neighbor tight-binding model is used. For a compound AB, binding energies for the A and B atoms on the (111), (1̄1̄1̄), (100), and (110) surfaces are calculated. Energy to remove an atom from the nearly full surface, Ec (where the removed atom leaves behind a surface vacancy), and from the nearly empty surface, Ed (where the removed atom was isolated on the surface), is obtained. Results are presented for Si, GaAs, CdTe, and HgTe. The surface sublimation energies are shown to depend on surface coverage and do not exhibit a simple linear relationship to the number of bonds broken, as is often assumed in modeling growth by molecular-beam epitaxy (MBE). Although the anion and cation extraction energies depend on surface coverage and orientation, when averaged over a double layer, they always sum to the bulk cohesive energy. Moreover, Ec−Ed can be positive, implying effective attractive in-plane surface interactions, or negative, implying effective repulsive interactions. Ec−Ed tends to be positive for covalent and narrow-gap semiconductors, and negative for wide-gap and more ionic semiconductors. Surface sublimation energies are important input parameters for the modeling of MBE growth; their importance is demonstrated using a simple thermodynamic growth model and results are shown to explain anomalies found in MBE growth of HgCdTe.