We present a kinetic Monte Carlo model describing the growth by molecular beam epitaxy (MBE) of semiconductor compounds and including a local photoemission model with reflection high-energy electron diffraction (RHEED) intensity for comparison. We investigate the cases of both homoepitaxial and heteroepitaxial growth. The valence force field approximation is used for the strain energy calculations in mismatched thin films In homoepitaxial growth of GaAs, we have study the variations of photoemission current and RHEED intensity and examined the GaAs morphology. In high lattice mismatch heteroepitaxial growth (CdTe/GaAs), we have shown the formation of grooves corresponding to (111) facets, precursor to the formation of misfit defects.We present a kinetic Monte Carlo model describing the growth by molecular beam epitaxy (MBE) of semiconductor compounds and including a local photoemission model with reflection high-energy electron diffraction (RHEED) intensity for comparison. We investigate the cases of both homoepitaxial and heteroepitaxial growth. The valence force field approximation is used for the strain energy calculations in mismatched thin films In homoepitaxial growth of GaAs, we have study the variations of photoemission current and RHEED intensity and examined the GaAs morphology. In high lattice mismatch heteroepitaxial growth (CdTe/GaAs), we have shown the formation of grooves corresponding to (111) facets, precursor to the formation of misfit defects