Fabrication of self-assembled arrays of nanocrystals (NCs) by physical vapor deposition (PVD) is a promising technique rated highly for its potential for various electronic, photonic, and sensing applications. However, the self-assembly process is not straightforward to control and direct in a desired way. A detailed understanding of how to control the size, shape, and density of self-assembled NCs by varying the accessible PVD process conditions, such as deposition rate, duration, or temperature, is critical for the potential of self-assembled nanofabrication to be fully realized. In this paper, we report a systematic kinetic Monte Carlo modeling that explicitly represents PVD synthesis of self-assembled metallic NCs on a crystalline substrate. We investigate how varying the duration of deposition, deposition rate, temperature, and substrate wetting conditions may affect the morphologies of arrays of self-assembled metallic islands and compare our results with previously reported experimentally observed surface morphologies generated by PVD and theoretical studies.