Theory of ionization potentials of nonmetallic solids

Since the ionization potential (IP) is one of the fundamental quantities in a solid, ruling the physical and chemical properties and electronic device performances, many researchers have quantified the IPs using first-principles calculations of slab models recently. However, the breakdown into bulk and surface contributions has remained a contentious issue. In this study, we discuss how to decompose the IP into the bulk and surface contributions by using the macroscopic average technique. Although this procedure quantifies well-defined macroscopic dipoles and corroborates with the continuous model, it is not consistent with the physical intuition. This is because the strong charge fluctuation inside solids significantly contributes to the macroscopic dipole potential. We also discuss the possibility of an alternative splitting procedure that can be consistent with the physical intuition, and conclude that it is possible only when both bulk and surface charge density is well decomposed into a superposition of spherical charges. In the latter part, we evaluate the IPs of typical semiconductors and insulators such as Si, diamond, GaAs, GaN, ZnO, and MgO, using atomic-charge and molecular-charge approximations, in which the charge density of a solid is described as a superposition of charge density of the constituent atoms and molecules, respectively. We find that the atomic-charge approximation also known as the model-solid theory can successfully reproduce the IPs of covalent materials, but works poorly for ionic materials. On the other hand, the molecular-charge approximation, which partly takes into account the charge transfer from cations to anions, shows better predictive performance overall.