Bond dipole-based geometric theory of band alignment

The band alignment (BA) between two materials is a fundamental property that governs the functionality and performance of electronic and electrochemical devices. However, despite decades of study, the inability to separate surface properties from those of the bulk has made a deep understanding of the physics of BAs elusive. Building on the theory of the ideal vacuum level to separate surface from bulk [Choe et al., Phys. Rev. B 103, 235202 (2021)], here we present a geometric theory for the band alignment, specifically explaining the insensitivity of the alignment to interfacial orientation between isotropic materials. First, we adopt a neutral polyhedron, termed Wigner-Seitz atoms (WSA), to partition the charge of atoms in a way that maintains crystal symmetry and tessellates the space. In contrast to the CWZ theory, the band alignment of two materials constructed from such WSAs is independent of interface orientation. Upon electron relaxation at the interface, we show that the interfacial charge transfer dipole can be accurately described by the sum of localized point dipoles that exist between atoms at the interface (bond dipoles). For interfaces between isotropic materials, the magnitude of the bond dipole can be factored out as a multiplier, leaving only geometric factors, such as crystal symmetry and dimension of the material, to determine band alignment, regardless of the orientation of the interface. We considered 29 distinct interfaces and found that this bond dipole theory yields excellent agreement (RMS deviation < 30 meV) with first-principles results. Our theory can be easily applied to interface between alloys, as well as between anisotropic systems.