Bond Dipole based Geometric Theory of Band Alignment

Abstract: The band alignment (BA) between two materials is a fundamental property that governs the functionality and performance of electronic, as well as electrochemical, devices. However, despite decades of study, the inability to separate surface properties from those of bulk have made a deep understanding of the physics of BA illusive. Building on the theory of ideal vacuum level to separate surface from bulk [CWZ, Phys. Rev. B 103, 235202 (2021)], here we present a geometric theory for the band alignment, particularly, explaining the insensitivity of the alignment to interfacial orientation between isotropic materials. First, we adopt charge neutral polyhedron, termed Wigner-Seitz atoms (WSA), to partition the charge of atoms in a way which maintains crystal symmetry and tessellates the space. In contrast to CWZ theory, the band alignment of two materials constructed from such WSAs is independent of interface orientation. Upon electron relaxation at the interface, here we show that the interfacial charge transfer dipole can be faithfully descibed by the sum of localized point dipoles which 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 the crystal symmetry and dimension of the material, to determine band alignment, irrespective 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 straightforwardly applied to interface between alloys, as well as between anisotropic systems.