  Understanding the band offset between materials is pivotal for electronic
device functionality. While traditional theories attribute this offset solely
to intrinsic properties of constituent materials, interfacial chemistry
introduces complexities, including charge transfer dipoles. We address this
challenge by defining a reference system based on Wigner-Seitz atoms, which is
a charge partitioning that tessellates space while retaining bulk crystal
symmetry. The interfacial dipole is then expressed entirely by localized
dipoles along interfacial bonds. Geometric analysis reveals that for isotropic
materials, both bulk and interfacial contributions to the band offset are
orientation independent. This finding is confirmed through first-principles
calculations and analysis of 28 distinct interfaces, which show very little (<
0.1 eV) dependence on orientation. Furthermore, the direction dependence of
anisotropic materials is well captured by the theory. This work provides
crucial insights into the geometric underpinnings of band offset, offering a
comprehensive understanding essential for advancing materials design in
electronic applications.
