Band offset models of three-dimensionally bonded semiconductors and insulators.

The band offsets of heterojunctions of three-dimensionally (3D) bonded semiconductors lie between two limits, the electron affinity rule (unpinned limit) and the matching of the charge neutrality levels (CNLs), equivalent to the pinned limit. It is shown that it has been difficult to compare the validity of these cases because most experimental and theoretical tests require a lattice matching across the heterojunction, and most semiconductors with the same lattice constant have similar average band energies referred to the vacuum level. A second point is that the CNL when referenced to the vacuum level varies surprisingly weakly with the midgap energy with respect to the vacuum level. A calculation of band offsets for heterojunctions with larger lattice mismatch provides a stronger test, and this result is found to favor the CNL matching model. This result is important for many practical device heterojunctions, where unmatched interfaces are common