Perturbative interpretation of the heterojunction band-offset problem

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Abstract
We introduce a new point of view in studying heterojunction band lineups. We focus on the fact that no charge transfer can occur between filled valence bands. Transfer must involve coupling to the conduction band which can be treated perturbatively because of the band gap. To illustrate this point, we develop a very simple model of a heterojunction involving two one-dimensional solids in contact, each of which possesses only two bands, a filled valence band and an empty conduction band. We treat this model by an exact calculation for a finite number of atoms and by perturbation theory. We determine the ‘‘neutral point’’ as that value of the valence-band offset for which there is no charge flow between the two materials. The perturbation approach implies that the ‘‘neutral point’’ is determined by a balance between the interface matrix elements coupling the left- (right-) hand valence band to the right- (left-) hand conduction band and the relevant heterogaps. For example, a large left-right coupling is compensated by increasing the left-right energy gap and reducing the right-left gap. The numerical work supports this interpretation and offers hope that this simple approach can be applied to real materials. In our model the ‘‘neutral point’’ of a heterojunction is strongly dependent on the boundary conditions and cannot be represented by intrinsic properties of the component materials. This result casts doubt on the conceptual basis of Tersoff’s heterojunction band lineup model, but no quantitative conclusions can be drawn since our model is not ‘‘covalent.’’