Self-consistent dipole theory of heterojunction band offsets

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Abstract
A theory of heterojunction band offsets is developed within the density-functional framework in the local-density approximation. The linear-muffin-tin-orbital method is used in conjunction with a superlattice geometry for solving Schrödinger’s equation of the heterojunction. The potential is constructed within the atomic-sphere approximation. Within this context the long-range electrostatics reduce to that of point charges, and the average electrostatic potential of the latter can be used as a local reference level. It is shown that, starting from an arbitrary alignment of the bulk potentials, the correct potential alignment is obtained by minimizing the total energy with respect to a single parameter: the interface dipole. This minimization is equivalent to screening the initially induced dipole by the macroscopic dielectric constant of the interface region of the heterojunction, which can be identified approximately with the harmonic average of the dielectric constants of the two semiconductors. The conditions under which this is valid are discussed. The calculations are performed within a so-called frozen-shape approximation, allowing the potentials to vary only by constant shifts. Almost perfect agreement between calculations using a different shift per atomic layer and calculations using a single shift per semiconductor provide a numerical demonstration that the self-consistent dipole is independent of the details of the dipole profile. They also show that the macroscopic dielectric constant of the heterojunction in the vicinity of the interface can be obtained with reasonable accuracy from the single-parameter variational calculation itself. The calculations also show that linear response is valid over a wide range. The theory is applied to an extensive set of lattice-matched semiconductor (110) interfaces and shown to be in excellent agreement with experimental results and previous more-involved calculations where available. The consequences of the present theory for interface-orientation dependence and metal-semiconductor interfaces are briefly discussed.

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