Band offset formation at semiconductor heterojunctions through density-based minimization of interface energy

Abstract

It is well known that the magnitude of band offset (BO) at any semiconductor heterojunction is directly derivable from the distribution of charge at that interface and that the latter is decided by a minimization of total energy. However, the fact that BO formation is governed by energy minimization has not been explicitly used in theoretical BO models, likely because the equilibrium charge densities at heterojunction interfaces appear difficult to predict, except via explicit calculation. In this paper, electron densities at a large number of (100), (110), and (111) oriented heterojunctions between lattice-matched, isovalent semiconductors with the zinc blende (ZB) structure have been calculated by first-principles methods and analyzed in detail for possible common characteristics among energy-minimized densities. Remarkably, the heterojunction electron density was found to largely depend only on the immediate, local atomic arrangement. In fact, it is so much so that a juxtaposition of local electron-densities generated in oligo-cells (LEGOs) accurately reproduced the charge densities that minimize the energy for the heterojunctions. Furthermore, the charge distribution for each bulk semiconductor was found to display a striking separability of its electrostatic effect into two neutral parts, associated with the cation and the anion, which are approximately transferrable among semiconductors. These discoveries form the basis of a neutral polyhedra theory (NPT) that approximately predicts the equilibrium charge density and BO of relaxed heterojunctions from the energy minimization requirement. Well-known experimentally observed characteristics of heterojunctions, such as the insensitivity of BO to heterojunction orientation and the identity of interface bonds, the transitivity rule, etc., are all in good agreement with the NPT. Therefore, energy minimization, which essentially decides the electronic properties of all other solid and molecular systems, also governs the formation of the charge density at these heterojunction interfaces. In particular, the approach presented here eliminates the need to invoke mechanisms that are specific to semiconductor interfaces.