Generalized energy band alignment model for van der Waals heterostructures with a charge spillage dipole

TL;DR

This paper introduces a generalized energy band alignment model for van der Waals heterostructures that accounts for interlayer charge spillage, providing a fast and accurate tool for device design and material screening.

Contribution

The authors develop a new linear response model incorporating charge spillage dipoles, improving upon traditional models for vdW heterostructures with minimal input requirements.

Findings

The gLR model achieves high accuracy ($r^2 ext{~}0.9$) in reproducing DFT band alignments.

Two descriptors, charge neutrality level offset and bandgap sum, dominate the model's physics.

The model is broadly transferable across different types of vdW heterostructures.

Abstract

The energy band alignment at the interface of van der Waals heterostructures (vdWHs) is a key design parameter for next-generation electronic and optoelectronic devices. Although the Anderson and midgap models have been widely adopted for bulk semiconductor heterostructures, they exhibit severe limitations when applied to vdWHs, particularly for type-III systems. Based on first-principles calculations for approximately $10^3$ vdWHs, we demonstrate these traditional models miss a critical dipole arising from interlayer charge spillage. We introduce a generalized linear response (gLR) model that includes this dipole through a quantum capacitance term while remaining analytically compact. With only two readily computed inputs, the charge neutrality level offset and the sum of the isolated-layer bandgaps, the gLR reproduces DFT band line-ups with $r^2\sim$0.9 across type-I, II, and III stacks. Machine-learning feature analysis confirms that these two descriptors dominate the underlying physics, indicating the model is near-minimal and broadly transferable. The gLR framework therefore provides both mechanistic insight and a fast, accurate surrogate for high-throughput screening of the vast vdW heterostructure design space.