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

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.