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The Anderson and midgap models are often used in the study of semiconductorheterojunctions, but for van der Waals (vdW) vertical heterostructures theyhave shown only very limited success. Using the group-IV monochalcogenidevertical heterostructures as a prototypical system, we propose a linearresponse model and compare the effectiveness of these models in predictingdensity functional theory (DFT) band alignments, band types and bandgaps. Weshow that the DFT band alignment is best predicted by the linear responsemodel, which falls in between the Anderson and midgap models. Our proposedmodel can be characterized by an interface dipole$\alpha\times(E_{m2}-E_{m1})$, where the linear response coefficient $\alpha$ =0 and 1 corresponds to the Anderson and midgap model respectively, and $E_{m}$is the midgap energy of the monolayer, which can be viewed as an effectiveelectronegativity. For group-IV monochalcogenides, we show that $\alpha$ = 0.34best captures the DFT band alignment of the vdW heterostructure, and we discussthe viability of the linear response model considering other effects such asstrains and band hybridization, and conclude with an application of the modelto predict experimental band alignments.

Simple linear response model for predicting energy band alignment of two-dimensional vertical heterostructure