Trends on band alignments: Validity of Anderson's rule in SnS2- and SnSe2-based van der Waals heterostructures

Van der Waals (vdW) heterostructures are promising candidates for building blocks in novel electronic and optoelectronic devices with tailored properties, since their electronic action is dominated by the band alignments upon their contact. In this work, we analyze 10 vdW heterobilayers based on tin dichalcogenides by first-principles calculations. Structural studies show that all systems are stable, and that commensurability leads to smaller interlayer distances. Using hybrid functional calculations, we derive electronic properties and band alignments for all the heterosystems and isolated two-dimensional (2D) crystals. Natural band offsets are derived from calculated electron affinities and ionization energies of 11 freestanding 2D crystals. They are compared with band alignments in true heterojunctions, using a quantum mechanical criterion, and available experimental data. For the ${\mathrm{hBN}/\mathrm{SnSe}}_{2}$ system, we show that hBN suffers an increase in band gap, while leaving almost unchanged the electronic properties of ${\mathrm{SnSe}}_{2}$. Similarly, ${\mathrm{MX}}_{2}$ (M = Mo, W; X = S, Se) over ${\mathrm{SnX}}_{2}$ preserve the natural discontinuities from each side of the heterobilayer. Significant charge transfer occurs in junctions with graphene, which becomes p-doped and forms an Ohmic contact with ${\mathrm{SnX}}_{2}$. Zirconium and hafnium dichalcogenides display stronger interlayer interactions, leading to larger shifts in band alignments with tin dichalcogenides. Significant orbital overlap is found, which creates zero conduction band offset systems. The validity of the Anderson electron affinity rule is discussed. Failures of this model are traced back to interlayer interaction, band hybridization, and quantum dipoles. The systematic work sheds light on interfacial engineering for future vdW electronic and optoelectronic devices.