Commensurate versus incommensurate heterostructures of group-III monochalcogenides

First-principles calculations based on density-functional theory were performed to investigate heterostructures of group-III monochalcogenides (GaS, GaSe, InS, and InSe) and the effects of incommensurability on their electronic structures. We considered two heterostructures: GaS/GaSe, which has a lattice mismatch of 4.7%, and GaSe/InS, with a smaller mismatch of 2.1%. We computed the cost of having commensurate structures, and we also examined the potential energy landscape of both heterostructures in order to simulate the realistic situation of incommensurate systems. We found that a commensurate heterostructure may be realized in GaSe/InS as the interaction energy of this system with the monolayers assuming the average lattice constant is smaller than the interaction energy of an incommensurate system in which each layer keeps its own lattice constant. For GaS/GaSe, on the other hand, we found that the incommensurate heterostructure is energetically more favorable than the commensurate one, even when taking into account the energetic cost due to the lack of proper registry between the layers. Since the commensurate condition requires that one (or both) layer(s) is (are) strained, we systematically investigated the effect of strain on the band gaps and band-edge positions of the monolayer systems. We found that, in all monolayers, the conduction-band minimum is more than two times more sensitive to applied strain than the valence-band maximum; this was observed to strongly affect the band alignment of GaS/GaSe, as it can change from type-I to type-II with a small variation in the lattice constant of GaS. The GaSe/InS heterostructure was found to have a type-II alignment, which is robust with respect to strain in the range of $\ensuremath{-}2%$ to $+2%$.