Abstract: It was recently shown that the electronic band alignment in lateral two-dimensional heterostructures is strongly dependent on the system geometry, such as heterostructure width and layer thickness. This is so even in the absence of polar edge terminations because of the appearance of an interface dipole between the two different materials. In this study, this work is expanded to include two-dimensional materials that possess an electronic dipole over their surface, i.e., in the direction transverse to the crystal plane. To this end, a heterostucture consisting of polar hydrofluorinated graphene and non-polar graphane layers is studied with first-principles calculations. As for nonpolar heterostructures, a significant geometry dependence is observed with two different limits for the band offset. For infinitely wide heterostructures, the potential step in the vacuum is equally divided over the two sides of the heterostructure, resulting in a finite potential step in the heterostructure. For infinitely thick heterostructure slabs, on the other hand, the band offset is reduced, similar to the three-dimensional case.

Abstract: The electronic band alignment in semiconductor heterostructures is a key factor for their use in electronic applications. The alignment problem has been intensively studied for bulk systems but is less well understood for low-dimensional heterostructures. In this work we investigate the alignment in two-dimensional lateral heterostructures. First-principles calculations are used to show that the electronic band offset depends crucially on the width and thickness of the heterostructure slab. The particular heterostructures under study consist of thin hydrogenated and fluorinated diamond slabs which are laterally joined together. Two different limits for the band offset are observed. For infinitely wide heterostructures the vacuum potential above the two materials is aligned leading to a large step potential within the heterostructure. For infinitely thick heterostructure slabs, on the other hand, there is no potential step in the heterostructure bulk, but a large potential step in the vacuum region above the heterojunction is observed. The band alignment in finite systems depends on the particular dimensions of the system. These observations are shown to result from an interface dipole at the heterojunction that tends to align the band structures.