Structure and electron affinity of the 4H-SiC (0001) surfaces: a methodological approach for polar systems

The ability to accurately and consistently determine the surface electronic properties of polar materials is of great importance for device applications. Polar surface modelling is fundamentally limited by the spontaneous polarisation of these materials in a periodic boundary condition scheme. Surface data are sensitive to supercell parameters, including slab and vacuum thicknesses, as well as the non-equivalence of surface adsorbates on opposite surfaces. Using 4H-SiC as a specific case, this study explores calculation of electron affinities (EAs) of (0001̄) and (0001) surfaces varying chemical termination as a function of computational parameters. We report the impact in terms of band-gap, electric fields across the vacuum and slab for single and double cell slab models, where the latter is constructed with inversional symmetry to eliminate the electric field in the vacuum regions. We find that single cells are sensitive to both slab and vacuum thickness. The band-gap narrows with slab thickness, ultimately vanishing and inducing charge transfer between opposite surfaces. This has a consequence for predicted EAs. Adsorbate species are found to play a crucial role in the rate of narrowing. Back to back cells with inversional symmetry have larger electric fields present across the slab than the single slab cases, resulting in a greater band-gap narrowing effect, but the vacuum thickness dependence is completely removed. We discuss the relative merits of the two approaches.