Importance of bulk states for the electronic structure of semiconductor surfaces: implications for finite slabs

TL;DR

This study demonstrates that the electronic structure of semiconductor surfaces, specifically Si(100), is highly dependent on slab thickness in DFT calculations, with convergence achieved only at slabs thicker than 60 layers.

Contribution

It shows the critical importance of using sufficiently thick slabs in DFT simulations to accurately capture surface and bulk electronic states.

Findings

Surface band structure converges at >30 layers.

Complete convergence of surface and bulk bands occurs at >60 layers.

Slab thickness significantly influences the accuracy of electronic structure calculations.

Abstract

We investigate the influence of slab thickness on the electronic structure of the Si(100)-p(2x2) surface in density functional theory (DFT) calculations, considering both density of states and band structure. Our calculations, with slab thicknesses of up to 78 atomic layers, reveal that the slab thickness profoundly affects the surface band structure, particularly the dangling bond states of the silicon dimers near the Fermi level. We find that, to precisely reproduce the surface bands, the slab thickness needs to be large enough to completely converge the bulk bands in the slab. In case of the Si(100) surface, the dispersion features of the surface bands, such as the band shape and width, converge when the slab thickness is larger than 30 layers. Complete convergence of both the surface and bulk bands in the slab is only achieved when the slab thickness is greater than 60 layers.