1 Introduction

The calculation of the band structure for a periodic system consists of two steps. First, the charges in the system must be calculated using a converged k-point sampling. Then, keeping the obtained charges fixed, the one-electron levels must be calculated for k-points chosen along specific lines for which the band structure should be determined in the Brillouin-zone.

The current tutorial uses GaAs as example. You can download the input files and the scripts used in this tutorial from the overview page about the howtos. The input file for DFTB+ must be named dftb_in.hsd, so you have to rename the file dftb_in.charge.hsd to run DFTB+ for creating the charges, or rename dftb_in.band.hsd to calculate the band structure.

Please note, that the quality of the band structure you obtain depends very much on the parametrisation you use. Most parametrisations were made without paying attention to a correct conduction band structure. Additionally, they are usually done using a minimal basis, which in many cases makes it impossible to obtain a correct conduction band (e.g. silicon with sp-basis results in a direct-gap semiconductor). Therefore, make sure, that the parametrisation you use is capabable of describing the regions of the band structure which you are interested in.

This tutorial uses the GaAs parameters from the hyb-0-1 parametrisation set to calculate the band structure of GaAs. The parameters for GaAs were tuned to obtain a sensible description of the GaAs surface. No attention was paid to the band structure. Consequently, the gap obtained with that parametrisation is far too large. The shape of the band edges, however, is qualitatively right.

The tutorial assumes, that you downloaded the parametrisation set hyb-0-1 and extracted it into the directory, where the input for DFTB+ is located. (The parameters are not part of the tgz-archive containing the input files for the tutorial.)