Properties of group IV and III-V Semiconductors

Many physical properties can be obtained from the calculation of the total energy $E_{\hbox{{Tot}}}$ of a system, which can be used to test functionals when compared with known experimental values. For solids, structural properties such as the lattice constant $a_0$ and bulk modulus $B_0$ are usually determined, and the cohesive energy is used to assess the energetic predictions of the functional. These quantities are therefore used to test the HCTH functional.

Results of calculations performed using the HCTH functional are now presented for several group IV and III-V insulators and semiconductors. It is noted that Kurth et al. [108] have already applied HCTH to determine equilibrium unit cell volumes and bulk moduli for a range of solids using the linearised augmented plane-wave (LAPW) method, however, their calculations were not self-consistent as they used densities obtained from the PBE GGA functional [63].

Ultrasoft pseudopotentials [31] have been generated for each system using HCTH, and also PW91. So all of the results presented are fully consistent. Figs 3.1(a) and 3.1(b) show the kinetic energy cutoff and $k$-point sampling convergence tests for Si using HCTH. This convergence is typical for the diamond and zinc-blende systems examined here. Consequently all calculations performed in this chapter use a converged kinetic energy cutoff of $300$ eV, and a $4\times4\times4$ Monkhorst-Pack special $k$-point set for the Brillouin-zone integrations, which corresponds to $28$ $k$-points in the irreducible wedge. The experimental results are taken from Ref. [109], unless otherwise stated.

Figure 3.1: Example convergence tests are shown for bulk Si, determined using the HCTH functional. The total energy per atom (in eV) is converged with respect to (a) the kinetic energy cutoff, and (b) the number of $k$-points in the irreducible wedge.