Total energy calculations were performed on GaAs, InAs and AlSb using a plane wave energy cutoff of 250eV where total energy differences are found to be converged. The ions are allowed to move under the influence of the Hellmann-Feynman forces until all forces are below 0.04eV/Å. The initial configuration of each compound at each of the volumes considered was the one given by . This does not introduce any additional symmetry into the structure. Identical sets of four equally weighted special k-points were chosen for each structure. To check the validity of this approximation it was found that increasing the number of k-points to the Monkhorst-Pack set gave no appreciable difference in energy or forces of any of the three semiconductors considered here.
The results of the total energy calculations for GaAs, InAs and AlSb are shown in Figure 4.30. The main results are summarised in Table 4.5.
Figure 4.30: The total energy of GaAs, InAs and AlSb in the zincblende (points marked by a square) and SC16 structures (points marked by a circle).
Table: Results of total energy calculations on compound semiconductors in the SC16 structure. Values of the transition pressure from zincblende to the high pressure metallic phase, P(zb-metal), are taken from experiment and represent upstroke measurements. The units are in GPa, eV and Å. is in fractional coordinates.
The energy differences between the zincblende and SC16 structures are much less than the 0.11eV/atom difference for that of silicon (BC8-diamond structures). This reduction in energy may be partially due to the ionic character of the III-V compounds which favours the denser SC16 structure while the 4-fold coordination can simultaneously accomodate covalency.
For the three compounds considered here, the calculated pressure at which the zincblende phase undergoes a structural transition to the SC16 structure is significantly lower than the corresponding transition pressure associated with the semiconducting zincblende to the sixfold coordinated metallic phase. For example, these calculations predict that GaAs transforms from zincblende to SC16 at only 2.0 GPa, whereas the earliest experimental indications of a structural transition are not observed until 16.4 GPa to the metallic structure. The transition on the downstroke is not complete until 5.5 GPa. It must be emphasized that the total energy calculations presented above only yield energy differences at zero temperature and do not take kinetic factors of phase transitions into account - this point will be returned to later.