The valence charge density in a plane containing both A and B bonds is shown in Figure 4.32. It can be seen that there is a significant charge transfer from the Ga to the As atom. If the ionicity of the Ga-As bond were significantly higher in the SC16 structure than in the zincblende structure it could be argued that wrong bond defects which are likely to be present in the high pressure recovered phase would be more unfavourable in the SC16 structure than in either zincblende or -Sn phases.
Figure 4.32: Valence charge density for GaAs in the SC16 structure. The overall asymmetry of the valence charge distribution can be used to derive an ionicity scale.
To explore this possibility the ionic character of the Ga-As bond in the zincblende and SC16 structures are investigated. An ab initio method of doing this was recently suggested by Garcia and Cohen. The method allows an ionicity scale to be defined using only the overall asymmetry of the charge density as a fundamental quantity. The charge density is decomposed into symmetric and antisymmetric part as follows:
The origin of the coordinates is defined so that atoms of different species are interchanged upon inversion through the origin. The origin is therefore half way along the A bond.
Fourier decomposition of the symmetric and antisymmetric parts of the charge density give
from which a measure of the amount of asymmetry, S, over the entire unit cell can be defined:
The overall degree of charge asymmetry, g, is then given by
This method applied to GaAs gives g=0.3014 in the zincblende structure which agrees well with the value of 0.316 reported by Garcia and Cohen. For SC16 GaAs it is found that g=0.3090. This near equality of the calculated ionicities suggests that wrong bond energies in each structure will be similar, although the effect of atomic size should be noted - this will be greater in the denser SC16 structure.