Direct method of calculation of dynamic effective charges: Application to GaAs

A method is described for the calculation of effective charges and piezoelectric constants in crystals directly from self-consistent electronic calculations. The central equations are based upon moments of the change in electronic charge density (r) caused by the displacement of an atom. The long-range Coulomb interactions are taken into account, and it is shown that the moments are rigorously convergent and define longitudinal effective charges and piezoelectric constants. The method is not limited to small displacements and, in fact, uses exactly the same techniques which have been extensively developed for the calculation of surface and interface dipoles. Results are presented for the effective charge in GaAs using the same ionic pseudopotentials and density functional for the electrons that predict accurately the lattice constant and phonon energies. The predicted charge is e₋^*=0. 16|e| (positive on Ga) compared to the experimental value e₋^*=eₓ^{*}{₀}=0. 20|e|.