General theory of the transverse dielectric constant of III-V semiconducting compounds

Abstract

We have developed a general model of the transverse dielectric constant of III-V compounds using a hybrid method which combines the k\ensuremath{\cdot}p method with a nonlocal pseudopotential calculation. In our method we partition the Brillouin zone into three regions by expanding the energy bands and matrix elements about the \ensuremath{\Gamma}, X, and L symmetry points. The real and imaginary parts of the dielectric constant are calculated as a sum of the individual contributions of each region. By using this partition method, we are able to get good insight into the dependence of the dielectric constant on the shape of the band structure. Hence, it is seen that the X and L regions contribute 90--95 % and the \ensuremath{\Gamma} region only 5--10 % to the zero-frequency dielectric constant. In general, our results for ${\ensuremath{\epsilon}}_{1}$(0) and ${\ensuremath{\epsilon}}_{2}$(\ensuremath{\omega}) agree well with the experimental data.