Selfconsistent calculation of disorder-induced corrections to the VCA band-structures of AlxGa1-xAs and AlxGa1-xP

A selfconsistent second order perturbation theory on the basis of the pseud opotential method is used to calculate the disorder-induced corrections to the virtual crystal band-structure of the lattice-matched ternary alloys Al xGa1-xAs and AlxGa1-xP. The corrections are given in terms of x- and k-depe ndent complex self-energy, which is found to be negligible at the valence b and maximum in both AlxGa1-xAs and AlxGa1-xP. For the lowest conduction ban d the x- as well as the k-dependcnce of the corresponding real and imaginar y parts are presented. In the case of AlxGa1-xAs the x-dependence of both t he real and imaginary part shows partially significant deviations from a si mple x(1-x) behaviour due to the direct-indirect crossover at x(c) approxim ate to 0.4. Nevertheless, by fitting the entire x-dependence of the real pa rt with respect to -bx(1-x) bowing parameters b for the Gamma- and X-gap ha ve been obtained in remarkably good agreement with experimental values. For the less investigated L-gap a value of b approximate to 0.17 eV has been f ound. Investigation of the k-dependence of the real part around the Gamma-p oint yields an increase of the Gamma-electron effective mass with respect t o the linear interpolated values especially in the direct gap region. The x -dependence of the imaginary part at the Gamma-point reproduces the experim entally observed increase in the broadening of the Gamma-electron states fo r x > x(c) very well. For the always indirect AlxGa1-xP the x-dependence of the real and imaginary part can be well described by relations proportiona l to x(1-x). The k-dependence is similiar to that of AlxGa1-xAs excepting t he anomaly in the real-part behaviour near Gamma.