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Selfconsistent Calculation of Disorder‐Induced Corrections to the VCA Band‐Structures of Al x Ga 1—x As and Al x Ga 1—x P
Author(s) -
Böhm G.,
Unger K.
Publication year - 1999
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/(sici)1521-3951(199912)216:2<961::aid-pssb961>3.0.co;2-6
Subject(s) - x ray absorption spectroscopy , physics , materials science , condensed matter physics , chemistry , optics , absorption spectroscopy
A selfconsistent second order perturbation theory on the basis of the pseudopotential method is used to calculate the disorder‐induced corrections to the virtual crystal band‐structure of the lattice‐matched ternary alloys Al x Ga 1— x As and Al x Ga 1— x P. The corrections are given in terms of a x ‐ and k ‐dependent complex self‐energy, which is found to be negligible at the valence band maximum in both Al x Ga 1— x As and Al x Ga 1— x P. For the lowest conduction band the x ‐ as well as the k ‐dependence of the corresponding real and imaginary parts are presented. In the case of Al x Ga 1— x As the x ‐dependence of both the real and imaginary part shows partially significant deviations from a simple x (1— x ) behaviour due to the direct‐indirect crossover at x c ≈ 0.4. Nevertheless, by fitting the entire x ‐dependence of the real part with respect to — bx (1— x ) bowing parameters b for the Γ‐ and X‐gap have been obtained in remarkably good agreement with experimental values. For the less investigated L‐gap a value of b ≈ 0.17 eV has been found. Investigation of the k ‐dependence of the real part around the Γ‐point yields an increase of the Γ‐electron effective mass with respect to the linear interpolated values especially in the direct gap region. The x ‐dependence of the imaginary part at the Γ‐point reproduces the experimentally observed increase in the broadening of the Γ‐electron states for x > x c very well. For the always indirect Al x Ga 1— x P the x ‐dependence of the real and imaginary part can be well described by relations ∝ x (1— x ). The k ‐dependence is similiar to that of Al x Ga 1— x As excepting the anomaly in the real‐part behaviour near Γ.