Theory of optical spectra in a magnetic field in doped semiconductor quantum wells: Impurity-induced broadening and transitions.

Abstract

The effect of carrier-impurity interactions on luminescence- and excitation-spectroscopy line shapes and the Landau-level spectral density in a strong quantizing magnetic field is examined in modulation-doped semiconductor quantum wells. The line-shape function is obtained by summing the ladder diagrams,'' extending our previous one-rung'' approximation. Apart from yielding a line broadening, the carrier-impurity interaction is found to induce off-diagonal transitions (ODT) ({ital n}{r arrow}{ital n}{prime}; {ital n}{prime}{ne}{ital n}) between the Landau levels in the conduction and valence bands, breaking the usual {ital n}{r arrow}{ital n} selection rule. Here the first and second integers indicate the Landau quantum numbers in the conduction (valence) and valence (conduction) bands, respectively, for luminescence (excitation), for example, in an {ital n}-type system. The Landau-level spectral density (essential for obtaining the line-shape functions) is investigated by a self-consistent Born approximation which includes inter-Landau-level impurity scattering. The theory is applied to an {ital n}-type strained In{sub {ital x}}Ga{sub 1{minus}{ital x}}As/GaAs quantum well, where optical transitions arise between the conduction band and the strain-split in-plane light-hole'' band. For excitation spectra, the theory predicts that ODT introduce lines below the usual {ital n}{sub {ital F}}{r arrow}n{sub F} threshold transition as well as satellite lines between the usual main {ital n}{rmore » arrow}{ital n} lines above the threshold (i.e., {ital n}{ge}{ital n}{sub {ital F}}). Here {ital n}{sub {ital F}} is the quantum number of the lowest-lying empty or partially filled conduction-band Landau level. The luminescence line shape is dominated by ODT 1, 2,...{r arrow}0 (in addition to the main 0{r arrow}0 transition) at low temperatures and by the usual {ital n}{r arrow}{ital n} transitions at high temperatures.« less