Photoionization Cross Section for Manganese Acceptors in Gallium Arsenide

Abstract

Optical-transmission measurements at 20 and 77 K were used to deduce the magnitude and spectral dependence of the optical cross section ${\ensuremath{\sigma}}_{I}$ for transitions from neutral Mn acceptors to the valence bands of GaAs. The threshold energy for such transitions is ${E}_{a}=0.11$ eV, and ${\ensuremath{\sigma}}_{I}$ was studied from threshold to 0.7 eV. The crystals used had ${10}^{17}$ to ${10}^{18}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ of uncompensated Mn acceptors, as determined by analysis of Hall-effect data over the 60-400-K range. The spectral dependence of ${\ensuremath{\sigma}}_{I}$ over the range 0.11-0.45 eV is in good agreement with Lucovsky's $\ensuremath{\delta}$-function potential model, as has been reported previously. Comparisons between experiment and Lucovsky's model are complicated for photon energies above 0.46 eV by transitions to the split-off band of GaAs. In contrast to previous reports, we find that the magnitude of ${\ensuremath{\sigma}}_{I}$ (a maximum of 8 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}17}$ ${\mathrm{cm}}^{2}$ at 0.22 eV) is in good agreement with Lucovsky's model for an effective-field ratio of unity. Thus we find that dielectric reinforcement of the electric vector for a photon interacting with a Mn acceptor (wave-function radius 10.1 \AA{}) is negligible. A comparison of our data with quantum-defect models is less satisfactory than the $\ensuremath{\delta}$-function model at low energies, but becomes more favorable in the spectral region for which the split-off band is involved.