Photoionization Cross Section for Manganese Acceptors in Gallium Arsenide

Optical-transmission measurements at 20 and 77 K were used to deduce the magnitude and spectral dependence of the optical cross section ${\sigma }_I$ for transitions from neutral Mn acceptors to the valence bands of GaAs. The threshold energy for such transitions is $E_a=0.11\mathrm{}$ eV, and ${\sigma }_I$ was studied from threshold to 0.7 eV. The crystals used had ${10}^{17}$ to ${10}^{18}$ ${\mathrm{cm}}^{-3\mathrm{}}$ of uncompensated Mn acceptors, as determined by analysis of Hall-effect data over the 60-400-K range. The spectral dependence of ${\sigma }_I$ over the range 0.11-0.45 eV is in good agreement with Lucovsky's $\delta$-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 ${\sigma }_I$ (a maximum of 8 × ${10}^{-17\mathrm{}}$ ${\mathrm{cm}}^2$ 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 Å) is negligible. A comparison of our data with quantum-defect models is less satisfactory than the $\delta$-function model at low energies, but becomes more favorable in the spectral region for which the split-off band is involved.