Critical evaluation of the light-scattering spectrum for single-particle excitations inn-GaAs at 300 K

The line shape of the light-scattering spectrum for single-particle excitations in semiconductors such as $n$-GaAs has been commonly represented to be a simple Gaussian for a Maxwellian distribution of electrons. In this form it has been used as a probe of nonequilibrium populations of electrons. We present a critical evaluation of the adequacy of this approximation, based both on theory and on detailed, high-resolution measurements with Nd-doped yttrium aluminum garnet (Nd:YAlG) laser radiation at 1.06 μm for a series of $n$-GaAs samples at 300 K, for concentrations in the range $\sim {10}^{13}<n<\mathrm{}{10}^{18}$ ${\mathrm{cm}}^3$. For low concentrations ($n<\mathrm{}5\mathrm{}\times {10}^{15}/{\mathrm{cm}}^3$), we found a highly structured, competitive contribution to the spectrum from two-phonon-difference frequency combinations. This has to be subtracted from the measured spectrum to yield the single-particle contribution, and puts a lower limit of ∼5×${10}^{14}$/${\mathrm{cm}}^3$ on the electron populations that can be analyzed. Even for the corrected single-particle spectra, there are departures from a Gaussian line shape due to a variety of factors all inherent in the theory as formulated by Hamilton and McWhorter, but never fully analyzed or compared with experiment. These factors include band-structure effects (momentum dependence of the resonant enhancement term), overlapping contributions from Landau-damped plasmons, collisions, and a nonnegligible but always neglected zero-shift Compton-scattering term. The individual role and significance of these factors, as a function of carrier concentration, was determined from the theory and correlated with the experimental spectra. This analysis was carried out for the three scattering mechanisms associated with the charge-, energy-, and spin-density fluctuations of the solid-state electron plasma. We have found the spin-density fluctuation mechanism to be best suited to serve as a probe of electron distributions, but not without necessary corrections for the various experimental and theoretical factors.