Extracting electron densities in n-type GaAs from Raman spectra: Comparisons with Hall measurements

We demonstrate quantitatively how values of electron densities in GaAs extracted from Raman spectra of two samples depend on models used to describe electric susceptibility and band structure. We, therefore, developed a theory that is valid for any temperature, doping level, and energy ratio proportional to q ²=(ω + iγ) (where q is the magnitude of wave vector, ω is Raman frequency, and γ is plasmon damping). We use a full Mermin-Lindhard description of Raman line shape and compare n-type GaAs spectra obtained from epilayers with our simulated spectra. Our method is unique in two ways: (1) we do a sensitivity analysis by employing four different descriptions of the GaAs band structure to give electron densities as functions of Fermi energies and (2) one of the four band structure descriptions includes bandgap narrowing that treats self-consistently the many-body effects of exchange and correlation in distorted-electron densities of states and solves the charge neutrality equation for a two-band model of GaAs at 300 K. We apply these results to obtain electron densities from line shapes of Raman spectra and thereby demonstrate quantitatively how the values of electron densities extracted from Raman spectra of n-type GaAs depend of various models for susceptibility and band structure.