Extracting electron densities in n-type GaAs from Raman spectra: Comparisons with Hall measurements
Maicol A. Ochoa, James E. Maslar, Herbert S. Bennett
Raman measurements can be utilized as a non-destructive method for determining carrier density in compound semiconductors. Rigorous determination of carrier density involves comparing measured and simulated coupled phonon-plasmon Raman spectra. Theories of varying degrees of complexity have been employed for simulating spectra in which spectra are generated as a function of Fermi energy (or carrier density in the degenerate limit). In general, previously utilized spectral models are strictly valid only for a temperature near 0 K and either for the classical or degenerate doping limit. However, such models cannot necessarily capture all the spectral information. To overcome this limitation, we developed a model that is valid at any temperature, any doping level, and for arbitrary values of the ratio q/(ω + iγ) (where q is the magnitude of the wavevector, ω is the frequency used in the Raman measurements, and γ is the plasmon damping). We compare measured n-type GaAs spectra, obtained from epilayers with different carrier concentrations, with simulated spectra obtained with this new spectral model employing different descriptions of the band structure as a function of Fermi energy. The theory we use is unique in two respects. First, it is valid at any temperature, including room temperature, for arbitrary values of the ratio q/(ω + iγ). Second, the bandgap narrowing (BGN) theoretical model used here treats self-consistently the many-body effects of exchange and correlation in the distorted-electron densities of states. Our theoretical calculations solve the charge neutrality equation self-consistently for a two-band model of GaAs at 300 K. This includes the effects of high carrier concentrations and dopant densities on the distorted- perturbed densities of states. We then apply the results to obtain the carrier concentrations from Fermi energies in the context of line shapes in the Raman spectrum due to the coupling between longitudinal optical phonons and plasmons.