GaSb band-structure models for electron density determinations from Raman measurements

We investigate the use of Raman spectroscopy to measure carrier concentrations in $n-\text{type}$ GaSb epilayers to aid in the development of this technique for the nondestructive characterization of transport properties in doped semiconductors. The carrier concentration is quantified by modeling the measured coupled optical phonon-free carrier plasmon mode spectra. We employ the Lindhard-Mermin optical susceptibility model with contributions from carriers in the two lowest GaSb conduction-band minima, the $\Gamma$ and $L$ minima. Furthermore, we evaluate three conduction-band models: (1) both minima parabolic and isotropic, (2) the $\Gamma$ minimum non-parabolic and isotropic and the $L$ minima parabolic and isotropic, and (3) the $\Gamma$ minimum non-parabolic and isotropic and the $L$ minima parabolic and ellipsoidal. For a given epilayer, the carrier concentration determined from the spectral simulations was consistently higher for the ellipsoidal $L$ minima model than the other two models. To evaluate the conduction-band models, we calculated the $L$ to $\Gamma$ electron mobility ratio necessary for the electron concentrations from the Raman spectral measurements to reproduce those from the Hall effect measurements. We found that the model with the ellipsoidal $L$ minima agreed best with reported carrier-dependent mobility-ratio values. Hence, employing isotropic $L$ minima in GaSb conduction-band models, a common assumption when describing the GaSb conduction band, likely results in an underestimation of carrier concentration at room temperature and higher doping levels. This observation could have implications for Raman spectral modeling and any investigation involving the GaSb conduction band, e.g., modeling electrical measurements or calculating electron mobility.