 Solution

The broad feature has the scale expected for a carrier plasmon, a longitudinal collective oscillation of the mobile electron density. Using the parameters just estimated and $N=10^{24}{\mathrm{m}}^{-3}$ givesConversely a bare screened plasma oscillation at $340{\mathrm{cm}}^{-1}$ would require $N\simeq 1.16\times 10^{18}{\mathrm{cm}}^{-3}$ for the same parameters, consistent with the source's approximate density. Its broadness is also consistent with carrier damping, unlike the much sharper lattice line near $270{\mathrm{cm}}^{-1}$.

This identifies a plasmon-related feature, not a uniquely determined undamped pure electronic mode. Gallium arsenide is polar, and its longitudinal optical phonon couples to the carrier plasmon. A more complete dielectric model has longitudinal eigenfrequenciesThe measured Raman scattering maximum can also shift with damping and the scattering matrix elements. Experimental Raman scattering from these coupled modes and carrier-collision broadening is established independently.^[ref] The supplied approximate density and one broad spectrum do not determine a unique coupled-mode fit. Treating $340{\mathrm{cm}}^{-1}$ as an exact pure-plasmon eigenfrequency would overstate the available information.