A1(LO)phonon structure in degenerate InN semiconductor films

Abstract

We have studied the $A_1\left(\mathrm{LO}\right)$ structure of InN thin films from a low $(n_e=6.7\times {10}^{17}∕{\mathrm{cm}}^3)$ to a very high $(n_e=9.6\times {10}^{20}∕{\mathrm{cm}}^3)$ carrier concentration using Raman scattering experiments. Theoretically we investigated this structure using a wave vector $\mathbf{q}$ dependent dielectric function $\epsilon (q,\omega )$ which takes into account the coupling of longitudinal-optical (LO) phonon and degenerate electrons with nonparabolic energy dispersion. Interaction of the phonon and undamped wave-vector-dependent plasmon yields two coupled modes with energies much different from the observed structure and thus cannot explain the origin of this structure. However, phonon interaction with electron-hole pair excitations forms a well-defined structure in $\mathrm{Im}\epsilon {(q,\omega )}^{-1}$ which begins to emerge at smaller values of $\mathbf{q}$ from the electron-hole pairs spectrum when the higher-energy coupled mode becomes Landau damped. With increasing values of $\mathbf{q}$, the peak position of this structure moves towards the experimental value. This peak structure is formed by a comparatively weaker (relative to the plasmon) interaction between the LO-phonon and electron-hole pair excitations. Experimentally it is observed that the energy of this structure increases with increasing value of electron density.