Infrared Lattice Vibrations and Free-Electron Dispersion in GaN

Infrared reflectivity and absorption measurements have been made on single-crystal epitaxial GaN on (0001) $\ensuremath{\alpha}\ensuremath{-}$${\mathrm{Al}}_{2}$${\mathrm{O}}_{3}$ crystals. Analysis of the normal-incidence reflectance data on low-carrier-concentration layers using the Kramers-Kronig technique and dielectric oscillator fits yields the values ${\ensuremath{\omega}}_{\mathrm{TO}}^{\ensuremath{\perp}}=560$ ${\mathrm{cm}}^{\ensuremath{-}1}$ and ${\ensuremath{\omega}}_{\mathrm{LO}}^{\ensuremath{\perp}}=746$ ${\mathrm{cm}}^{\ensuremath{-}1}$ for the optical mode frequencies at 300 K. Adopting ${\ensuremath{\epsilon}}_{\ensuremath{\infty}}^{\ensuremath{\perp}}=5.35$ from a fit to Ejder's refractive-index data the additional quantities ${\ensuremath{\epsilon}}_{o}^{\ensuremath{\perp}}=9.5$ for the static dielectric constant, ${e}_{B}^{*\ensuremath{\perp}}=2.65e$ for the Born effective charge, and ${\ensuremath{\alpha}}^{\ensuremath{\perp}}=0.44$ for the polaron coupling constant are derived. Reflectivity measurements at 50\ifmmode^\circ\else\textdegree\fi{} incidence with $s$ and $p$ polarizations show that the longitudinal lattice mode is nearly isotropic. Using the value ${\ensuremath{\omega}}_{\mathrm{TO}}^{\ensuremath{\parallel}}=533$ ${\mathrm{cm}}^{\ensuremath{-}1}$ from Raman data the values ${\ensuremath{\omega}}_{\mathrm{LO}}^{\ensuremath{\parallel}}=744$ ${\mathrm{cm}}^{\ensuremath{-}1}$, ${\ensuremath{\epsilon}}_{o}^{\ensuremath{\parallel}}=10.4$, ${e}_{B}^{*\ensuremath{\parallel}}=2.82e$, and ${\ensuremath{\alpha}}^{\ensuremath{\parallel}}=0.49$ are obtained from oscillator fits to the 50\ifmmode^\circ\else\textdegree\fi{} incidence data. Information on the free-carrier effects in GaN was obtained by studying the normal-incidence reflectance as a function of carrier concentration in the 2\ifmmode\times\else\texttimes\fi{}${10}^{17}$ to 1\ifmmode\times\else\texttimes\fi{}${10}^{20}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ range. By fitting the reflectance minima versus concentration data, a value of $\frac{{m}^{*}}{m}=(0.20\ifmmode\pm\else\textpm\fi{}0.02)$ for the optical effective mass is obtained. Measurements at 50\ifmmode^\circ\else\textdegree\fi{} incidence show that the plasma frequency is isotropic within experimental precision.