Infrared Lattice Vibrations and Free-Electron Dispersion in GaN

Infrared reflectivity and absorption measurements have been made on single-crystal epitaxial GaN on (0001) $\alpha -$ ${\mathrm{Al}}_2$ ${\mathrm{O}}_3$ 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 ${\omega }_{\mathrm{TO}}^{\perp }=560\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$ and ${\omega }_{\mathrm{LO}}^{\perp }=746\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$ for the optical mode frequencies at 300 K. Adopting ${\epsilon }_{\infty }^{\perp }=5.35\mathrm{}$ from a fit to Ejder's refractive-index data the additional quantities ${\epsilon }_o^{\perp }=9.5\mathrm{}$ for the static dielectric constant, $e_B^{*\perp }=2.65e$ for the Born effective charge, and ${\alpha }^{\perp }=0.44\mathrm{}$ for the polaron coupling constant are derived. Reflectivity measurements at 50° incidence with $s$ and $p$ polarizations show that the longitudinal lattice mode is nearly isotropic. Using the value ${\omega }_{\mathrm{TO}}^{\parallel }=533\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$ from Raman data the values ${\omega }_{\mathrm{LO}}^{\parallel }=744\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$, ${\epsilon }_o^{\parallel }=10.4\mathrm{}$, $e_B^{*\parallel }=2.82e$, and ${\alpha }^{\parallel }=0.49\mathrm{}$ are obtained from oscillator fits to the 50° 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×${10}^{17}$ to 1×${10}^{20}$ ${\mathrm{cm}}^{-3\mathrm{}}$ range. By fitting the reflectance minima versus concentration data, a value of $\frac{m^{*}}{m}=(0.20\mathrm{}\pm 0.02)$ for the optical effective mass is obtained. Measurements at 50° incidence show that the plasma frequency is isotropic within experimental precision.