Infrared Lattice Vibrations and Free-Electron Dispersion in GaN

TLDR

Infrared reflectivity and absorption measurements on single‑crystal epitaxial GaN on sapphire were used to probe lattice vibrations and to study free‑carrier effects across a carrier concentration range of 2×10¹⁷–1×10²⁰ cm⁻³. The reflectance analysis determined the transverse and longitudinal optical phonon frequencies, static dielectric constants, Born effective charges, and polaron coupling constants for both polarizations, found the longitudinal lattice and plasma frequencies to be isotropic, and measured an optical effective mass of 0.20 m.

Abstract

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.