Infrared Lattice Vibrations and Free-Electron Dispersion in GaN

Infrared reflectivity and absorption measurements have been made on single-crystal epitaxial GaN on (0001) α-Al₂O₃ 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 ω_TO^⊥=560 cm^-1 and ω_LO^⊥=746 cm^-1 for the optical mode frequencies at 300 K. Adopting ε_∞^⊥=5.35 from a fit to Ejder's refractive-index data the additional quantities ε_o^⊥=9.5 for the static dielectric constant, e_B^*⊥=2.65e for the Born effective charge, and α^⊥=0.44 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 ω_TO^∥=533 cm^-1 from Raman data the values ω_LO^∥=744 cm^-1, ε_o^∥=10.4, e_B^*∥=2.82e, and α^∥=0.49 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 2×10¹⁷ to 1×10²⁰ cm^-3 range. By fitting the reflectance minima versus concentration data, a value of m^*/m=(0.20±0.02) for the optical effective mass is obtained. Measurements at 50° incidence show that the plasma frequency is isotropic within experimental precision.