Free-carrier and phonon properties of n- and p-type hexagonal GaN films measured by infrared ellipsometry

Abstract

Infrared spectroscopic ellipsometry (IRSE) over the wave-number range from 300 to 1200 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ is used to determine the anisotropic room-temperature optical properties of highly resistive, Si-doped n-type and Mg-doped p-type \ensuremath{\alpha}-GaN. The approximately 1-\ensuremath{\mu}m-thick films were deposited on c-plane sapphire by molecular beam epitaxy without a buffer layer. The free-carrier concentrations are obtained from Hall measurements. The IRSE data are analyzed through model calculations of the infrared optical dielectric functions parallel (\ensuremath{\parallel}) and perpendicular (\ensuremath{\perp}) to the c axis of the \ensuremath{\alpha}-GaN films. We obtain the thin-film phonon frequencies and broadening values and the optical mobility and effective-mass parameters for n- and p-type \ensuremath{\alpha}-GaN. In agreement with Perlin et al. [Appl. Phys. Lett. 68, 1114 (1996)] we determine the effective electron masses as ${m}_{e,\ensuremath{\perp}}{/m}_{0}=0.237\ifmmode\pm\else\textpm\fi{}0.006$ and ${m}_{e,\ensuremath{\parallel}}{/m}_{0}=0.228\ifmmode\pm\else\textpm\fi{}0.008.$ For p-type GaN with hole concentration ${N}_{h}=8\ifmmode\times\else\texttimes\fi{}{10}^{17}{\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$ we find ${m}_{h}{/m}_{0}=1.40\ifmmode\pm\else\textpm\fi{}0.33,$ which agrees with recent theoretical studies of the Rashba-Sheka-Pikus parameters in wurtzite GaN. However, no substantial anisotropy of the effective hole mass is obtained to within 25%. The ellipsometry data also allow for derivation of the model quantities ${\ensuremath{\epsilon}}_{\ensuremath{\infty},j}$ $(j=\ensuremath{\perp},\ensuremath{\parallel}),$ which are almost isotropic but may vary between 4.92 and 5.37 depending on whether the films are undoped or doped. In heavily-Si-doped n-type \ensuremath{\alpha}-GaN we observe a thin carrier-depleted surface layer and additional infrared-active vibrational modes at 574, 746, and 851 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$. Raman measurements of the GaN films are also performed, and the results are compared to those obtained from the IRSE investigations.