Free-carrier and phonon properties ofn- andp-type hexagonal GaN films measured by infrared ellipsometry

Infrared spectroscopic ellipsometry (IRSE) over the wave-number range from 300 to 1200 ${\mathrm{cm}}^{\mathrm{-}1}$ is used to determine the anisotropic room-temperature optical properties of highly resistive, Si-doped n-type and Mg-doped p-type α-GaN. The approximately 1-μm-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 (∥) and perpendicular (⊥) to the c axis of the α-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 α-GaN. In agreement with Perlin et al. [Appl. Phys. Lett. 68, 1114 (1996)] we determine the effective electron masses as $m_{e,\perp }{/m}_0=0.237\mathrm{}\pm 0.006$ and $m_{e,\parallel }{/m}_0=0.228\mathrm{}\pm \mathrm{0.008.}$ For p-type GaN with hole concentration $N_h=8\mathrm{}\times {10}^{17}{\mathrm{cm}}^{\mathrm{-}3}$ we find $m_h{/m}_0=1.40\mathrm{}\pm 0.33,$ 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 ${\epsilon }_{\infty ,j}$ $(j=\perp ,\parallel ),$ 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 α-GaN we observe a thin carrier-depleted surface layer and additional infrared-active vibrational modes at 574, 746, and 851 ${\mathrm{cm}}^{\mathrm{-}1}$. Raman measurements of the GaN films are also performed, and the results are compared to those obtained from the IRSE investigations.