Infrared studies of hole-plasmon excitations in heavily-doped p-type MBE-grown GaAs:C

Abstract

Infrared reflectivity measurements (200--5000 ${\mathrm{cm}}^{\ensuremath{-}1})$ and transmittance measurements (500--5000 ${\mathrm{cm}}^{\ensuremath{-}1})$ have been carried out on heavily-doped GaAs:C films grown by molecular-beam epitaxy. With increasing carbon concentration, a broad reflectivity minimum develops in the 1000--3000 ${\mathrm{cm}}^{\ensuremath{-}1}$ region and the one-phonon band near 270 ${\mathrm{cm}}^{\ensuremath{-}1}$ rides on a progressively increasing high-reflectivity background. An effective-plasmon/one-phonon dielectric function with only two free parameters (plasma frequency ${\ensuremath{\omega}}_{p}$ and damping constant $\ensuremath{\gamma})$ gives a good description of the main features of both the reflectivity and transmittance spectra. The dependence of ${\ensuremath{\omega}}_{p}^{2}$ on hole concentration $p$ is linear; at $p=1.4\ifmmode\times\else\texttimes\fi{}{10}^{20}$ ${\mathrm{cm}}^{\ensuremath{-}3},$ ${\ensuremath{\omega}}_{p}$ is 2150 ${\mathrm{cm}}^{\ensuremath{-}1}.$ At each doping, the damping constant $\ensuremath{\gamma}$ is large and corresponds to an infrared hole mobility that is about half the Hall mobility. Secondary-ion mass spectroscopy and localized-vibrational-mode measurements indicate that the Hall-derived $p$ is close to the carbon concentration and that the Hall factor is close to unity, so that the Hall mobility provides a good estimate of actual dc mobility. The observed dichotomy between the dc and infrared mobilities is real, not a statistical-averaging artifact. The explanation of the small infrared mobility resides in the influence of intervalence-band absorption on the effective-plasmon damping, which operationally determines that mobility. This is revealed by a comparison of the infrared absorption results to Braunstein's low-$p$ $p$-GaAs spectra and to a $\mathbf{k}\mathbf{\ensuremath{\cdot}}\mathbf{p}$ calculation extending Kane's theory to our high dopings. For $n$-GaAs, which lacks infrared interband absorption, the dc and infrared mobilities do not differ.