Theoretical and experimental results for<i>p</i>-type GaAs electrolyte electroreflectance

Abstract

The intermediate-field (effective-mass) theory is used to predict the electroreflectance of p-type GaAs as a function of space-charge voltage and dopant density. The effect of the inhomogeneous electric field in the space-charge layer is included by modeling as reflection from a series of thin films, and the transition oscillator strength is determined by comparison with the published optical properties of GaAs. The extent of thermal broadening is determined by comparison with experimental electrolyte electroreflectance (EER) spectra which were measured for 2\ifmmode\times\else\texttimes\fi{}${10}^{16}$, 7\ifmmode\times\else\texttimes\fi{}${10}^{16}$, 4\ifmmode\times\else\texttimes\fi{}${10}^{17}$, and 2\ifmmode\times\else\texttimes\fi{}${10}^{18}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$ doped p-type GaAs in 0.5M ${\mathrm{H}}_{2}$${\mathrm{SO}}_{4}$(aq) and 1.0M KOH(aq) by holding the electrodes at a dc potential and adding an ac modulation of 15 mV. Agreement with theory is sufficiently good for us to be able to measure the space-charge voltage in electrodes by comparison of experimental EER line shapes with theory and thereby to deduce the presence of partial Fermi-level pinning in the 7\ifmmode\times\else\texttimes\fi{}${10}^{16}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$ samples which we measured, an interpretation that was supported by the unusually unstable impedance behavior of electrodes made from this crystal.