Optical Properties of <i>n</i>-Type GaAs. I. Determination of Hole Diffusion Length from Optical Absorption and Photoluminescence Measurements

Abstract

Hole diffusion lengths L were determined for several Te-doped GaAs crystals with electron concentrations ranging from 2×1016 to 6.5×1018 cm−3. The values of L were obtained by fitting experimental photoluminescence spectra to a theoretical expression which contains the measured absorption coefficients. This expression was derived from radiative recombination statistics, taking into account the reabsorption of emitted photons and the diffusion of minority carriers. The idea used by van Roosbroeck and Shockley of introducing the measured absorption coefficient by means of the principle of detailed balance is shown here to be valid for both nondegenerate and degenerate n-type GaAs. It was found that the hole diffusion lengths are nearly independent of electron concentration n for n &amp;lt; 1×1018 cm−3. This result is attributed to a constant total hole lifetime associated with a nearly constant concentration of ``frozen-in'' defects. For n &amp;gt; 2×1018 cm−3 values for diffusion length decrease rapidly with increasing n. This decrease is attributed to the formation of additional defects associated with donor complexes or precipitates, or both. The diffusion lengths determined in this work are in good agreement with those found by Wittry and Kyser from the electron-beam excitation method but are larger than those obtained by Aukerman et al. from short-circuit current measurements on n-type surface barrier diodes subjected to high-energy electron bombardment.