Quantum Efficiency and Radiative Lifetime of the Band-to-Band Recombination in Heavily Doped<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>n</mml:mi></mml:math>-Type GaAs

Abstract

The dependence of the absolute internal quantum efficiency and the radiative lifetime of the band-to-band recombination on the impurity concentration for melt-grown heavily doped $n$-type GaAs crystals have been determined from measurements of photoluminescence and optical-absorption spectra, the excess-carrier lifetime, and the external efficiency. It is shown that the observed external efficiency at 2\ifmmode\times\else\texttimes\fi{}${10}^{18}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ is determined by the combined effects of the position and slope of the absorption edge, the hole lifetime, the surface loss, and the photon reabsorption of the emitted radiation. The radiative lifetime exhibits a minimum at 1.5\ifmmode\times\else\texttimes\fi{}${10}^{18}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ because of the effects of the impurity on the slope and position of the absorption edge. This is in contrast to the case of lightly doped nondegenerate crystals in which the radiative lifetime is inversely proportional to the impurity concentration.