Band-to-band auger effect in long wavelength multinary III-V alloy semiconductor lasers

Abstract

Band-to-band Auger effects and radiative recombination rates are theoretically compared for long wavelength multinary III-V compound semiconductor lasers. Stern's band model and matrix element are used for the calculation of gain coefficient and radiative recombination rate. Overlap integrals for Auger processes are obtained by a <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k \cdot p</tex> perturbation method. Approximate statistical weight function is used, which includes the weakly degenerate effect. It is found that the Auger effect involving excited split-off band (CHSH process) is dominant when bandgap E <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</inf> is greater than split-off gap Δ, while the Auger effect involving excited conduction band (CHCC process) predominates over others when <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E_{g} &lt; \Delta</tex> . When E <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</inf> is comparable to or slightly larger than Δ, the total Auger effect is weak and the quantum efficiency is recovered. This explains the experimentally reported low threshold current in AlGaAsSb and GaInAsSb lasers at about 1.8 μm. In all the possible III-V lasers, the quantum efficiency is reduced to less than 5 percent for wavelengths <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\lambda &gt; 2.2 \mu</tex> m at room temperature and for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\lambda &gt; 4.4 \mu</tex> m at 77 K, respectively. The calculated values of Auger currents include an error of factor two or three, mainly caused by the ambiguity in band parameters.