Temperature dependence of emission efficiency and lasing threshold in laser diodes

Abstract

It is found that in GaAs <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-x</inf> P <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</inf> injection lasers both the spontaneous emission efficiency η and the laser threshold <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">j</tex> vary exponentially with the temperature <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T: \eta = \eta_{0} \exp(-T/\theta_{1})</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">j = j_{0} \exp(T/\theta_{2})</tex> . θ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> and θ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> are usually nearly equal and range between 50 and 110°K. The behavior of the external efficiency is correlated with the temperature dependence of the absorption along the propagation path of the radiation: as the temperature increases, the exponential absorption edge shifts to lower energies faster than the emission peak. The difference between the two shifts is nearly linear with temperature. The effect of self-absorption on external efficiency was tested by measuring the light emitted transversely to the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p-n</tex> junction through a layer of constant thickness. With such a geometry, it is shown that the efficiency should vary as <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\exp [-A \exp (T/\theta)]</tex> . The experiment agrees with this prediction.