Superlinear dependence of gain on current density in GaAs injection lasers

Measurements of threshold-current density and incremental efficiency on homostructure and heterostructure GaAs lasers show an increasingly superlinear dependence of gain <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</tex> on current density <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">J</tex> with increasing temperature. The index <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> in the relation <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g ∝ Jⁿ</tex> satisfies the relation <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n = [1 + (kT/Eₜ)²]1/2</tex> where E <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</inf> is a measure of the band-tail depth.