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
g
on current density
J
with increasing temperature. The index
n
in the relation
g \propto J^{n}
satisfies the relation
n = [1 + (kT/E_{t})^{2}]^{1/2}
where E
t
is a measure of the band-tail depth.