Effect of band shapes on carrier distribution at high temperature

This paper indicates both experimentally and graphically how the distribution of carriers changes above a critical temperature T
c
, which is related to the density of states ρ in the band tails. Thus,
kT_{c} = E_{0}
, where
\rho = \rho_{0} \exp (\DeltaE/E_{0}
). The emission spectrum shifts with changing excitation (band filling) at lower temperatures (
T < T_{c}
) and stays at a constant value independent of excitation at higher temperatures (
T > T_{c}
). Experimental results of photoluminescence studies with GaAs crystals show that the quantity E
0
, obtained from the dependence of the peak energy upon the degree of excitation is the same as the quantity
kT'_{c}
, obtained from the dependence of the peak energy upon temperature. This is in agreements with the analysis. For lasing diodes, the threshold will increase steeply with increasing temperature above T
c
, if the excited carriers are located mostly in the exponential states of the band tail.
E_{0} = (10 \sim 20)
meV and T
c
= (
120 \sim 250\deg
K) are typical for crystals of heavily compensated GaAs.