The Boltzmann distribution of carriers, applicable to the high-energy part of the emission spectrum, results in an exponential dependence of the emission intensity on energy, i. e.

I к exp [-hvl(kTc) (6.1)

where Tc is the carrier temperature. The high-energy slope of the spectrum is given by

d(lnI)

-1

(6.2)

d(hv)

Thus, the carrier temperature can be directly inferred from the slope. Because the carrier temperature is generally higher than the junction temperature, e. g. due to high-energy injection of carriers into the active region, this method gives an upper limit for the actual junction temperature.

Semiconductor alloys exhibit substantial broadening of the emission spectrum (and its high- energy slope) due to alloy broadening, i. e. the statistical fluctuation of the chemical composition occurring in ternary and quaternary semiconductors (Schubert et al., 1984). De-convolution of the alloy-broadening effect and the kT-broadening effect allows for a more accurate estimate of the carrier temperature.

The determination of the carrier temperature using the high-energy slope works best for binary compounds such as GaAs or InP. Such semiconductors do not exhibit alloy broadening and thus the high-energy slope is more representative of the true carrier temperature.