Carrier temperature and high-energy slope of spectrum
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
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.
Figure 6.1 shows the evaluation of the carrier temperature from the emission spectrum of a GaInN and an AlGaInP LED (Chhajed et al., 2005; Gessmann et al., 2003). Inspection of the figure reveals that the carrier temperature increases along with the current level. At low current levels, the GaInN device has a carrier temperature of 221 °C and the AlGaInP device has a carrier temperature of 212 °C. At high current levels, the carrier temperature increases to 415 °C and 235 °C for the GaInN and AlGaInP LED, respectively. Due to the alloy-broadening effect occurring in ternary and quaternary semiconductor alloys, these temperatures overestimate the true carrier 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.