The thermal conductivity is modeled by a power law:
For AlN the variation of the measured values for the thermal conductivity is smaller (Fig. 4.2). We assume =350 W/mK, which is close to the value reported in . The parameter , which models the decrease with temperature, is calibrated against measured data [299,300,301].
As of today no studies of the temperature dependent thermal conductivity of InN are available. Based on  a =176 W/mK at 300 K is assumed. This is a theoretical estimation, while the measured value was only 45 W/mK due to phonon scattering by point-defects and grain-boundaries.
Several expressions exist for the thermal conductivity
of semiconductor alloys. As an example, Adachi et al.  use
one based on Abeles's complex model . However, an even more
straightforward approach is proposed in , where a harmonic
mean is used to model the conductivity at 300 K, while the exponent
is linearly interpolated as there is no experimental data for
temperatures other than 300 K yet:
For InGaN =1.5 W/mK is adopted, again matching the model in  (Fig. 4.4) and the experimental data of Pantha et al. . For InAlN a fit to the only available experimental data  resulted in an =1.2 W/mK (Fig. 4.5).