The thermal conductivity is modeled by a power law:

where is the value at 300 K. From early experiments =130 W/mK for ``bulk'' GaN [292] was extracted. However, later measurements of epitaxial structures yielded higher values [293], and a strong dependence on the dislocation density was observed [294]. Based on various studies [292,293,295,296,297,298] we give two parameter sets in Table 4.4, applicable for different material quality. Fig. 4.1 compares the two model sets with other models and experimental data.

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 [299]. 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 [302] 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.* [303] use
one based on Abeles's complex model [304]. However, an even more
straightforward approach is proposed in [305], 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:

Applying this expressions, a value of 3.1 W/mK is adopted for of AlGaN. This results in a fair agreement with the experimental data of Daly

For InGaN =1.5 W/mK is adopted, again matching
the model in [303] (Fig. 4.4) and the
experimental data of Pantha *et al.* [307]. For
InAlN a fit to the only available experimental data
[308] resulted in an =1.2 W/mK
(Fig. 4.5).

S. Vitanov: Simulation of High Electron Mobility Transistors