4.2.4 Specific Heat

The lattice specific heat $c_\ensuremath{\mathrm{L}}$ is modeled by the following expression proposed in [305]:

$$c_\ensuremath{\mathrm{L}}(\ensuremath{T_{\mathrm{L}}}) = c_\ensur... ...uremath{\mathrm{K}}}\right)^\beta + \frac{c_1}{c_\ensuremath{\mathrm{L,300}}}},$$

where $c_\ensuremath{\mathrm{L,300}}$ is the value of the specific heat at 300 K and $c_1$ and $\beta$ are fitting parameters. Fig. 4.6 shows a comparison between the calibrated model (values are listed in Table 4.5) and measurements as a function of temperature for GaN. The results both of Kremer et al. [309] and Danilchenko et al. [310] are from bulk wurtzite GaN while most previous measurements were conducted on polycrystalline powder samples. Our model is calibrated against the model of Danilchenko et al., which is in excellent agreement with their own measurements for the heat capacity in the 0 K$-$300 K range and also with experimental results given in [309].

Figure 4.6: GaN specific heat as a function of lattice temperature.

Table 4.5: Parameter values for the specific heat model.

Material	$c_{300}$	$c_1$	$\beta$
	[J/ kg K]	[J/ kg K]
GaN	431	171	1.75
AlN	748	482	2.29
InN	296	108	1.5

The parameter values for AlN are based on the summarized results in [138].

For the heat capacity of InN several works are based on the experimental data provided by Krukowski et al. [302]. Their results are shown in Fig. 4.7 together with the models of Leitner et al. [311] and Zieborak et al. [312], which both provide models based on measurement results. In the present work the model is calibrated against the data in [311].

Figure 4.7: InN specific heat as a function of lattice temperature.

The specific heat coefficients for alloy materials are expressed by a linear interpolation between the values of the binary materials [305]:

$$c_\ensuremath{\mathrm{L}}^\ensuremath{\mathrm{ABC}}=(1-x)c_\ensur... ...ensuremath{\mathrm{AC}} + x c_\ensuremath{\mathrm{L}}^\ensuremath{\mathrm{BC}}.$$