3.2.4 Specific heat

The specific heat capacity $c_{{\mathrm{L}}}$ is modeled by

$$c_{\mathrm{L}}(T_{\mathrm{L}}) = c_{300} + c_1\cdot \frac{\d... ...rm{L}}}{\mathrm{300 K}}\right)^\beta + \frac{c_1}{c_{300}}}}.$$ (3.58)

$c_{300}$ is the value for the specific heat at 300 K [92]. The model is used for the basic materials and for insulators. In Fig. 3.5, Fig. 3.6, and Fig. 3.7 we present comparisons between experimental data and the results obtained with our model for the specific heat. Note the excellent agreement it gives in a wide temperature range (50 K - 800 K). The parameter values used are summarized in Table 3.7.

Table 3.7: Parameter values for the specific heat

Material	$c_{300}$ [J/K kg]	$c_1$ [J/K kg]	$\beta$	Reported $c_{300}$ [J/K kg]	References
Si	711	255	1.85	700	[85]
Ge	360	130	1.3	310	[85]
GaAs	322	50	1.6	350	[85,92]
AlAs	441	50	1.2	490	[92]
InAs	394	50	1.95	394	[92]
InP	410	50	2.05	410	[92]
GaP	519	50	2.6	519	[92]
SiO$_2$	709	696	1.5	1000	[85]
Si$_3$N$_4$	709	820	1.5	800	[98]

The specific heat capacity coefficients for alloy materials are expressed by a linear interpolation between the values of the basic materials (A and B).

$$c_{\mathrm{L}}^{\mathrm {AB}} = \left(1-x\right)\cdot c_{\mathrm{L}}^{\mathrm {A}} + x\cdot c_{\mathrm{L}}^{\mathrm {B}}$$ (3.59)

The specific heat capacity is then expressed by (3.58).

Figure 3.5: Temperature dependence of the specific heat: Comparison between experimental data and the model for Si and Ge

Figure 3.6: Temperature dependence of the specific heat: Comparison between experimental data and the model for GaAs and AlAs

Figure 3.7: Temperature dependence of the specific heat: Comparison between experimental data and the model for SiO$_2$