3.2.1 Bandgap-Energy

It has been reported that the photoluminescence measurements yielded an exciton energy gap $E_\mathrm{gx}$ of 3.265 eV [112] and 3.023 eV [116] at T = 4.2 K for 4H- and 6H-SiC, respectively. The absorption measurements value obtained for $\alpha$-SiC (most likely 6H-SiC) yield the temperature dependence of $E_\mathrm{gx}$ 2.6 eV to 3.03 eV at temperatures from 77K to 717K [116]. The minimum energy gap is found to be 2.86 eV at 300 K, and above this temperature d $E_{\mathrm{g}}$/d $T_\mathrm{L}=-3.3\times 10^{-4}$ ev/K.

The temperature dependence of 4H-SiC is assumed to be similar to the temperature dependence of 6H-SiC as long as no further experimental data is available. At present there are no reliably measured values about the binding energy $E_{x}$ of free exciton in any $\alpha$-SiC polytype [117]. The values, however, required in order to obtain the indirect bandgap, which is given by

$$E_{\mathrm{g}}= E_\mathrm{gx}+E_\mathrm{x}.$$ (3.63)

Results obtained by comparing experimental data with a theory claim the values of $E_\mathrm{x}$ range from 10-80 meV [117]. Hence, a mean indirect bandgap can be assumed by shifting $E_\mathrm{gx}$ by 20 meV and 40 meV for 4H- and 6H-SiC, respectively. These measured data for two different temperature ranges can be piecewise modeled by

$$E_{\mathrm{g}}(T)=E_{\mathrm{g}}^{T_{0}}-\alpha ^{E_{\mathrm{g}}}\cdot\frac{T_\mathrm{L}^{2}}{\beta ^{E_{\mathrm{g}}}+T_\mathrm{L}}\,.$$ (3.64)

Fig. 3.5 depicts the resulting temperature dependence of the bandgap energy in $\alpha$-SiC.

Table 3.2: Temperature dependent measured exciton energy gap in $\alpha$-SiC.

	$E_{g}^{T_{0}}$ [eV]	$\alpha ^{E_{g}}$ [eV/K]	$\beta ^{E_{g}}$ [K]	$T_\mathrm{L}$ [K]
4H-SiC	$3.265$	$3.3\times 10^{-2}$	$1.0\times 10^{5}$	$4-700$
6H-SiC	$3.023$	$3.3\times 10^{-2}$	$1.0\times 10^{5}$	$4-700$

Figure 3.5: Temperature dependence of bandgap energy in $\alpha$-SiC.

T. Ayalew: SiC Semiconductor Devices Technology, Modeling, and Simulation