3.2.4 Effective Density of States

The effective density of states are modeled according (3.33) and (3.34):

$$N_C = 2 \cdot M_C \bigg( \frac{2\pi \cdot m_n \cdot {\it k}_{\mathrm{B}}\cdot {\it T}_\mathrm{L}}{h^2}\bigg)^{3/2}$$ (3.32)

$$N_V = 2 \cdot \bigg( \frac{2\pi \cdot m_p\cdot {\it k}_{\mathrm{B}}\cdot {\it T}_\mathrm{L}}{h^2}\bigg)^{3/2}$$ (3.33)

where $M_C$ is the number of the equivalent energy minima. Table 3.12 gives the values of $M_C$ for the binary semiconductors. For the ternary semiconductors $M_C^{AB}$ is composed using the effective masses. For the transition between an indirect to a direct semiconductor ternary alloy (in a HEMT e.g. for Al$_x$Ga$_{1-x}$As with x= 0.45), the following equation is used:

$$M_C^{AB} = M_C^A \cdot \exp \bigg(- \frac{E^{AB}}{{\it k}_{\mathr... ...\frac{E^{AB}}{{\it k}_{\mathrm{B}}\cdot {\it T}_\mathrm{L}}\cdot x \bigg)\bigg)$$ (3.34)

Table 3.12: Model parameters for effective density of states for basic semiconductors.

Material	Valley	M$_C$	References
GaAs	$\Gamma$	1	-
AlAs	X	3	-
InAs	$\Gamma$	1	-
InP	$\Gamma$	1	-
GaN	$\Gamma$	1	[38]
AlN	$\Gamma$	1	[204]
InN	$\Gamma$	1	[203]
Si	X	6	-