3.2.9 Direct Generation/Recombination

In semiconductors with a direct band gap such as GaAs, InAs, InP, and GaN and the corresponding direct ternary compounds, direct generation/recombination is very important. This has also been confirmed by numerous optical experiments for HEMTs. The effect is modeled using the following term:

$$R^{DIR} = C^{DIR} \cdot ( n \cdot p - n_i^2)$$ (3.60)

Values for $C^{DIR}$ are compiled in Table 3.24.

Table 3.24: Model parameters for direct recombination at $T_L$= 300 K.

Material	Composition	$C^{DIR}$	References
		[cm$^3$/s]
GaAs	-	1.1e-10	[284]
	-	7.2e-10	[40,300]
	-	1.5e-10	[278]
	-	2e-10	[7]
InAs	-	2.1e-11	[294]
		8.5e-11	[300]
InP	-	1.26e-9	[300]
	-	2e-10	[7]
GaP	-	3.0e-15	[294]
		5.4e-14	[159]
GaN	-	6.6e-10	[224]
Si	-	1.1e-14	[101]
	-	1.8e-15	[159]
Al$_{x}$Ga$_{1-x}$As	0.38	1.4e-10	[8]
In$_{x}$Ga$_{1-x}$As	0.53	4e-10	[123]
In$_{x}$Al$_{1-x}$As	0.52	1.4e-10	-
In$_{x}$Ga$_{1-x}$P	0.5	5e-11	[272]

As several publications have shown [7], the lifetime in AlGaAs is dominated by SRH recombination. For InGaAs the data to determine $C^{DIR}$ is taken from [123]. For InAlAs no experimental data was found, so data from the similar AlGaAs is assumed. For the indirect semiconductor Si and GaP the radiative recombination is relatively more inefficient.