3.2.10 Auger Generation/Recombination

The Auger generation/recombination processes are one subclass of the three particle processes. The related three particle process impact ionization is discussed in the next section. For HEMTs Auger effects are discussed in relation to the Off-state breakdown [25]. The band-to-band Auger recombination/generation rate R$^{Au}$ is modeled according to (3.64).

$$R^{Au} = (C^{Au}_n \cdot n + C^{Au}_p \cdot p) \cdot ( n \cdot p - n_i^2)$$ (3.61)

Parameter values can be found in Table 3.25. The carrier concentrations prevailing for the values reported are also given. Comparing different direct III-V semiconductor materials Auger coefficients $C_\nu^{Au}$ increase for decreasing band gap as was shown by Riech et al. in [231]. The temperature dependence of the coefficients in Silicon [126] can e.g. be fitted by a simple power law with $\alpha$= 0.5-0.6 using:

$$C^{Au}_{\nu}({\it T}_\mathrm{L}) = C^{Au} _{\nu,300K} \cdot \bigg(\frac{{\it T}_\mathrm{L}}{300 K} \bigg)^{\alpha}$$ (3.62)

For III-V semiconductors most of the data is available for ${\it T}_\mathrm{L}$= 300 K, which is compiled in Table 3.25. For AlGaAs a material dependent model is presented in [286] as a function of temperature. A behaviour similar to Si of $C^{Au}_\nu$ is found in AlGaAs. However, the temperature dependence cannot be generalized as a material property alone due to the different underlying band-to-band process. For quantum wells, as indicated by the distinction made for In$_{0.53}$Ga$_{0.47}$As, the rates are significantly modified depending on the thickness of the quantum well (QW). The value given is determined for a 11 nm wide well [254]. Further a consistent calculation is given [100], that supplies the material dependence as a function of In content.

Table 3.25: Model parameters for Auger generation/recombination at $T_L$= 300 K.

Material	Composition	$C^{Au}_n$	$C^{Au}_p$	n,p	References
	x	[cm$^6$/s]	[cm$^6$/s]	[cm$^{-3}$]
GaAs	-	2-6e-30	1.6e-29	p: 1e19	[231,295]
	-	-	4e-30	-	[35]
InAs	-	-	2.2e-27	-	[231]
		1e-26	-	-	[231]
		3e-27	-	-	[99]
InP	-	1.7e-33	9·10-31	-	[99]
AlGaAs	0	1.9e-31	12e-31	5e18	[286]
	0.1	1.2e-31	8.5e-31	5e18	[286]
	0.2	0.7e-31	6.1e-31	5e18	[286]
In$_{0.53}$Ga$_{0.47}$As (QW)	-	7-9e-29	-	1.9e18	[254]
In$_{0.53}$Ga$_{0.47}$As (bulk)	-	2e-27	-	1.9e18	[254]
In$_x$Ga$_{1-x}$As	0	-	6.5e-30	degenerate	[100]
In$_x$Ga$_{1-x}$As	0.1	-	1.5e-29	degenerate	[100]
In$_x$Ga$_{1-x}$As	0.2	-	3.6e-29	degenerate	[100]
In$_x$Ga$_{1-x}$As	0.5	-	3.8e-29	degenerate	[100]
In$_x$Ga$_{1-x}$As	1	-	2.2e-27	degenerate	[100]
InAlAs	0.52	1.4-3e-28	-	-	[183]
GaN	-	1e-30	1e-31	-	[58]
Si	-	1e-31	2.28e-31	-	[265]
		3.7e-31		nid	[126]