3.2 Material Models

In this section the models are described that define and distinguish the relevant III-V materials used. Using a similar set of parameters AlGaAs/GaAs and InGaP/GaAs HBTs [207] and in a simplified modeling approach pseudomorphic AlGaAs/InGaAs HEMTs have been simulated using MINIMOS-NT[50]. Special effort was made to obtain an extended and more complete set of parameters for a wide range of material compositions and new materials systems. In the modeling concept applied the ternary materials are composed from their binary constituents using a second order interpolation. Table 3.1 shows the naming convention of the ternary materials and the energetic order of the valleys in k-space as a function of material composition. For Al$_x$Ga$_{1-x}$N the investigations are restricted so far to the situation of the $\Gamma$ valley having a direct band gap due to uncertainties in the band structure [103,158], which is sufficient for all technically relevant AlGaN/GaN HEMTs.

Table 3.1: Minimum valley as a function of material composition.

Material	Composition Range	Minimum	Composition Range	Minimum	References
	$x$		$x$
Al$_{x}$Ga$_{1-x}$As	0-0.45	$\Gamma$	0.45-1	X	[250]
In$_{x}$Ga$_{1-x}$As	0-1	$\Gamma$	-	-
In$_{x}$Al$_{1-x}$As	0-0.3	X	0.3-1	$\Gamma$	[113]
Al$_{x}$Ga$_{1-x}$N	0-0.4	$\Gamma$	-	-	[158]