3.2.2 Permittivity

The parameters for the permittivity model at ${\it T}_\mathrm{L}$= 300 K of MINIMOS-NT are summarized in Table 3.3. As for most of the parameters, there is a range of values indicated in the data compilations to allow the evaluation of the stability of the default value. For ternary alloys the permittivity is modeled as a function of the material composition:

$$\varepsilon_{r}^{AB} = x \cdot \varepsilon_r^{A} + (1-x) \cdot \varepsilon_r^{B}+(1-x)\cdot x \cdot C_{\varepsilon}$$ (3.20)

For ternary semiconductors typical values are also found in Table 3.4. For the quaternary material In$_x$Al$_{y}$Ga$_{1-y}$As is composed from the ternary constituents from values obtained for the ternary materials in Table 3.3.

Table 3.3: Relative static permittivity parameter values for binary semiconductors and insulators.

Material	$\varepsilon_{r}$	Reported Range	References
GaAs	13.1	12.5-13.18	[4,42,194]
AlAs	10.1	10.0-10.06	[4,265]
InAs	14.60	14.55-15.5	[3,52,91]
InP	12.4	12.3-12.61	[3,85]
In$_{0.52}$Al$_{0.48}$As	12.46	-	[118,163]
Al$_{0.51}$Ga$_{0.49}$As	11.63	-	[118]
GaN	9.7	10.4 $\parallel$ c-axis, 9.5 $\perp$ c-axis, 8.9	[89,294]
AlN	8.5	-	[89]
InN	13.52	13.52-15.3	[89,203]
Si	11.9	11.8	[194,284]
SiN$_x$	7.0	6.2-7.5	[194,284]
SiO$_2$	3.9	-	[194]
Al$_{2}$O$_3$ (sapphire)	9.8	9.3-9.8	[173]
BCB	2.6	2.65	[61]
BeO (Berryllia)	6.5	-	[173]
SiC 6H	9.66 $\parallel$ c, 10.3 $\perp$ c	-	[114]
Diamond	5.7	-	[73]

Table 3.4: Relative static permittivity parameters for ternary alloys.

Material	C $_{\varepsilon}$	$\varepsilon_{r}^{AB}$	Reported Range	References
Al$_{x}$Ga$_{1-x}$As	0	-	-	[4]
In$_{x}$Ga$_{1-x}$As	-1	13.1 ( $x$=0.53)	13.94	[3,163]
In$_{x}$Al$_{1-x}$As	-1	12.46 ($x$=0.52)	-	[163]
Al$_{x}$Ga$_{1-x}$N	0	-	-	[89]
In$_{x}$Ga$_{1-x}$N	0	-	-	[89]
In$_{0.52}$Al$_{x}$Ga$_{1-x}$As	0	-	-	[119]