3.2.1 Permittivity

The dielectric constant or relative permittivity $\varepsilon_{\mathrm{r}}^{\mathrm{}}$ is one of the basic properties of semiconductor and insulating materials. The data reported in literature shows minor discrepancies about the values of this parameter (see Table 3.2). The temperature dependence, if any at all, can be neglected. Recently, insulating materials with high dielectric constants (high-$k$ materials) attract much interest as possible replacement of the gate oxide (SiO$_2$) in MOSFETs in order to avoid tunneling gate leakage currents. Table 3.2 includes in addition some of these materials.

Table 3.2: Parameter values for the relative permittivity

Material	Default $\varepsilon_{\mathrm{r}}^{\mathrm{}}$	Reported Range	References
Si	11.9	11.7 - 11.9	[84,85,86]
Ge	16.0	16.0 - 16.2	[85,86]
GaAs	13.1	12.9 - 13.18	[87,88,73,89]
AlAs	10.1	10.06 - 10.1	[90,91,89,92,93]
InAs	14.6	14.55 - 15.15	[88,73,93,94]
InP	12.4	12.35 - 12.61	[95,96,93,94]
GaP	11.1	11.1	[73,90,91]
SiO$_2$	3.9	3.75 - 3.9	[97,86]
Si$_3$N$_4$	7.4	6.0 - 8.0	[98,86]
BaSrTiO$_3$	200.0	60.0 - 300.0	[99,100,101]
Ta$_2$O$_5$	30.0	20.0 - 75.0	[99,100]
TiO$_2$	20.0	4.0 - 100.0	[99,100]
Al$_2$O$_3$	9.8	8.5 - 13.0	[100,101]

The permittivities of alloy materials $\mathrm{A}_{1-x}\mathrm{B}_{x}$ are interpolated from the values of the basic materials as a quadratic function of $x$ [73].

$$\varepsilon_{\mathrm{r}}^{\mathrm{AB}} = \left(1-x\right)\cd... ...r}}^{\mathrm{B}} + x\cdot\left(1-x\right)\cdot C_\varepsilon$$ (3.53)

$C_\varepsilon$ is referred to as a nonlinear or bowing parameter. Setting $C_\varepsilon =0$ yields a linear interpolation. The parameters used in this model are summarized in Table 3.3.

Table 3.3: Parameter values for the permittivity bowing factor

Material	$C_\varepsilon$	Reported Range	References
SiGe	0.0
AlGaAs	0.0
InGaAs	-1.0	13.1-14.1	[102,93] x=0.53
InAlAs	-1.0	12.46	[102] x=0.52
InAsP	0.0
GaAsP	0.0
InGaP	0.0	11.75	[103] x=0.51