4.2.1 Permittivity

The dielectric constant of the three materials GaN, InN, and AlN is discussed in Section 3.2, Section 3.3, and Section 3.4, respectively. Here, the range of the reported values is shown in Table 4.2. The values used for the static permittivity for GaN, AlN, and InN are 8.9, 8.5, and 15.3, respectively.

Table 4.2: Model parameters for the static permittivity.

	GaN	AlN	InN	References
range	8.5-10.4	8.5	11.0-15.3	[284,285,176,222]
used	8.9	8.5	15.3

The permittivity of a ternary semiconductor alloy A$_x$B$_{1-x}$C depending on the material composition $x$ is interpolated by a quadratic function of the permittivities of the basic materials $\varepsilon_\ensuremath{\mathrm{s}}^\ensuremath{\mathrm{AC}}$ and $\varepsilon_\ensuremath{\mathrm{s}}^\ensuremath{\mathrm{BC}}$ [286]:

$$\varepsilon_\ensuremath{\mathrm{s}}^\ensuremath{\mathrm{ABC}}=(1-... ...h{\mathrm{AC}} + x \varepsilon_\ensuremath{\mathrm{s}}^\ensuremath{\mathrm{BC}}$$ (4.64)

A linear interpolation is used for the three ternaries [287,288].