4.8 Compact Models

Several compact modeling approaches have been suggested to describe impact ionization within a device, mostly applied to InAlAs/InGaAs devices. In [75,271,270] a gate current analysis is given, which suggests the following model: the gate current ${\it I}_{\mathrm{G}}$ is composed of a thermionic field emission and an impact ionization component.

$${\it I}_{\mathrm{G}} = I_\mathrm {II}+ I_\mathrm {TFE}$$ (4.31)

The impact ionization contribution was fitted to the following term:

$$I_\mathrm {II} = A \cdot {\it I}_{\mathrm{D}}\exp \cdot \bigg( \frac{-B}{{\it V}_{\mathrm{GD}}-{\it V}_{\mathrm{T}}} \bigg)$$ (4.32)

The thermionic contribution was calculated according to the model [270]:

$$I_\mathrm {TFE} \propto \int \frac{E_\mathrm {gate}^2(x)}{m^* \phi_B} \exp \bigg(\propto -\frac{\sqrt{m^* \phi_B^3}}{E_\mathrm {gate}(x)}\bigg) dx$$ (4.33)

$A$ and $B$ are fit parameters and $E_\mathrm {gate}$ represents an effective field at the gate. In [19] another compact model was demonstrated including physical geometries for the evaluation of gate currents and breakdown voltages in InAlAs/InGaAs HEMTs. In [20,230] it is mentioned that in a simple macroscopic exponential model for impact ionization the coefficients obtained from bulk impact ionization experiments could not be verified fitting gate currents. To understand these discrepancies the information on the interaction of impact ionization with temperature, the other generation/recombination mechanisms, the geometry aspect, and the complete information of the energy distribution of the carriers must be considered in device simulation.