3.2.5.5 Alternative High Field Mobility Model

To clarify the interaction of the model and model parameters a second variant of the high field mobility is supplied. (3.49) is a variant of the Hänsch model, used e.g. in [178]. The formula reads:

$$\mu^{LIT}(T_\nu) =  \frac{\mu^{LI}_{\nu}} {\displaystyle \bigg( 1... ...T}_\mathrm{L}\big) ^ {\frac{1}{\beta}}\bigg)^{\beta}},   \text{where}  \nu= n,p$$ (3.46)

In this approach an additional parameter $\beta$ is introduced as demonstrated in HEMT simulations in [50]. It was used with constant energy relaxation times and the parameter $\beta$ allows to match static overshoot effects obtained by MC simulation in the channel. This stresses the interaction of the high field parameters obtained within one model. Section 3.6 shows the acquisition of high field parameters when using the DD, the HD approach in (3.49), and a HD approach using (3.46) and (3.48) with non-constant energy relaxation times. Physical effects such as static velocity overshoot can be introduced with the different high field mobility concepts. Under no circumstances the parameters can be mixed, once calibrated for an particular approach. Furthermore, each approach supplies a different amount of information. E.g., the ${\it V}_{\mathrm{DS}}$ bias dependence of the channel velocities under no circumstances can be fit with the DD approach. However, using ${\it v}_{{sat}}$ and $\beta$ in (3.43) as fitting parameters, agreement of the channel velocities can be obtained for one bias, as was shown by Bude et al. in [54].