3.4.4 High-Field Mobility for DD Equations

In the case of Si the mobility reduction due to a high field is modeled by

$$\mu^{\mathrm{LISF}}_{\nu} = \frac{2\cdot\mu^{\mathrm{LIS}}_{\nu}} {1+\left(1+ \displaystyle{\... ...F_{\nu}} {v^{\mathrm{sat}}_{\nu}}\right)}^{\beta_{\nu}}\right)^{1/\beta_{\nu}}}$$ (3.124)

$$F_{\nu} = \left\vert {\rm grad} \psi + \frac{s_\nu}{\nu}\cdot {\rm grad} {\left(U_{T\nu}\cdot \nu\right)}\right\vert$$ (3.125)

$$s_n = -1, s_p=+1$$ (3.126)

Here $F_{\nu}$ represents the driving forces for carrier $\nu$, and $U_{T\nu}$ are the carrier temperature voltages. The saturation velocities $v^{\mathrm{sat}}_{\nu}$ are calculated in a separate model by (3.134). A more detailed discussion on mobility models for III-V compounds can be found in [177,178]. For III-V materials two models are available, one giving a monotonic velocity versus field curve, while the other one includes an area with negative differential mobility [179].

$$\mu^{\mathrm{LIF}}_{\nu}\left(F_{\nu}\right) = \frac{\mu^{\m... ...}^{\beta_{\nu}}\right)^{1/\beta_{\nu}}} ,\hspace{5mm} \nu=n,p$$ (3.127)

$$\mu^{\mathrm{LIF}}_{n}\left(F_{n}\right) = \frac{\mu^{\mathr... ...+\displaystyle{{\frac{F_{n}^{\beta_{n}}}{F_{0}^{\beta_{n}}}}}}$$ (3.128)

$F_{\nu}$ represents the driving force and $v^{\mathrm{sat}}_{\nu}$ the saturation velocities according to (3.125) and (3.134), respectively. The default parameter values used in (3.124) and (3.127) are summarized in Table 3.27.

Table 3.27: Parameter values for DD high-field mobility model

Material	$\beta_n$	$\beta_p$
Si	2.0	1.0
III-Vs	2.0	1.0

(3.128) is taken for the electron mobility in III-V materials. It includes an additional model parameter, $F_0$, which is the critical driving force approximately at which the overshoot in the velocity-field characteristics appear. The default parameter values are summarized in Table 3.28.

Table 3.28: Parameter values for DD high-field mobility model

Material	$\beta_n$	$F_0$[V/cm]
GaAs	4.0	4e3
AlAs	4.0	4e3
InAs	4.0	2.2e3
InP	3.0	10e3
GaP	2.0	10e3