Subsections

• 3.4.5.1 Semiconductor Alloys

3.4.5 High-Field Mobility for HD Equations

The deviation from the ohmic low-field mobility is modeled as a function of the carrier temperature, $T_\nu$, after Hänsch [180].

$$\mu^{\mathrm{LIST}}_\nu = \frac{\mu^{\mathrm{LIS}}_{\nu}}{1 + \alpha_{\nu}\cdot\left(T_{\nu}- T_{{\mathrm{L}}}\right)}$$ (3.129)

$$\alpha_{\nu} = \frac{3\cdot \mathrm{k_B}\cdot \mu^{\mathrm{LIS}}_{\nu}}{2\cdot \mathrm{q}\cdot \tau_{\epsilon} \cdot \left(v^{\mathrm{sat}}_{\nu}\right)^2}$$ (3.130)

$\tau_{\epsilon}$ denotes the energy relaxation times and $v^{\mathrm{sat}}_{\nu}$ are the saturation velocities calculated respectively in (3.138) and in (3.134).

For some III-V semiconductor materials a multi-valley mobility model can be used. In the following model a weighted mean is calculated from the low-field mobilities of the $\Gamma$- and $\mathrm {L}$-electrons [181].

$$\mu^{\mathrm{LIT}}_n = \frac{\mu^{\mathrm{LI}}_{n,\Gamma}+\mu^{\mathrm{LI}}_{n,\mathrm {L}}\cdot P_{\mathrm{L}}}{1+P_{\mathrm{L}}}$$ (3.131)

$$P_{\mathrm{L}} = 4\cdot\left(\frac{m_{\mathrm{L}}}{m_\Gamma}\right)^{3/2} \cdot\exp\left(-\frac{E_{C,{\mathrm{L}}}-E_{C,\Gamma}}{\mathrm{k_B}\cdot T_n}\right)$$ (3.132)

$P_{\mathrm {L}}$ denotes the ratio of the $\Gamma$ and $\mathrm {L}$-valley populations [86]. The valley mobilities ${\mu^{\mathrm{LI}}_{n,\Gamma}}$ and ${\mu^{\mathrm{LI}}_{n,\mathrm {L}}}$ account for impurity scattering after (3.97), and are constant with respect to the lattice temperature.

Table 3.29: Parameter values for the two-valley HD mobility model

Parameter	GaAs	Unit
$\mu^{\mathrm{L}}_{n,\Gamma}$	8000	cm$^2$/Vs
$\mu^{\mathrm{L}}_{n,\mathrm {L}}$	400	cm$^2$/Vs
$\mu^{\mathrm{min}}_{n}$	1500	cm$^2$/Vs
$C^{\mathrm{ref}}_{n}$	1.426e+17	cm$^{-3}$
$\alpha_{n}$	0.5385
$\tau_{n,\Gamma}$	1.2	ps
$\tau_{n,\mathrm {L}}$	0.6	ps
$v^{\mathrm{sat}}_{n,\Gamma}$	2.5e5	m/s
$v^{\mathrm{sat}}_{n,\mathrm {L}}$	0.9e5	m/s

3.4.5.1 Semiconductor Alloys

In the case of alloy materialsthe model employs the low-field mobilities $\mu^{\mathrm{LI}}$ of the basic materials (A and B) and combines them by a harmonic mean.

$$\frac{1}{\mu^{\mathrm{AB}}} =\frac{1-x}{\mu^{\mathrm{A}}}+\frac{x}{\mu^{\mathrm{B}}}+ \frac{\left(1-x\right)\cdot x}{C_\mu}$$ (3.133)

$C_\mu$ is referred to as nonlinear or bowing parameter.

Table 3.30: Parameter values for mobility model for alloy materials

Material	$C_{\mu,n}$ [cm$^2$/Vs]	$C_{\mu,p}$ [cm$^2$/Vs]
SiGe	1e6	-100
AlGaAs	180	1e6
InGaAs	1e6	1e6
InAlAs	1e6	1e6
InAsP	1e6	1e6
GaAsP	1e6	1e6
InGaP	1e6	1e6

For calculation of the high field mobilities no additional parameters need to be specified for the model. The respective interpolations between the basic materials are carried out in the models for the saturation velocities and, in the case of HD simulation, of the energy relaxation times.