4.3.2 Mobility
Typical measured v(E) characteristics of IIIV bulk material
exhibit a local maximum as shown in Figure
2.4. Simulations with a v(E) characteristics including a local
maximum revealed low impact on the results of HEMTs but very unstable convergence
in comparison to a v(E) monotonous characteristics like that of
silicon.
The minor impact of the local maximum is because the electrons under the gate are in saturation for almost all relevant bias voltages of HEMTs which will be shown in Sections 5.3.1 and 5.3.2. The local maximum is obtained only for a certain range of electric fields between the constant mobility and the saturation velocity regime. Therefore, it has to be expected that this electric field is reached only in very small areas of the current path. On the other hand, the spatial velocity overshoot (described later in this section) and the saturation velocity (described in Section 2.1) of electrons in quantum wells is not known exactly. Thus, one can assume that the error made by neglecting the static velocity overshoot is small compared to uncertainties in the saturation velocity and spatial velocity overshoot.
In addition, convergence is usually poor if the thermionic field emission
interface model (i. e. including tunneling) and a local maximum in the
v(E) characteristics are combined. Therefore, the v(E) characteristics
with a local maximum was not used further and a silicon like characteristics
was assumed. The DD mobility for electrons and holes are modeled by
, 
(44)

and . 
(45)

(46)

, 
(47)

For the HD model the mobility is modeled as a function of the carrier
temperature T_{np}:
. 
(48)

Considering energy balance, using a local approximation, and (25)
the energy transport equation (21)
and (22) reduce
to
(49)

(50)

(51)

(52)

Using (52) in (48)
the mobility can be expressed as a function of the electric field:
. 
(53)

(54)

. 
(55)

. 
(56)

. 
(57)

As shown in (46) and (47)
the gradient of the carrier temperature for the driving force is neglected
for the DD model. This is different to the driving force of the HD model
which reads
(58)

(59)

In addition to the different relations between carrier temperature and driving force for the DD and the HD model another important difference can be observed in Figure 4.3 and Figure 4.4. The maximum of both the carrier temperature and the driving force is reached for a larger distance from the end of the gate. This is because a finite energy relaxation time is used for the HD model whereas the carriers in the DD model relax instantaneously, thus, a local relation between electric field and carrier velocity exists for the DD model.
As a nonlocal behavior of the carriers is taken into account in the
HD model a spatial velocity overshoot can be obtained. The importance and
modeling of the spatial velocity overshoot will be discussed further in
Section 5.2.
Next: 5 Simulation Up: 4.3
Physical Parameters Previous: 4.3.1 Effective
Mass and Band Edge Energy
Helmut Brech 19980311