To extract the parameters for the hydrodynamic impact ionization model, a combination of experimental results and comparison with a MC model is used. Using the Keldish [91] impact ionization model in a one-dimensional MC simulation, the impact ionization rates can be evaluated for the same potential situation as in the simulation by MINIMOS-NT.
Additionally gate current information is available from
measurements, where a separation of impact ionization and
thermionic field emission effects is necessary. From gate current
analysis as a function of temperature, we obtain further
experimental data for the temperature dependent modeling.
Fig. 3.31 shows a comparison of the measured and modeled
gate currents
for two different lattice temperatures
.
As was consistently stated for
InGa
As [75,179,193] there
is a positive temperature coefficient for the impact ionization.
As can clearly be seen for GaAs in Fig. 3.18 and was
shown for pseudomorphic HEMTs with In contents
0.25 [75] a negative coefficient for impact ionization
is observed, as the rates decrease with rising
. The
positive coefficient can further be derived from the on-state
breakdown voltage, as will be seen in Fig. 6.13 in Chapter 6.
To realistically model the transition from the pseudomorphic
AlGa
As/In
Ga
As HEMT with x= 0.25, a
metamorphic In
Al
As/In
Ga
As with
x= 0.3-0.6 [314], and lattice matched to InP (
= 0.53) the transition for the
impact ionization coefficient from a positive to negative value as a function of
In content
must be found. In [235] Rohdin et al. stated,
that with the use of
= 0.41 in a metamorphic structure no specific
change of the on-state breakdown behavior
was observed relative to metamorphic HEMTs with
= 0.53. Consequently, the area of interest is between
= 0.25 to about
= 0.4,
while the barrier material In
Al
As becomes an indirect semiconductor at y= 0.3,
which in this case deteriorates the transport properties of InAlAs significantly [47].
The potential in the mid-channel from the HD solution is taken and transferred into a one-dimensional MC code. Using the MC code [306] generation rates per carrier are calculated for this potential profile. The impact ionization simulation is also performed with MINIMOS-NT using (3.76) to (3.79), so that the resulting rates can be compared to MC rates obtained for this potential profile. From this procedure the parameters given in Table 3.31 and Table 3.32 are obtained at
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In Fig. 3.32 the midchannel hydrodynamic impact
ionization generation rates are shown for a single recess device
pseudomorphic HEMT for the same current
. The rate is given
along the middle of the channel and the gate extends between x =
0 and 0.14
m. We see an impact ionization rate at the drain
side of the gate that negligible for
= 1 V, while for
= 5 V a significant rate
cm
is
observed, as the device is not protected by a second recess and
has a gate to drain breakdown voltage
of about 5 V.