3.6.7 Impact Ionization Parameters

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 ${\it I}_{\mathrm{G}}$ for two different lattice temperatures ${\it T}_\mathrm{L}$.

As was consistently stated for In$_{0.53}$Ga$_{0.47}$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 $x$$<$ 0.25 [75] a negative coefficient for impact ionization is observed, as the rates decrease with rising ${\it T}_\mathrm{L}$. 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 Al$_{0.2}$Ga$_{0.8}$As/In$_{x}$Ga$_{1-x}$As HEMT with x= 0.25, a metamorphic In$_x$Al$_{1-x}$As/In$_x$Ga$_{1-x}$As with x= 0.3-0.6 [314], and lattice matched to InP ($x$= 0.53) the transition for the impact ionization coefficient from a positive to negative value as a function of In content $x$ must be found. In [235] Rohdin et al. stated, that with the use of $x$= 0.41 in a metamorphic structure no specific change of the on-state breakdown behavior was observed relative to metamorphic HEMTs with $x$= 0.53. Consequently, the area of interest is between $x$= 0.25 to about $x$= 0.4, while the barrier material In$_y$Al$_{1-y}$As becomes an indirect semiconductor at y= 0.3, which in this case deteriorates the transport properties of InAlAs significantly [47].

Figure 3.31: Gate currents $I_G$ as a function of temperature $T_{sub}$ for an InP based InAlAs/InGaAs HEMT.

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 ${\it T}_\mathrm{L}$= 300 K.

Figure 3.32: Two-dimensional HD impact ionization generation rates in a single recess AlGaAs/ InGaAs HEMT at $V_{DS}$= 1 V and $V_{DS}$= 5 V using MINIMOS-NT.

In Fig. 3.32 the midchannel hydrodynamic impact ionization generation rates are shown for a single recess device pseudomorphic HEMT for the same current ${\it I}_{\mathrm{D}}$. The rate is given along the middle of the channel and the gate extends between x = 0 and 0.14 $\mu$m. We see an impact ionization rate at the drain side of the gate that negligible for ${\it V}_{\mathrm{DS}}$ = 1 V, while for ${\it V}_{\mathrm{DS}}$= 5 V a significant rate $\geq 10^{29}$ cm $^{-3}s^{-1}$ is observed, as the device is not protected by a second recess and has a gate to drain breakdown voltage ${\it BV}_{\mathrm{GD}}$ of about 5 V.