3.6.6 Carrier Concentrations and Velocities

For the global calibration of the high field parameters such as energy relaxation times and saturation velocity a comparison between MC data is performed for different devices. The critical issue of the comparison with MC simulation is the impact of Real Space Transfer (RST) [212]. RST modifies the high field transport and reduces the velocity overshoot, thus a one-dimensional simulator will always overestimate the velocities. Electrons accelerated by the field in the channel can either undergo k-space transfer (KST) in the channel, or undergo real space transfer into the barrier or buffer, and after that KST in the buffer/barrier.

Figure 3.29: Mid-channel velocity curve obtained by DAMOCLES for $V_{DS}$= 2 V, $V_{GS}$= 0 V and corresponding carrier concentration in mid-channel.

In Fig. 3.29 the mid-channel velocity profile and the electron concentration is shown. A ${\it l}_{\mathrm{g}}$= 250 nm Al$_{0.25}$Ga$_{0.75}$As/In$_{0.3}$Ga$_{0.7}$As double heterojunction HEMT is simulated with the two-dimensional MC device simulator DAMOCLES. The same device is then simulated with  MINIMOS-NT for the same bias ${\it V}_{\mathrm{DS}}$ = 2 V, contact situation, doping, and geometry. The ohmic contact situation is assumed as (III) in Fig. 3.25. Fig. 3.29 shows the electron concentration $n$ diminishing at the drain end of the gate, while the maximum overshoot amounts to ${\it v}_{\mathrm{max}}$= 2.5$\times$10$^7$ cm/s for this ${\it V}_{\mathrm{DS}}$ bias. For the maximum overshoot normally occurs near ${\it V}_{\mathrm{DS}}$= 1 V, a value of ${\it v}_{\mathrm{max}}$=  3.3$\times$10$^7$ cm/s is found in the hydrodynamic simulation.

Figure 3.30: Three-dimensional energetic and local electron distribution obtained by using the simulator DAMOCLES.

Fig. 3.30 shows the two-dimensional energetic and local distribution of electrons in the device. Electrons with a kinetic energy up to 2 eV can be seen at the drain end of the gate. Parts of the hot electron population surmount the barrier instead of undergoing k-space transfer in the channel, are accelerated again and undergo k-space transfer in the AlGaAs barrier. This mechanism which is the only means of current transport for the contact situations (II) and (III), directly relates the high field transport to the charge control of the device. In Fig. 3.29 and Fig. 3.30 the importance of RST is clearly visible.

Typical one-dimensional MC simulations provide overshoot values for the average velocities as high as 6 $\times10^7$ cm/s. In the two-dimensional simulation these values are significantly reduced for the same potential profile in the x-direction, which delivers the results presented e.g. in Fig. 3.29. Based on this extraction procedure for other HEMTs devices results such as in Fig. 3.28 are obtained for the velocities. Using this concept good agreement with experimental data is obtained e.g. for ${\mit g}_{\mathrm{m}}$ which is directly related to the velocity and shown in Chapter 7.