To investigate the accuracy of the six moments (SM) model we consider a series of onedimensional  teststructures. Although these structures are not of practical relevance, they still display similar features as contemporary MOS and bipolar transistors like velocity overshoot and a mixture of a hot and a cold distribution function in the 'drain' region.
Here we present results of numerical solutions of six moments models (SM) and compare them to selfconsistent Monte Carlo data (SCMC). Relaxation times and mobilities are extracted from bulk Monte Carlo data as a function of the carrier temperature and the doping.
In addition to the SM model we consider the corresponding energytransport (ET) model formulated in moments (see Equations 2.24, 2.25), where the equation for is kept but the equation for the energyflux is closed with , corresponding to a heated Maxwellian distribution. This decouples the equation for from the lower order equations and provides an estimate for and thus [GKGS01], [SYT^{+}96].
The doping concentrations were taken to be and . The channel length was varied from down to while maintaining a maximum electric field of .
A comparison of the average velocity and the kurtosis obtained from the SM and ET models with the SCMC simulation is shown in Fig. 4.4 and Fig. 4.5 for the nm device. The spurious velocity overshoot is significantly reduced in the SM model, consistent with previous results [GKS01], while the kurtosis produced by the ET model is only a poor approximation to the MC results.
Despite the fact that SM models provide the kurtosis of the distribution function, they do not require a heated Maxwellian closure in the energy flux relation. This has a significant impact on the resulting device currents for channel lengths smaller where the ET models show the wellknown overestimation of the device currents (see Figure 4.6). The results of the SM model, on the other hand, stay close to the SCMC results which makes the SM model a good choice for TCAD applications.



Previous: 4.6 Variations of the Up: 4. Tuning of the Next: III. Quantum Simulation of