5.3 Small Signal Response

In this section results of the small signal analysis are presented. A comparison is made between non-degenerate and degenerate electron gases. Finally, small signal analysis of strained Si is performed.

Fig. 5.29 shows the differential velocity in relaxed Si for both the non-degenerate and degenerate cases. The differential velocity obtained from the non-degenerate algorithm displays a weak oscillatory character, while the differential velocity from the degenerate algorithm does not show any oscillations. This can be explained by analyzing the energy distribution functions of the two ensembles introduced in Chapter 4. The small difference of the distribution functions of the two ensembles in the non-degenerate algorithm (see Fig. 5.30) is responsible for the weak oscillation, while for the degenerate algorithm the ensembles have nearly the same distributions at the very beginning as depicted in Fig. 5.31. In addition, in the degenerate case the distribution functions significantly shift to higher energies as the lower energy levels have already been occupied and scattering to these states is quantum mechanically forbidden.

Fig. 5.32 show the differential velocity in the strained Si active layer grown on the relaxed $[001]$ $\textrm {Si}_{0.7}\textrm {Ge}_{0.3}$ substrate in comparison with the relaxed Si.

Figure 5.29: The differential velocity in non-degenerate and degenerate (n=$10^{21}$ cm$^{-3}$) relaxed Si for a stationary electric field $E_{s}=5$kV/cm.

Figure 5.30: Energy distribution functions for the two carrier ensembles in non-degenerate relaxed Si.

Figure 5.31: Energy distribution functions for the two carrier ensembles in degenerate relaxed Si.

Figure 5.32: The differential velocity in non-degenerate relaxed and strained Si for $E_{s}=5$kV/cm.

S. Smirnov: