It was discussed in Section 5.1 that the enhancement of the bulk low-field electron mobility saturates at around 1.7 [Dhar05b]. In order to maintain the desired mobility enhancement, the g-type and f-type coupling constants had to be adjusted to the values stated in Table 5.1. In addition, it was required to adjust the acoustic deformation potential from its original value of 8.9 eV [Jungemann03a] for analytical band Monte Carlo to 8.5 eV for full-band Monte Carlo simulation. The effect of impact ionization was neglected for the field regime investigated.
Fig. 5.11 presents the velocity-field characteristics for unstrained and strained Si for different field directions as obtained from Monte Carlo simulations. Also displayed are the results from Bufler [Bufler97], Canali [Canali71], Smith [Smith80], Fischer [Fischer99], and Ismail [Ismail93]. The simulation results agree well with measured data from Smith for the  field direction and with Canali for the  field direction for the unstrained case and with Jungemann [Jungemann03a], Bufler, and Ismail for the strained case.
The velocity-field characteristics for field along the  direction exhibit an untypical form for high strain levels. This phenomenon can be explained as follows. For field along  direction the -valleys are lowered in energy with increasing strain and have the longitudinal mass in the field direction. These valleys are located at a scaled distance of 0.85 and 1.15 from the center of the first Brillouin zone and are separated by an energy barrier of 129 meV at the X-point (Fig. 5.13). The average velocity in the left and right valley and also the average of these velocities are shown in Fig. 5.14. For low-fields, electrons in both valleys are slightly displaced with respect to the valley minima. This results in the initial velocity increase for both valleys shown in Fig. 5.14. However, as the field increases, electrons in both valleys gain energy, and electrons from one valley can surpass the energy barrier and drift to the valley in the next Brillouin zone. As sketched in Fig. 5.13, there are more electrons populating the right side of the double valley than the left side, giving rise to a slight increase in average velocity. If only the left valley is considered, there are more electrons populating the left edge of the single valley resulting in a negative valley velocity, as shown in Fig. 5.14.
|Parameter||Units||E ||E ||E |
|E ||E |
|[10 cm s]||1.026||1.058||1.042|
|Parameter||Units||E ||E ||E||E ||E |
|Parameter||Units||E ||E ||E ||E ||E |
|Parameter||Units||E ||E ||E ||E |
|[10 cms eV]||4.0975||2.8429||3.53||3.4858|
Fig. 5.16b shows a comparison of the velocity components and the total velocity as obtained from the interpolation and Monte Carlo simulations for field along the  direction for uniaxial tensile stressed Si. In this case the perpendicular velocity is negative.