5.1.1.2 Substrate Orientation Dependence

Here the electron mobility as a function of the substrate orientation is presented for two Ge compositions of the substrate. The second Euler angle $\beta$ is chosen as a parameter while the first one $\alpha$ varies between 0 and $\pi/2$. The third Euler angle is equal to 0 as discussed previously.

Fig. 5.6 illustrates the behavior of the perpendicular component $\mu _{\perp }$ of the electron mobility, while Fig. 5.7 shows the same dependence for $\mu _{\parallel }$. The two components $\mu _{\perp }$ and $\mu _{\parallel }$ for $\beta =40^{\circ }$ reach their maximum values at $\alpha=\pi/4$ because at this value of $\alpha$ the population of the $X$ valley with orientation $[001]$ is the highest and due to the orientation the influence of the longitudinal masses $m^{X}_{l}$ of the $X$ valleys oriented along $[100]$ and $[010]$ is minimal. However, the influence of the $X$ valleys of these orientations is significant at $\alpha=0^{\circ}$ and $\alpha=90^{\circ}$ where the two components have their minima.

The analogous results for $\mu _{\perp }$ and $\mu _{\parallel }$ for a substrate composition of $y=0.9$ are depicted in Fig. 5.8 and Fig. 5.9. The main difference from the case of $\textrm {Si}_{0.5}\textrm {Ge}_{0.5}$ substrate is that here the $L$ valley comes into play which causes an additional intervalley scattering process between $X$ and $L$ valleys.

The repopulation processes are most clearly seen in Fig. 5.10 and Fig. 5.11, which display the populations of different orientations of both the $X$ and $L$ valleys. As can be seen from Fig. 5.10, the $X$ valleys with the orientation $[001]$ are the most populated ones while all the $L$ valleys remain empty. In the case of substrates with higher Ge mole fraction (see Fig. 5.11) the $L$ valley oriented along $[111]$ becomes important.

The next three figures Fig. 5.12, Fig. 5.13, and Fig. 5.14 show the dependence of the in-plane component of the electron mobility $\mu _{\parallel }$ on the in-plane angle, that is the third Euler angle $\gamma$, in polar coordinates for three substrate orientations. The mobility on these figures is obviously anisotropic. This means that the in-plane transport turns out to be dependent on the orientation of devices grown on the substrate.

Figure 5.6: $\mu _{\perp }$ as a function of $\alpha$ for $\beta=40^{\circ},\thickspace 60^{\circ}$, and $80^{\circ }$ in Si/ $\textrm {Si}_{0.5}\textrm {Ge}_{0.5}$.

Figure 5.7: $\mu _{\parallel }$ as a function of $\alpha$ for $\beta=40^{\circ},\thickspace 60^{\circ}$, and $80^{\circ }$ in Si/ $\textrm {Si}_{0.5}\textrm {Ge}_{0.5}$.

Figure 5.8: $\mu _{\perp }$ as a function of $\alpha$ for $\beta=40^{\circ},\thickspace 60^{\circ}$, and $80^{\circ }$ in Si/ $\textrm {Si}_{0.1}\textrm {Ge}_{0.9}$.

Figure 5.9: $\mu _{\parallel }$ as a function of $\alpha$ for $\beta=40^{\circ},\thickspace 60^{\circ}$, and $80^{\circ }$ in Si/ $\textrm {Si}_{0.1}\textrm {Ge}_{0.9}$.

Figure 5.10: The valley populations as functions of $\alpha$ for $\beta =40^{\circ }$ in Si/ $\textrm {Si}_{0.5}\textrm {Ge}_{0.5}$.

Figure 5.11: The valley populations as functions of $\alpha$ for $\beta =40^{\circ }$ in Si/ $\textrm {Si}_{0.1}\textrm {Ge}_{0.9}$.

Figure 5.12: The in-plane electron mobility $\mu _{\parallel }$ (cm$^{2}$/V$\cdot$s) as a function of $\gamma$ in Si grown on $[110]$ $\textrm {Si}_{1-y}\textrm {Ge}_{y}$.

Figure 5.13: The in-plane electron mobility $\mu _{\parallel }$ (cm$^{2}$/V$\cdot$s) as a function of $\gamma$ in Si grown on $[412]$ $\textrm {Si}_{1-y}\textrm {Ge}_{y}$.

Figure 5.14: The in-plane electron mobility $\mu _{\parallel }$ (cm$^{2}$/V$\cdot$s) as a function of $\gamma$ in Si grown on $[123]$ $\textrm {Si}_{1-y}\textrm {Ge}_{y}$.

Thus in order to reach their optimal characteristics devices, or more specifically, their active strained regions (base, channel, or other parts) can be properly oriented on the surface of the substrate. Where it is necessary this can be used to increase output currents. Additionally, this effect can also be used to reduce leakages by orienting some parts of the device so as to reduce the mobility along the possible leakage directions.

S. Smirnov: