5.1.1.1 Ge Composition Dependence of Perpendicular and In-plane Components

Fig. 5.1 shows $ \mu _{\perp }$, the electron mobility perpendicular to the interface for several substrate orientations, while Fig. 5.2 $ \mu _{\parallel }$, the mobility parallel to the interface.

Figure 5.1: The perpendicular component of the low field electron mobility $ \mu _{\perp }$.
\includegraphics[width=0.87\linewidth]{figures/figure_V_Si_SiGe_y_perp}
Figure 5.2: The in-plane component of the low field electron mobility $ \mu _{\parallel }$.
\includegraphics[width=0.87\linewidth]{figures/figure_V_Si_SiGe_y_parl}
Figure 5.3: The valley population for the substrate orientation $ [001]$.
\includegraphics[width=0.87\linewidth]{figures/figure_V_Si_SiGe_y_popl_001}
Figure 5.4: The valley population for the substrate orientation $ [111]$.
\includegraphics[width=0.87\linewidth]{figures/figure_V_Si_SiGe_y_popl_111}

Fig. 5.3 and Fig. 5.4 show the population of the $ X$ and $ L$ valleys for different orientations. As can be seen from Fig. 5.3, the $ X$ valleys with orientations $ [100]$ and $ [010]$ are not split in accordance with (3.60). The $ L$ valleys remain unpopulated in this case as they are much higher than the $ X$ valleys. The decrease of $ \mu _{\perp }$ and increase of $ \mu _{\parallel }$ is explained by the population of the $ X$ valleys with orientation $ [001]$ which contribute through $ m^{X}_{t}$ to the in-plane and $ m^{X}_{l}$ to the perpendicular transport.

Fig. 5.4 provides an explanation of the mobility components for the substrate orientation $ [111]$. The $ X$ valleys are not split in accordance with (3.60). When the Ge composition in the substrate increases, the splitting of the $ L$ valleys becomes important. The valleys with orientations $ [\overline{1}11]$, $ [\overline{1} \overline{1} 1]$ and $ [1\overline{1}1]$ go up and remain empty while the $ L$ valley oriented along $ [111]$ goes strongly down as stated by (3.63). This valley is dominant at high Ge mole fractions. Now the in-plane and perpendicular transport is determined by $ m^{L}_{t}$ and $ m^{L}_{l}$, respectively. The increase of $ \mu _{\parallel }$ at high compositions $ y$ is related to the decrease of the $ X\rightarrow L$ intervalley transitions. $ \mu _{\perp }$ does not increase due to the higher value of $ m^{L}_{l}$. The range of Ge compositions where the $ X\rightarrow L$ transitions are most effective can be seen in Fig. 5.5, showing the band edges versus the substrate composition $ y$.

Figure 5.5: The band edges in strained Si grown on the substrate with the orientation $ [111]$.
\includegraphics[width=0.87\linewidth]{figures/figure_V_Si_SiGe_y_111_energy}

S. Smirnov: