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 $\mu _{\perp }$.

Figure 5.2: The in-plane component of the low field electron mobility $\mu _{\parallel }$.

Figure 5.3: The valley population for the substrate orientation $[001]$.

Figure 5.4: The valley population for the substrate orientation $[111]$.

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 $[111]$.

S. Smirnov: