5.1.2 $\textrm {Si}_{1-x}\textrm {Ge}_{x}$ layers on $\textrm {Si}_{1-y}\textrm {Ge}_{y}$ substrates

In this subsection the Monte Carlo simulation results for the low field electron mobility in $\textrm {Si}_{1-x}\textrm {Ge}_{x}$ undoped active layers are given. The essential difference in comparison with Si active layers is that in this case alloy scattering strongly influences the transport properties of the active layers. Alloy scattering is described by expression (2.138). As a function of the Ge composition $x$ in the active layer it has a maximum at $x=0.5$. Therefore it is expected that electron mobility in this case has its minimum at the same point. However, it is shown below that this is not always the case. The reason for this is both the change of the effective masses and various repopulation effects between valleys both of the same and different types. These effects can be strong enough to suppress the decrease of the electron mobility due to alloy scattering.

The results for the perpendicular $\mu _{\perp }$ and in-plane $\mu _{\parallel }$ components of the electron low field mobility are presented as functions of the layer composition $x$ for several substrates parameterized by their Ge compositions $y$ as well as their orientations in terms of the Miller indices. Again the Miller indices specify only two Euler angles $\alpha$ and $\beta$ while the third Euler angle $\gamma$ is kept constant equal to zero.

Fig. 5.15 compares Monte Carlo simulation results and experimental data for a $\textrm {Si}_{1-x}\textrm {Ge}_{x}$ active layer grown on a relaxed Si substrate oriented along $[001]$. As it is expected the curves have the minima at $x=0.5$. The electron mobility in the strained case has Si like character over the whole range of Ge mole fractions. In the case of the perpendicular component $\mu _{\perp }$ the mobility in the strained layer is higher than that in the unstrained case up to $x=0.8$. It follows from the fact that the two $X$ valleys along $[001]$ move up and have only little contribution to the mobility. Thus only four in-plane valleys with transverse effective masses determine the mobility. This gives an increase in comparison with unstrained SiGe. At very high Ge mole fractions the mobility in the unstrained case increases rapidly while for the strained SiGe it has lower values. This is related to the increase of biaxial compressive strain which at high $x$ makes the four in-plane valleys move strongly down setting them equal or even lower than the $L$ valleys. In the case of the in-plane component $\mu _{\parallel }$ the mobility in the strained layer is lower compared to that in unstrained SiGe. This is explained by the fact that unlike in the relaxed material, where four transverse effective masses determine the electron mobility, only two transverse effective masses are left in strained SiGe which leads to a decrease of the in-plane component.

Figure 5.15: The electron mobility $\mu _{\perp }$ and $\mu _{\parallel }$ in relaxed and strained $\textrm {Si}_{1-x}\textrm {Ge}_{x}$ on the Si substrate with the orientation $[001]$.

Figure 5.16: $\mu _{\perp }$ in $\textrm {Si}_{1-x}\textrm {Ge}_{x}$ on $\textrm {Si}_{0.7}\textrm {Ge}_{0.3}$ for several substrate orientations.

Figure 5.17: $\mu _{\parallel }$ in $\textrm {Si}_{1-x}\textrm {Ge}_{x}$ on $\textrm {Si}_{0.7}\textrm {Ge}_{0.3}$ for several substrate orientations.

Figure 5.18: $\mu _{\perp }$ in $\textrm {Si}_{1-x}\textrm {Ge}_{x}$ on $\textrm {Si}_{0.1}\textrm {Ge}_{0.9}$ for several substrate orientations.

Figure 5.19: $\mu _{\parallel }$ in $\textrm {Si}_{1-x}\textrm {Ge}_{x}$ on $\textrm {Si}_{0.1}\textrm {Ge}_{0.9}$ for several substrate orientations.

Figure 5.20: The valley populations as functions of the active layer composition for the $\textrm {Si}_{0.1}\textrm {Ge}_{0.9}$ substrate with the orientation $[221]$.

Fig. 5.16 to Fig. 5.19 display $\mu _{\perp }$ and $\mu _{\parallel }$ in $\textrm {Si}_{1-x}\textrm {Ge}_{x}$ grown on $\textrm {Si}_{0.7}\textrm {Ge}_{0.3}$ and $\textrm {Si}_{0.1}\textrm {Ge}_{0.9}$ for several substrate orientations.

Fig. 5.20 explains the behavior of the mobility components in the case of $\textrm {Si}_{0.1}\textrm {Ge}_{0.9}$ substrates oriented along $[221]$. It shows the populations of the $X$ and $L$ valleys with different orientations and the repopulation between them. The $L$ valley oriented along $[111]$ is the most populated one up to $x\approx 0.8$. Thus the contribution of the longitudinal effective masses of the $L$ valley plays the main role up to this value of the Ge composition. This reduces the mobility components $\mu _{\perp }$ and $\mu _{\parallel }$. The increase of the in-plane component $\mu _{\parallel }$ is related to the effective mass interpolation. When the Ge mole fraction is greater than $x=0.8$, the repopulation between different $L$ valleys comes into play. First, electrons scatter from the valley located along $[111]$ to the valleys located along $[\overline{1}11]$, $[1\overline{1}1]$ and $[\overline{1} \overline{1} 1]$ and then from $[111]$ and $[\overline{1} \overline{1} 1]$ to $[\overline{1}11]$, $[1\overline{1}1]$. In this way the influence of the longitudinal masses decreases while the transverse masses contribute stronger, leading to the mobility increase.

S. Smirnov: