5.2 Low Field Electron Mobility in Doped Layers

In this section the results of Monte Carlo simulation of the electron low field mobility in doped strained SiGe layers are presented. Two scattering mechanisms appear additionally to the phonon and alloy scattering, namely plasmon and ionized impurity scattering. The influence of the strain on the screening parameters and its interplay with the Pauli exclusion principle are discussed.

Fig. 5.21 shows the Monte Carlo simulation results for the majority electron mobility in relaxed $[001]$ Si in comparison with experimental data.

Fig. 5.22 and Fig. 5.23 demonstrate the doping dependence of $\mu _{\perp }$ and $\mu _{\parallel }$ in the Si active layer grown on relaxed $\textrm {Si}_{0.7}\textrm {Ge}_{0.3}$. In Fig. 5.23 the curve for the perpendicular component $\mu _{\perp }$ exhibits an increase for the substrate oriented along $[001]$ when the doping level becomes high enough. The same increase can be seen in Fig. 5.24, which displays the doping dependence of the perpendicular component $\mu _{\perp }$ in strained Si on a relaxed $\textrm {Si}_{0.1}\textrm {Ge}_{0.9}$ substrate of orientation $[111]$. At the same time the in-plane component does not increase as shown in Fig. 5.25. This effect can be explained by the influence of the quantum mechanical Pauli exclusion principle which starts playing an important role at high electron densities.

At low doping level, the $L$ valley oriented along $[111]$ is the lowest one. It is fully populated (see Fig. 5.26) and $\mu _{\perp }$ is determined by $m^{L}_{l}$, while $\mu _{\parallel }$ is determined by $m^{L}_{t}$. As the donor concentration increases, lower energy levels are forbidden to scatter in by the Pauli exclusion principle and thus electrons scatter to higher energy levels. At doping level about $10^{19}$   cm$^{-3}$ electrons occupy energies high enough to be able to scatter to the unsplit $X$ valleys which lie higher than the $L$ ones due to strain. The intervalley $L-X$ scattering becomes possible and gets stronger as the donor concentration increases. Finally, most of the electrons are equally distributed between the $X$ valleys. The influence of $m^{L}_{l}$ on $\mu _{\perp }$ is significantly reduced and which turns out to be enough to suppress increasing ionized impurity scattering. However, the $X$ valleys are oriented in such a way that the influence of $m_{l}^{X}$ and $m_{t}^{X}$ on $\mu _{\parallel }$ is not strong enough to suppress the impurity scattering, and as a result $\mu _{\parallel }$ does not show an increase.

Figure 5.21: The majority electron mobility in relaxed Si.

Figure 5.22: The doping dependence of $\mu _{\perp }$ in Si on $\textrm {Si}_{0.7}\textrm {Ge}_{0.3}$.

Figure 5.23: The doping dependence of $\mu _{\parallel }$ in Si on $\textrm {Si}_{0.7}\textrm {Ge}_{0.3}$.

Figure 5.24: The doping dependence of $\mu _{\perp }$ in Si on $\textrm {Si}_{0.1}\textrm {Ge}_{0.9}$.

Figure 5.25: The doping dependence of $\mu _{\parallel }$ in Si on $\textrm {Si}_{0.1}\textrm {Ge}_{0.9}$.

Figure 5.26: The valley population in strained Si grown on the $\textrm {Si}_{0.1}\textrm {Ge}_{0.9}$ substrate oriented along $[111]$.

Figure 5.27: The composition dependence of $\mu _{\perp }$ in $\textrm {Si}_{1-x}\textrm {Ge}_{x}$ on $[001]$ Si at several doping levels.

Figure 5.28: The composition dependence of $\mu _{\parallel }$ in $\textrm {Si}_{1-x}\textrm {Ge}_{x}$ on $[001]$ Si at several doping levels.

Fig. 5.27 and Fig. 5.28 show the Ge composition dependence of $\mu _{\perp }$ and $\mu _{\parallel }$ in strained $\textrm {Si}_{1-x}\textrm {Ge}_{x}$ layers grown on Si $[001]$ substrates. The increase of the perpendicular component at high doping levels and low composition $x$ can be explained in the following manner. In the undoped material there are two factors which depend on the Ge mole fraction: the splitting of the $X$ valleys and alloy scattering. The first factor increases the perpendicular component of the electron mobility and the second one decreases it. In doped SiGe at high doping levels, ionized impurity scattering dominates the alloy scattering and thus suppresses the second factor leaving the first one that leads to the increase. The in-plane component does not have this increase because both the energy splitting and alloy scattering decrease $\mu _{\parallel }$. Thus after removing the second factor there still exists the second one which decreases the parallel component.

S. Smirnov: