List of Figures

• . Momentum and quasi-momentum differ by the vector $\vec {D}=\frac{i\hbar}{m_{0}}\int u_{n\vec {k}}^{*}(\vec {r})\nabla u_{n\vec {k}}(\vec {r})\,d\vec {r}$.
• 2.2. Momentum and quasi-momentum for different shapes of the surface of constant energy.
• . Evolution of a domain in the $(\vec{r},\vec{k})$ space. The domain changes its form but its volume is the same during the semiclassical evolution process.
• 2.4. The Fermi-Dirac distribution at zero and finite temperatures.
• 2.5. The Pauli exclusion principle forbids transitions to the states which are already occupied by electrons.
• 2.6. The surfaces of constant energy for Si and Ge.
• 2.7. Angels $\alpha$ and $\beta$ with respect to the coordinate system which diagonalizes $m^{-1}$.
• 3.1. Edge dislocation.
• 3.2. Screw dislocation.
• 3.3. S-MODFET structure.
• . Full degeneracy reduction due to the applied stress for a hypothetical band structure. For a general orientation of applied forces $\varepsilon_{1}\neq\varepsilon_{2}\neq\varepsilon_{3}\neq\varepsilon_{4}$.
• . Partial degeneracy reduction due to the applied stress for a hypothetical band structure. For applied forces oriented along high symmetry axes $\varepsilon_{1}\neq\varepsilon_{2}=\varepsilon_{3}\neq\varepsilon_{4}$.
• 3.6. The stress tensor components in terms of the applied forces.
• 3.7. Repopulation effect between $X$ and $L$ valleys in strained material.
• 4.1. Graphical representation of the first iteration term.
• 4.2. Graphical representation of the second iteration term.
• 4.3. The same integration area can be covered either vertically a) or horizontally b).
• 4.4. Schematic illustration of the scattering processes at high degeneracy.
• . Schematic representation of the zero field Monte Carlo algorithm. Here $\vec{k}_{b}$ and $\vec {k}_{a}$ denote before- and after-scattering states, respectively.
• 4.6. Zero field Monte Carlo flow chart.
• 4.7. Schematic representation of the small-signal algorithm.
• 4.8. Flow chart of the small-signal algorithm.
• 5.1. The perpendicular component of the low field electron mobility $\mu _{\perp }$.
• 5.2. The in-plane component of the low field electron mobility $\mu _{\parallel }$.
• 5.3. The valley population for the substrate orientation $[001]$.
• 5.4. The valley population for the substrate orientation $[111]$.
• 5.5. The band edges in strained Si grown on the substrate with the orientation $[111]$.
• 5.6. $\mu _{\perp }$ as a function of $\alpha$ for $\beta=40^{\circ},\thickspace 60^{\circ}$, and $80^{\circ }$ in Si/ $\textrm {Si}_{0.5}\textrm {Ge}_{0.5}$.
• 5.7. $\mu _{\parallel }$ as a function of $\alpha$ for $\beta=40^{\circ},\thickspace 60^{\circ}$, and $80^{\circ }$ in Si/ $\textrm {Si}_{0.5}\textrm {Ge}_{0.5}$.
• 5.8. $\mu _{\perp }$ as a function of $\alpha$ for $\beta=40^{\circ},\thickspace 60^{\circ}$, and $80^{\circ }$ in Si/ $\textrm {Si}_{0.1}\textrm {Ge}_{0.9}$.
• 5.9. $\mu _{\parallel }$ as a function of $\alpha$ for $\beta=40^{\circ},\thickspace 60^{\circ}$, and $80^{\circ }$ in Si/ $\textrm {Si}_{0.1}\textrm {Ge}_{0.9}$.
• 5.10. The valley populations as functions of $\alpha$ for $\beta =40^{\circ }$ in Si/ $\textrm {Si}_{0.5}\textrm {Ge}_{0.5}$.
• 5.11. The valley populations as functions of $\alpha$ for $\beta =40^{\circ }$ in Si/ $\textrm {Si}_{0.1}\textrm {Ge}_{0.9}$.
• 5.12. The in-plane electron mobility $\mu _{\parallel }$ (cm$^{2}$/V$\cdot$s) as a function of $\gamma$ in Si grown on $[110]$ $\textrm {Si}_{1-y}\textrm {Ge}_{y}$.
• 5.13. The in-plane electron mobility $\mu _{\parallel }$ (cm$^{2}$/V$\cdot$s) as a function of $\gamma$ in Si grown on $[412]$ $\textrm {Si}_{1-y}\textrm {Ge}_{y}$.
• 5.14. The in-plane electron mobility $\mu _{\parallel }$ (cm$^{2}$/V$\cdot$s) as a function of $\gamma$ in Si grown on $[123]$ $\textrm {Si}_{1-y}\textrm {Ge}_{y}$.
• 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 $[001]$.
• 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.
• 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.
• 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.
• 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.
• 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 $[221]$.
• 5.21. The majority electron mobility in relaxed Si.
• 5.22. The doping dependence of $\mu _{\perp }$ in Si on $\textrm {Si}_{0.7}\textrm {Ge}_{0.3}$.
• 5.23. The doping dependence of $\mu _{\parallel }$ in Si on $\textrm {Si}_{0.7}\textrm {Ge}_{0.3}$.
• 5.24. The doping dependence of $\mu _{\perp }$ in Si on $\textrm {Si}_{0.1}\textrm {Ge}_{0.9}$.
• 5.25. The doping dependence of $\mu _{\parallel }$ in Si on $\textrm {Si}_{0.1}\textrm {Ge}_{0.9}$.
• 5.26. The valley population in strained Si grown on the $\textrm {Si}_{0.1}\textrm {Ge}_{0.9}$ substrate oriented along $[111]$.
• 5.27. The composition dependence of $\mu _{\perp }$ in $\textrm {Si}_{1-x}\textrm {Ge}_{x}$ on $[001]$ Si at several doping levels.
• 5.28. The composition dependence of $\mu _{\parallel }$ in $\textrm {Si}_{1-x}\textrm {Ge}_{x}$ on $[001]$ Si at several doping levels.
• 5.29. The differential velocity in non-degenerate and degenerate (n=$10^{21}$ cm$^{-3}$) relaxed Si for a stationary electric field $E_{s}=5$kV/cm.
• 5.30. Energy distribution functions for the two carrier ensembles in non-degenerate relaxed Si.
• 5.31. Energy distribution functions for the two carrier ensembles in degenerate relaxed Si.
• 5.32. The differential velocity in non-degenerate relaxed and strained Si for $E_{s}=5$kV/cm.
• B.1. Feynman diagram for a single link.

S. Smirnov: