3.2.1 General Description of the Conduction Band Splitting in Strained SiGe

In this work the linear deformation potential theory is used to calculate the conduction band splitting in thin strained SiGe layers. As Si and Ge have their conduction band extrema at quasi-momenta $\vec{k}\neq 0$, the applied stress reduces the original degeneracy^3.1 of band states with different quasi-momenta. This reduction depends on the relative orientation of the quasi-momentum for a given conduction band extremum and the applied forces as schematically illustrated in Fig. 3.4 and Fig. 3.5. For a general orientation of applied forces all band extrema can be split. However, if the forces are applied along some axes with high symmetry the degeneracy reduction can be partial. Extrema are forming subsets within which the degeneracy is conserved, but extrema from different subsets are no longer degenerate.

Figure: Full degeneracy reduction due to the applied stress for a hypothetical band structure. For a general orientation of applied forces $\varepsilon_{1}\neq\varepsilon_{2}\neq\varepsilon_{3}\neq\varepsilon_{4}$.

In $\textrm {Si}_{1-x}\textrm {Ge}_{x}$ layers grown on relaxed $\textrm {Si}_{1-y}\textrm {Ge}_{y}$ substrates stress due to lattice mismatch always arises when the Ge compositions are different, $x\neq y$. The direction and the magnitude of the applied forces in such a system depend on the orientation of the $\textrm {Si}_{1-y}\textrm {Ge}_{y}$ substrate and the Ge compositions $x$ and $y$. This stress leads to a deformation of the perfect crystal. It is assumed that the thickness is below the critical value which implies absence of dislocations. As a result the degeneracy of the conduction band is reduced. The splitting of the conduction band minima has a strong impact on the transport properties of strained SiGe active layers in comparison with unstrained ones. In particular it causes anisotropy of transport quantities such as electron

Figure: Partial degeneracy reduction due to the applied stress for a hypothetical band structure. For applied forces oriented along high symmetry axes $\varepsilon_{1}\neq\varepsilon_{2}=\varepsilon_{3}\neq\varepsilon_{4}$.

mobility. For Si, Ge and SiGe the low field electron mobility is represented by a scalar, that is, the mobility tensor is diagonal with equal diagonal elements. In the strained layer the diagonal elements are in general different. The difference of the kinetic properties for different orientations can be significant and can be used to optimize the characteristics of advanced semiconductor devices. S. Smirnov: