7. Summary and Conclusions

STRAIN techniques are used by many prominent microprocessor manufacturers primarily for their sub-130 nm CMOS technologies. The most prominent strain technologies were outlined in this work. A revision of current strain technologies showed that shear strain induced by uniaxial stress in $\langle110\rangle$ direction is widely used to enhance the electron mobility for {001} Si substrate. Hence, in this work special emphasis was put on this strain configuration.

The effect of strain on the band structure of Si was investigated systematically using the linear deformation potential theory and the kp method. Shear strain lifts the degeneracy of the two lowest conduction bands $\Delta _1$ and $\Delta _{2'}$ at the zone boundary X points. The change of the shape of the lowest conduction band was quantified in terms of (i) an effective mass change, (ii) a shear-strain-induced valley splitting, and (iii) a change in position of the valley minimum in $\mathitbf{k}$-space. Additionally, the empirical pseudopotential method was adapted to incorporate strain effects. The results from numerical band structure calculations were compared to the analytical expressions derived using the kp theory and good agreement was observed.

Furthermore, the effect of strain on the subband structure of Si inversion layers formed at the surface between one or two Si-SiO$_2$ interfaces with {001}, {110}, and {111} substrate orientation was shown. The transport masses and the degeneracy of the subband ladders depend on the substrate orientation and can be modified by strain. The strain configurations that enhance carrier mobility were identified for each substrate orientation.

Fullband MC simulations were performed using VMC to analyze the effect of strain on the electron mobility. MC simulations using an analytical description of the electron bands were shown to be valid in a limited range of shear strain ( $<\!\pm0.5\%$). At larger shear strain the band deformation is so pronounced, that fullband modeling is required. Hence, for modeling of transport in strained Si a fullband description is of particular importance. MC simulations and a rigorous modeling of the strain effect on the electron band structure reproduce experimentally observed mobility data for bulk Si and Si inversion layers on different substrate orientations.

A method for the inclusion of the Pauli principle in a Monte Carlo algorithm is presented to study the effect of degeneracy both on the phonon-limited mobility and the effective mobility including surface-roughness scattering in Si inversion layers. It is shown that at room temperature and for {001} substrate orientation incidentally degeneracy has a minor effect on the effective mobility, despite non-degenerate statistics yields unphysical subband populations and an underestimation of the mean electron energy. In general a correct treatment of the degenerate carrier statistics of the 2DEG is important.

E. Ungersboeck: Advanced Modelling Aspects of Modern Strained CMOS Technology