Chapter 9
Summary and Outlook

The kp approach is a powerful tool which allows to obtain the wave functions and the eigenenergies of stationary states in confined electron systems. A two-band kp model including spin is employed to find the electron subband energies and the corresponding wave functions in thin silicon films under shear strain. To describe spin properties in silicon films an important ingredient, the intrinsic spin-orbit interaction is taken into account. The kp model is extensively verified by comparing the results to a computationally more demanding but more accurate method which allows to represent the wave function by an appropriate linear combination of bulk band Bloch functions. The Bloch functions are obtained from a non-local pseudo-potential solver.

The use of the two-band kp model with spin-orbit interaction included allows to investigate the subband structure including spin. In (001) oriented silicon films the degeneracy of the unprimed subbands is lifted by shear strain. The value of the splitting depends on the in-plane wave vector value, the film thickness, the external electric field, and strain. This leads to the transport effective mass dependence on strain. By taking into account this dependence the mobility in thin films is expected to be enhanced by 30-40% along the [110] direction of tensile strain. The usually ignored dependence of the surface roughness and electron-phonon scattering matrix elements on shear strain results in additional 70% mobility enhancement resulting in an overall two-fold mobility enhancement in thin silicon films.

The unprimed subbands degeneracy lifting is even more important for spin transport properties in silicon. Indeed, it is shown that when the spin-orbit interaction is taken into account the minimum value of the energy splitting between the spin-up and spin-down states from the two otherwise degenerate unprimed subbands is determined by the strength of the spin-orbit interaction alone. This leads to a strong mixing between the spin-up and spin-down states from the two unprimed subbands resulting in the formation of the hot spots characterized by strong spin relaxation. With shear strain the degeneracy is lifted, which results in an almost two orders of magnitude increase of the spin lifetime in thin silicon films. The calculations are performed by considering surface roughness and electron-phonon interaction mediated spin relaxation. Both transversal and longitudinal acoustic phonons are included. Because of the necessity to perform double integration with respect to the in-plane momentum on which the wave functions depend upon, the use of analytically found wave functions was a critical to reduce the computation time. It was found that, in contrast to the momentum relaxation time determined by the intravalley scattering, intervalley processes between equivalent valleys (g-processes) are the most important for spin relaxation.

The same but properly rotated two-band kp Hamiltonian with spin also allows to find the dispersions and the wave functions of the primed subbands. Evaluation of the spin relaxation due to optical phonons mediated scattering between non-equivalent valleys (f-processes) demonstrates that in thin films f-scattering can be neglected, in contrast to bulk silicon where it is mostly responsible for spin lifetime. The inclusion of the zero-strain valley splitting is done by considering the valley coupling through the Γ-point. This softens the spin relaxation hot spots, although the strong spin lifetime enhancement with strain is preserved.

The long spin lifetime in strained silicon films make these structures attractive for use as spin conducting channels in spin field-effect transistors. It is shown that in short silicon channels the conduction band mismatch between the channel and the ferromagnetic contacts allows to modulate tunneling magnetoresistance but only at low temperature. At room temperature the magnetoresistance oscillations are preserved only if the Schottky barriers between the channel and the contacts are present. It is shown that due to the larger transport mass and therefore stronger spin-orbit interaction the length of the channel needed to observe the maximum magnetoresistance modulation is shorter for [001] oriented silicon fins making them preferred candidates for practical implementations. However, even in this case the length of the channel is close to a micron, and finding efficient ways to manipulate spins in silicon by purely electrical means become paramount.

The spin properties and spin transport in silicon films are promising for designing low power devices in the near future. The methods developed in the thesis can be generalized to study the spin transport in three-dimensional structures and FinFETs. Because the numerical solution of the Schršodinger equation is required, developing fast Schršodinger equation solver, interpolation schemes, and extensive use of accelerators (Intel Xeon PhiTMor GPU) is necessary in the future for an ultimate evaluation of spin properties in confined silicon systems.