Chapter 6
Summary and Outlook

”Try not to become a man of success, but rather try to become a man of value.”
Albert Einstein

The k p model is a powerful tool which allows to obtain the subband wave functions and the eigenenergies of stationary states in confined electron systems. The spin degree of freedom is incorporated in a two-band k p model which is in turn developed at the vicinity of the X-point in the Brillouin zone including the uniaxial shear tensile stress in [110] direction. This allows to find the electron subband energies and the corresponding spin-wave functions in thin silicon films under strain. The expressions of the wave functions are then obtained analytically, when their spin is parallel to the injection orientation.

In (001) oriented silicon films the degeneracy of the unprimed subbands is lifted by strain, which leads to a transport effective mass dependence on strain. The momentum relaxation time is observed to be increasing with strain but not significantly. The unprimed subbands degeneracy lifting turns out to be the most important effect for spin transport properties in silicon, because intervalley processes between equivalent valleys (g-processes) are dominant for spin relaxation. This is in contrast to the momentum relaxation time which is solely determined by the intravalley scattering. The minimum value of the unprimed subbands splitting, or the valley splitting, is determined by the strength of the spin-orbit interaction alone. The strongest mixing between the up-spin and down-spin states from the two unprimed subbands is observed, when the valley splitting reaches its minimum, which in turn results in the formation of the spin hot spots characterized by strong spin relaxation. For higher strain values the hot spots are pushed to higher energies away from the subband minima, causing a strong increase of the spin lifetime. The calculations are performed by considering surface roughness and electron-phonon interaction mediated spin relaxation. The transversal and longitudinal acoustic phonons are included. It turns out that strain routinely used to enhance mobility can also be used to boost the spin lifetime.

Including the primed subband into consideration, the evaluation of the spin lifetime due to the optical phonon induced scattering between non-equivalent valleys (f-processes) has been investigated. In thin films of less than 4nm the contributions from the optical phonons can be neglected, whereas the spin lifetime in bulk is primarily determined by them. In addition, the [001] equivalent valley coupling through the Γ-point results in a subband splitting even in the absence of strain, which in turn softens the spin hot spots. This eventually results in the less pronounced nature of the spin lifetime dependence on strain, although almost two orders of magnitude enhancement is predicted.

The spin relaxation is also sensitive to the spin injection orientation, and its inter- and intrasubband components are equally sensitive to it. The surface roughness, the acoustic, and the optical phonon mediated spin lifetimes increase, when the injection direction is drawn from the perpendicular-plane ([001] direction) towards the in-plane (i.e. [100] direction) of the sample, by a factor of two. The long lifetime in such a film is essential to build spin interconnects for all-spin logic devices and the developed direction sensitive model can be used as an extra degree of freedom for designing such circuits.

The spin drift-diffusion model is widely used to describe the classical transport of charge carriers and their spins in a semiconductor. The spin injection from a semiconductor ferromagnet into silicon is analyzed for charge neutrality and means to improve the injection efficiency by an electric field. When the charge neutrality condition is violated, the additional interface charge screening is noted to impact the spin density near the interface. The bulk spin injection efficiency is increased (decreased), when injected from a charge-depleted (accumulated) source. However, the injection efficiency is always limited by the bulk spin polarization in the ferromagnetic side.

By investigating spin injection in silicon from only a space-charge layer, one finds substantial differences in the spin signals. At a fixed interface spin polarization and fixed charge current, the interface spin current is enhanced through injecting more charge, but the bulk spin current is almost unchanged from that obtained at the charge neutrality condition. In contrast, the spin current (and the spin density) in both interface and the bulk is reduced, when spin is injected from a charge depletion region. This is an important phenomenon which implies that the observation of a spin current reduction serves as a signature of the injection of spins from a charge and spin depleted layer. In a broader perspective, these results will have consequences in the spin control in the mesoscopic devices.