Silicon is an ideal material for spintronic applications due to its long spin lifetime,
however, considerable spin relaxation in gated silicon structures was experimentally observed. Surface roughness scattering determines the transport in the channel at high carrier concentrations in thin silicon films.
We investigate the spin relaxation due to surface roughness. We present an analytical approach to analyze the surface roughness dominated spin relaxation in thin body silicon-on-insulator-based MOSFETs. To find the corresponding matrix elements for spin relaxation we use the effective k·p Hamiltonian for the two relevant valleys along the OZ-axis with the spin degree of freedom included.
The spin-orbit interaction couples the opposite spins from the opposite valleys. By applying a corresponding unitary transformation this coupling is effectively suppressed.
The transformed Hamiltonian describes the Kramers degenerate states pair with opposite spin directions. For each pair, the Hamiltonian is similar to the two-band k·p Hamiltonian for the conduction band written in the vicinity of the X point of the Brillouin zone. For the two-band k·p Hamiltonian the subband energies and wave functions are precisely determined, provided the confinement
potential is an infinite square well.
The surface roughness scattering matrix elements are proportional to the square of the product of the subband wave function derivatives at the interface.
To evaluate the electron spin relaxation due to spin-flip events we evaluate the matrix elements by using the wave functions with the opposite spin projections.
Normalized spin relaxation matrix elements display sharp peaks at the strain values where the intersubband splitting is reduced.
These minima determine the positions of the narrow hot spots (figure 1) characterized by strong spin relaxation.
Figure 2 shows the dependence of the spin lifetime on temperature in an unstrained film. As the temperature increases, the Fermi distribution becomes smoother around the Fermi energy. Therefore, the
number of hot spots responsible for spin relaxation also increases. This leads to a shorter spin lifetime at elevated temperatures.