Spin transport in Si-based spin metal-oxide-semiconductor field-effect transistors: Spin drift effect in the inversion channel and spin relaxation in the n+-Si source/drain regions

We have experimentally and theoretically investigated the electron spin transport and spin distribution at room temperature in a Si two-dimensional (2D) inversion channel of back-gate-type spin metal-oxide-semiconductor field-effect transistors (spin MOSFETs). The magnetoresistance ratio of the spin MOSFET with a channel length of 0.4$\mu$m was increased by a factor of 6 from that in our previous paper [Phys. Rev. B 99, 165301 (2019)] by lowering the parasitic resistances at the source/drain junctions with highly-phosphorus-doped n+-Si regions and by increasing the lateral electric field in the channel along the electron transport, called "spin drift". Clear Hanle signals with some oscillation peaks were observed for the spin MOSFET with a channel length of 10 $\mu$ m under the lateral electric field, indicating that the effective spin diffusion length is dramatically enhanced by the spin drift. By taking into account the n+-Si regions and the spin drift in the channel, one-dimensional analytic functions were derived for analyzing the effect of the spin drift on the spin transport through the channel and these functions were found to explain almost all the experimental results. From the calculated spin current and spin distribution, it was revealed that almost all the spins are unflipped during the spin-drift-assisted transport through the 0.4-$\mu$m-long inversion channel, but the most part of the injected spins from the source electrode are relaxed in the n+-Si regions of both the source and drain junctions. This means that the spin drift is useful and precise design of the device structure is essential to obtain a higher magnetoresistance ratio. Furthermore, we showed that the effective spin resistances that are introduced in this study are very helpful to understand how to improve the magnetoresistance ratio of spin MOSFETs for practical use.