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We have experimentally and theoretically investigated the spin injection/detection polarization in a Si-based ferromagnetic tunnel junction with an amorphous MgO layer, and demonstrated that the experimental features of the spin polarization in a wide bias range can be well explained using our theoretical model based on the band diagram of the junction and the direct tunneling mechanism. It is shown that the spin polarization originates from the band diagrams of the ferromagnetic Fe layer and n+-Si channel in the junction, while the spin selectivity of the MgO tunnel barrier is not necessary. Besides, we clarified the mechanism of the reduction in spin polarization when the bias is high and nonlinear properties are prominent, where the widely-used spin injection/detection model proposed by Valet and Fert is not applicable. The dominant mechanism of such reduction is found to be spin accumulation saturation (SAS) at the n+-Si interface in contact with the MgO layer as the bias is increased in the spin extraction geometry, which is inevitable in semiconductor-based ferromagnetic tunnel junctions. We performed numerical calculations on a two-terminal spin transport device with a n+-Si channel using the junction properties extracted from the experiments, and revealed that the magnetoresistance (MR) ratio is suppressed mainly by SAS in a higher bias range. Furthermore, we proposed methods for improving the MR ratio in two-terminal spin transport devices. Our experiments and theoretical model provide a deep understanding of the spin injection/detection phenomena in semiconductor-based spin transport devices, toward the realization of high performance under reasonably high bias conditions for practical use., Comment: Main manuscript:32 pages, 18 figures Supplemental material: 18 pages, 10 figures

Department of Electrical Engineering and Information Systems, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan Center for Spintronics Research Network (CSRN), The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan, Comment: 26 pages, 5 figures, 1 table

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.

We demonstrated that the spin injection/extraction efficiency is enhanced by an ultrathin Mg insertion layer (<= 2 nm) in Fe/Mg/MgO/n+-Si tunnel junctions. In diode-type vertical three-terminal devices fabricated on a Si substrate, we observed the narrower three-terminal Hanle (N-3TH) signals indicating true spin injection into Si, and estimated the spin polarization in Si to be 16% when the thickness of the Mg insertion layer is 1 nm, whereas no N-3TH signal was observed without Mg insertion. This means that the spin injection/extraction efficiency is enhanced by suppressing the formation of a magnetically-dead layer at the Fe/MgO interface. We have also observed clear spin transport signals, such as non-local Hanle signals and spin-valve signals, in a lateral four-terminal device with the same Fe/Mg/MgO/n+-Si tunnel junctions fabricated on a Si-on-insulator substrate. It was found that both the intensity and linewidth of the spin signals are affected by the geometrical effects (device geometry and size). We have derived analytical functions taking into account the device structures, including channel thickness and electrode size, and estimated important parameters; spin lifetime and spin polarizations. Our analytical functions well explain the experimental results. Our study shows the importance of suppressing a magnetically-dead layer, and provides a unified understanding of spin injection/detection signals in different device geometries., Comment: 32 pages, 7 figures, 2 tables