  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.
