Electron spin and momentum lifetimes in two-dimensional Si accumulation channels: Demonstration of Schottky-barrier spin metal-oxide-semiconductor field-effect transistors at room temperature

Abstract

We have investigated the electron spin lifetime ${\ensuremath{\tau}}_{\mathrm{S}}$ and momentum lifetime $\ensuremath{\tau}$ in a two-dimensional (2D) accumulation channel of Schottky-barrier spin metal-oxide-semiconductor field-effect transistors (spin MOSFETs). The spin MOSFETs examined in this study have Fe/Mg/MgO/Si Schottky-tunnel junctions at the source/drain and a 15-nm-thick nondegenerated Si channel with a phosphorus donor doping concentration ${N}_{\mathrm{D}}$ of $1\ifmmode\times\else\texttimes\fi{}{10}^{17}\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}3}$. We estimated $\ensuremath{\tau}$ and the electron diffusion coefficient ${D}_{e}$ in the 2D accumulation channel from experimental results of a Hall-bar-type MOSFET device and self-consistent calculations using Poisson's and Schr\odinger's equations. The spin MOSFETs with various channel lengths ${L}_{\mathrm{ch}}\phantom{\rule{0.28em}{0ex}}(=0.3\ensuremath{-}10\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{m})$ exhibited transistor characteristics with a high on/off ratio of $\ensuremath{\sim}{10}^{6}$ as well as clear spin-valve signals at 295 K. From the spin-valve signals measured with various gate electric fields $(2\ensuremath{-}5\phantom{\rule{0.16em}{0ex}}\mathrm{MV}/\mathrm{cm}), {\ensuremath{\tau}}_{\mathrm{S}}$ and the electron spin diffusion length ${\ensuremath{\lambda}}_{\mathrm{S}}$ were estimated. We found that the spin-flip rate per one momentum scattering event $\ensuremath{\tau}/{\ensuremath{\tau}}_{\mathrm{S}}$ is $\ensuremath{\sim}1/14\phantom{\rule{0.16em}{0ex}}000$, which is almost unchanged by the gate electric field. The proportionality between ${\ensuremath{\tau}}_{\mathrm{S}}$ and $\ensuremath{\tau}$ indicates that the Elliott-Yafet mechanism is dominant in the Si 2D electron accumulation channel, and that the spin-flip rate per one phonon scattering event and that per one surface roughness scattering event are the same. Based on the Elliott-Yafet theory, there is a possibility that the spin-orbit coupling in the Si 2D accumulation channel is almost twice as strong as that in bulk Si materials.