Precise estimation of spin drift velocity and spin mobility in the absence of synthetic Rashba spin-orbit field in a Si metal-oxide-semiconductor

The discovery of built-in and synthetic Rashba fields in Si spin channels [S. Lee et al., Nat. Mater. 20, 1228 (2021)] challenged the conventional understanding of spin transport physics in semiconducting materials and forced researchers to reconsider the procedures used for estimating spin drift velocity and spin mobility. A conventional procedure for the estimation involves the detection of the Hanle-type spin precession under the application of an external magnetic field perpendicular to the plane; however, the in-plane effective magnetic fields due to the built-in Rashba fields hamper precise estimation because of the additional spin precession. In this work, we establish a precise method to estimate spin drift velocity and spin mobility, in addition to the spin lifetime and spin diffusion constant, by appropriately tuning the Rashba fields. Beyond the emblematic case of Si, the established method can be applied to other semiconductors, such as Ge and GaAs.

Figure 1

Schematic and top optical microscopic images of device structures for (a) nondegenerate $n$-type Si and (b) degenerate $n$-type Si. Schematic images of measuring setups for the (c) nonlocal four-terminal oblique Hanle measurement and (d) local three-terminal Hanle measurement.

Figure 2

(a) Results of the nonlocal four-terminal oblique Hanle measurement for various β in nondegenerate $n$-type Si. Solid lines show fitting results using the conventional fitting function for the Hanle-type spin precession (see also [21]). (b) The normalized spin voltages for various β as a function of $\mathrm{co}{\mathrm{s}}^2$β. The red solid line shows the fitting result obtained using Eq. (1). (c) The $V_{\mathrm{g}}$ dependence of the spin lifetime anisotropy ratio ζ in nondegenerate $n$-type Si.

Figure 3

(a) Results of the local three-terminal Hanle measurement using $I=200\mu \mathrm{A}$ and $V_{\mathrm{g}}=6\mathrm{V}$ in nondegenerate Si, where the Rashba field is fully suppressed. The red solid line shows the fitting result obtained using Eq. (4). (b) The source-drain electric field dependence of spin drift velocity. The red solid line shows the linear fitting used to extract spin mobility.

Figure 4

(a) Results of the nonlocal four-terminal oblique Hanle measurement for various β in degenerate $n$-type Si. Solid lines show fitting results using the conventional fitting function for the Hanle-type spin precession (see also [21]). (b) The normalized spin voltages for various β as a function of $\mathrm{co}{\mathrm{s}}^2$β. The red solid line shows the fitting result obtained using Eq. (1).