Spin relaxation through lateral spin transport in heavily doped $n$-type silicon

We experimentally study temperature-dependent spin relaxation including lateral spin diffusion in heavily doped $n$-type silicon ($n^{+}-\mathrm{Si}$) layers by measuring nonlocal magnetoresistance in small-sized CoFe/MgO/Si lateral spin-valve (LSV) devices. Even at room temperature, we observe large spin signals, 50-fold the magnitude of those in previous works on $n^{+}-\mathrm{Si}$. By measuring spin signals in LSVs with various center-to-center distances between contacts, we reliably evaluate the temperature-dependent spin diffusion length (${\lambda }_{\mathrm{Si}}$) and spin lifetime (${\tau }_{\mathrm{Si}}$). We find that the temperature dependence of ${\tau }_{\mathrm{Si}}$ is affected by that of the diffusion constant in the $n^{+}-\mathrm{Si}$ layers, meaning that it is important to understand the temperature dependence of the channel mobility. A possible origin of the temperature dependence of ${\tau }_{\mathrm{Si}}$ is discussed in terms of the recent theories by Dery and co-workers.

Figure 1

(a) Optical micrograph of a fabricated $n^{+}$-Si–based LSV. (b) Nonlocal magnetoresistance curve at 303 K. The inset shows nonlocal four-terminal Hanle-effect curves for the parallel and antiparallel magnetization configurations at 303 K. The solid curves are the results of fitting to Eq. (2) in Ref. [24].

Figure 2

$d$ dependence of $|\mathrm{\Delta }{R}_{\mathrm{NL}}|$ at 303 K. The dashed line shows the results of fitting to Eq. (1). The inset is the NL magnetoresistance curve at 303 K for a device with $d=$ 3.75 $\mu \mathrm{m}$.

Figure 3

Temperature dependence of ${\lambda }_{\mathrm{Si}}$ estimated by $d$ dependences of NL spin signals at various temperatures, as shown in the inset.

Figure 4

(a) Temperature dependence of $D$, estimated from Eq. (4) in Ref. [37]. (b) Temperature dependence of ${\tau }_{\mathrm{Si}}$ in the $n^{+}-\mathrm{Si}$ layer used, together with the theoretical fitting curve (gray dashed curve) is based on Eqs. (2, 3, 4, 5). The inset shows the temperature dependence of $\mu$ in the $n^{+}-\mathrm{Si}$ layer used.