Spin relaxation and donor-acceptor recombination of ${\mathrm{Se}}^{+}$ in 28-silicon

Selenium impurities in silicon are deep double donors and their optical and electronic properties have been recently investigated due to their application for infrared detection. However, a singly ionized selenium donor $\left({\mathrm{Se}}^{+}\right)$ possesses an electron spin which makes it a potential candidate as a silicon-based spin qubit, with significant potential advantages compared to the more commonly studied group V donors. Here we study the electron spin relaxation $\left(T_1\right)$ and coherence $\left(T_2\right)$ times of ${\mathrm{Se}}^{+}$ in isotopically purified 28-silicon, and find them to be up to two orders of magnitude longer than shallow group V donors at temperatures above $\sim 15\mathrm{K}$. We further study the dynamics of donor-acceptor recombination between selenium and boron, demonstrating that it is possible to control the donor charge state through optical excitation of neutral ${\mathrm{Se}}^0$.

Figure 1

X-band cw-ESR of ${\mathrm{Se}}^{+}$ in ${}^{28}\mathrm{Si}$ at X-band for ${}^{28}\mathrm{Si}$:${}^{\text{nat}}\mathrm{Se}$ (upper) and ${}^{28}\mathrm{Si}$:${}^{77}\mathrm{Se}$ (lower). The natural abundance of ${}^{77}\mathrm{Se}$ is $7.5\%$, with the remaining isotopes ($92.5\%$ abundance) possessing zero nuclear spin. The ${}^{77}\mathrm{Se}$-doped sample shows predominantly the hyperfine-split lines arising from coupling to the $I=1/2$ nuclear spin of ${}^{77}\mathrm{Se}$, while additional features in the spectrum correspond to residual isotopes of Se and the presence of SeH pairs. Microwave frequency = 9.38 GHz; temperature = 23 K.

Figure 2

Temperature dependence of electron spin relaxation $T_1$ in ${}^{28}\mathrm{Si}$:$\stackrel{+}{{}^{77}\mathrm{Se}}$ and Si:P at $B\sim 0.34\mathrm{T}$. Solid lines are fits to the experimental data, made up of contributions (dashed lines) from different relaxation mechanisms. Data for Si:P is from Ref. [20].

Figure 3

Measured and extrapolated $T_2$ in ${}^{28}\mathrm{Si}$:$\stackrel{+}{{}^{77}\mathrm{Se}}$ at $B\sim 0.34\mathrm{T}$. (a) $1/T_2$ as function of the refocusing pulse rotation angle ${\theta }_2$. The intercept of the linear fit gives the extrapolated $T_2$ corresponding to the suppression of the instantaneous diffusion (ID), while the slope gives a ${\mathrm{Se}}^{+}$ concentration of $4\times {10}^{13}{\mathrm{cm}}^{-3}$. (b) The value of $T_2$ is limited by $T_1$ above $\sim 12\mathrm{K}$. Below this temperature, the extrapolated value of $T_2$ (in the absence of ID) can be well described by a combination of spectral diffusion arising from $T_1$-induced spin flips of neighboring ${\mathrm{Se}}^{+}$ spins, combined with a temperature-independent mechanism that limits $T_2$ to about $80\mathrm{ms}$. The details of the fit of $T_2$ and its temperature dependence are described in the Supplemental Material [17].

Figure 4

Schematic representation of the recombination mechanisms in selenium doped silicon after above band gap illumination. (a) Under thermal equilibrium one of the electrons from a Se impurity moves to an acceptor B forming a DA pair (${\mathrm{Se}}^{+}{\mathrm{B}}^{-}$). Under $1047\mathrm{nm}$ illumination, electron-hole pairs are formed. (b) The excess charge carriers recombine through the impurity levels, forming a nonequilibrium state. (c) The process of DA recombination reestablishes thermal equilibrium. (d) Under $4\mu \mathrm{m}$ illumination an electron from ${\mathrm{Se}}^0$ is continuously pumped into the conduction band enhancing the rate at which thermal equilibrium is reestablished. The normalized concentration of selenium in the ${\mathrm{Se}}^{+}$ state ($\langle {\text{Se}}^{+}\rangle$) is monitored by plotting the normalized electron spin echo intensity, as a function of wait time, after a pulse of above band gap illumination, (e) in the dark, or (f) in the presence of $4\mu \mathrm{m}$ illumination. Red circles show normalized electron spin echo intensity and black lines are fits (see main text).