Electron Spin Coherence and Electron Nuclear Double Resonance of Bi Donors in Natural Si

Donors in silicon hold considerable promise for emerging quantum technologies, due to their uniquely long electron spin coherence times. Bismuth donors in silicon differ from more widely studied group V donors, such as phosphorous, in several significant respects: They have the strongest binding energy (70.98 meV), a large nuclear spin ($I=9/2$), and a strong hyperfine coupling constant ($A=1475.4\mathrm{MHz}$). These larger energy scales allow us to perform a detailed test of theoretical models describing the spectral diffusion mechanism that is known to govern the electron spin decoherence of P donors in natural silicon. We report the electron-nuclear double resonance spectra of the Bi donor, across the range 200 MHz to 1.4 GHz, and confirm that coherence transfer is possible between electron and nuclear spin degrees of freedom at these higher frequencies.

Figure 1

Electron spin resonance of $\mathrm{Si}:\mathrm{Bi}$ donors at the $X$ band (9.7 GHz). (a) Energy levels of the coupled electron-nuclear spin system as a function of magnetic field. The allowed EPR transitions at 9.7 GHz are indicated with vertical lines, each corresponding to a different $m_I$ projection for the $I=9/2$ ${}^{209}\mathrm{Bi}$ nuclear spin. (b) Experimental electron spin echo intensity as a function of magnetic field yields the 10 expected resonances. $\mathrm{\text{Temperature}}=16\mathrm{K}$; simulation parameters: $A=1475.4\mathrm{MHz}$, $g_e=2.00$, and ${\gamma }_{\mathrm{Bi}}=6.962\mathrm{MHz}/\mathrm{T}$.

Figure 2

Two-pulse electron spin echo decay of the $\mathrm{Si}:\mathrm{Bi}$ donor as a function of angle of the applied magnetic field $B_0$ with respect to the [100] crystal axis. Crystal rotation is performed in the [100]–[011] plane. $T=12\mathrm{K}$ and $B_0=5663\mathrm{G}$.

Figure 3

Extracted spectral diffusion times $T_{\mathrm{SD}}$ as a function of crystal orientation and magnetic field. (a) A fit to the electron spin echo decay curves provides a measure of $T_{\mathrm{SD}}$ as a function of the angle of the applied magnetic field $B_0$ with respect to the [100] crystal axis, performed on two of the ten hyperfine lines: 5663 (blue circles) and 2542 G (red squares). The solid curve is a spline fit through the data for 5663 G, which is multiplied by 1.05 to produce the dashed curve. (b) The inset shows the magnetic field dependence of $T_{\mathrm{SD}}$ for six field positions ($\theta =0°$), showing good agreement with the results of the simulation (see text). $\mathrm{\text{Temperature}}=12\mathrm{K}$.

Figure 4

ENDOR of ${}^{209}\mathrm{Bi}$ in silicon. (a) Dashed curves show the theoretical ENDOR frequencies as a function of field, for each $\Delta m_I=1$ transition. Symbols represent those values measured by Davies ENDOR at the $X$ band, at each of the 10 resonant fields of the EPR spectrum. (b) and (c) show two typical ENDOR peaks, at 1345.4 and 677.4 MHz with rf $\pi$-pulse $\mathrm{\text{length}}=4$ and $7\mu \mathrm{s}$, respectively.