Coupling of Erbium-Implanted Silicon to a Superconducting Resonator

Erbium-implanted silicon is promising for both photonic and quantum-technology platforms, since it possesses both telecommunications and integrated-circuit processing compatibility. However, several different $\mathrm{Er}$ centers are generated during the implantation and annealing process, the presence of which could hinder the development of these applications. When $\mathrm{Si}$ is coimplanted with ${10}^{17}{\mathrm{cm}}^{-3}$ $\mathrm{Er}$ and ${10}^{20}{\mathrm{cm}}^{-3}$ $\mathrm{O}$ ions, and the appropriate annealing process is used, one of these centers, which is present at higher $\mathrm{Er}$ concentrations, can be eliminated. Characterization of samples with $\mathrm{Er}$ concentrations of <${10}^{17}{\mathrm{cm}}^{-3}$ is limited by the sensitivity of standard electron paramagnetic resonance (EPR) instruments. The collective coupling strength between a superconducting (SC) $\mathrm{Nb}\mathrm{N}$ lumped-element resonator and a ${10}^{17}{\mathrm{cm}}^{-3}$ $\mathrm{Er}$-implanted $\mathrm{Si}$ sample at 20 mK is measured to be about 1 MHz, which provides a basis for the characterization of low-concentration $\mathrm{Er}$-implanted $\mathrm{Si}$ and for future networks of hybrid quantum systems that exchange quantum information over the telecommunication network. Of six known $\mathrm{Er}$-related EPR centers, only one trigonal center couples to the SC resonator.

Figure 1

EPR spectra of 10¹⁷ cm⁻³ $\mathrm{Er}$ and 10¹⁹ cm⁻³ $\mathrm{Er}$-implanted $\mathrm{Si}$. Resonances are assigned to the EPR centers in Table 1, $\mathrm{OE}\mathrm{r}-1$, $\mathrm{OE}\mathrm{r}-2$′ etc., as 1,2′ etc., and U is the unidentified EPR center. Microwave frequency is 9.61 GHz, and magnetic field is parallel to the [001] direction of the wafer.

Figure 2

PL spectra of 10¹⁷ cm⁻³ $\mathrm{Er}$ and 10¹⁹ cm⁻³ $\mathrm{Er}$-implanted $\mathrm{Si}$ at 65 K. PL peaks are assigned to orthorhombic $\mathrm{Er}-\mathrm{O}$1R, cubic $\mathrm{Er}-\mathrm{C},$ and unknown (PL-U) PL centers in Table 1 with arrows. Arrows are marked with 9, 7, or 9/7 if the peaks can be identified in the 10¹⁹ cm⁻³ $\mathrm{Er}$ spectrum, 10¹⁷ cm⁻³ $\mathrm{Er}$ spectrum, or both spectra, respectively.

Figure 3

(a) Image of the SC resonator that is coupled to the 10¹⁷ cm⁻³ $\mathrm{Er}$ sample. The [110] direction of the sample, which is placed on top of and covers the resonator, is shown, along with the 0° and 90° directions of the magnetic field. (b) Angular-dependent microresonator EPR measurements at 20 mK. (c) Simulated angular-dependent EPR spectrum using easyspin numerical modeling for the trigonal $\mathrm{OE}\mathrm{r}-2$′ center identified by Carey et al. [21] with g_ǁ= 0.69 and $g^{\mathrm{\perp }}$ = 3.24. (d) Simulated angular-dependent EPR extended to higher B₀ to show the positions of the three expected EPR resonances with trigonal symmetry. Microwave frequency is 3.04 GHz for all microresonator measurements and simulations.

Figure 4

Measured Q factor, with the baseline subtracted, of the microresonator EPR measurement with a field orientation of 0° fitted using Eq. (5). Inset shows the total measured Q factor without baseline subtraction.