Electron nuclear double resonance with donor-bound excitons in silicon

We present Auger-electron-detected magnetic resonance (AEDMR) experiments on phosphorus donors in silicon, where the selective optical generation of donor-bound excitons is used for the electrical detection of the electron spin state. Because of the long dephasing times of the electron spins in isotopically purified ${}^{28}\mathrm{Si}$, weak microwave fields are sufficient, which allow one to realize broadband AEDMR in a commercial electron spin resonance resonator. Implementing Auger-electron-detected electron nuclear double resonance (ENDOR), we further demonstrate the optically assisted control of the nuclear spin under conditions where the hyperfine splitting is not resolved in the optical spectrum. Compared to previous studies, this significantly relaxes the requirements on the sample and the experimental setup, e.g., with respect to strain, isotopic purity, and temperature. We show AEDMR of phosphorus donors in silicon with natural isotope composition, and discuss the feasibility of ENDOR measurements also in this system.

Figure 1

(a) Level scheme showing the donor-bound exciton transitions. (b) Level population scheme demonstrating the principle of AEDMR. For details see text. (c) Photoconductive spectrum at $B=351\mathrm{mT}$ showing the six electron-spin-selective transitions. (d) Frequency of the $m_I=-1/2$ resonance as a function of the magnetic field $B$. Solid black and red lines represent calculated $m_I=-1/2$ and $m_I=+1/2$ peak positions, respectively, for $g=1.99851$ and a hyperfine interaction $A=117.52$ MHz.

Figure 2

Auger-detected electron spin resonance experiments on ${}^{28}\mathrm{Si}$. (a) Pulse sequence showing the laser tuning (red line) and an mw pulse (blue), as well a typical conductivity trace. (b) Resonance spectra and (c) Rabi oscillations of the ${}^{31}\mathrm{P}$ electron spin. (d) Pulse sequence used for electron spin echo experiments. (e) Echo for ${\tau }_1=10\mu \mathrm{s}$; (f) echo decay, revealing a coherence time $T_2=1.1\mathrm{ms}$. The data points shown in gray have been excluded from the exponential fit.

Figure 3

Schematic representation of the Auger-electron-detected ENDOR experiments. (a) Pulse sequence showing the laser tuning (red line), the mw (blue), and rf (green) pulses, as well a typical conductivity trace. (b) Level population diagram at points (i)–(iv) indicated in (a). Boxes represent the level populations before (solid boxes) and after (dashed boxes) the mw and rf transitions indicated by blue and green dashed arrows, respectively. The results of resonant (NMR) and off-resonant (no NMR) rf pulses are discussed in the top row and the bottom row, respectively.

Figure 4

(a) Auger-electron-detected ENDOR spectrum showing the two ${}^{31}\mathrm{P}$ nuclear spin resonances. (b) Rabi oscillations of the nuclear spin. (c) Nuclear spin echo. The rf pulses are slightly off resonance $\left(\mathrm{\Delta }f\approx 2.2\mathrm{kHz}\right)$. (d) Nuclear spin echo decay, which is well described by an exponential decay (black line), revealing a coherence time $T_2=51\mathrm{ms}$, which is not significantly changed by the application of dynamical decoupling pulses (red triangles).

Figure 5

(a) Photoconductive spectrum of phosphorus-doped silicon with natural isotope composition at $B=350\mathrm{mT}$. (b) Pulsed AEDMR spectrum of the same sample. (c) Rabi oscillation of the phosphorus electron spin.