Long-Lived Spin Coherence in Silicon with an Electrical Spin Trap Readout

Pulsed electrically detected magnetic resonance of phosphorous (${}^{31}\mathrm{P}$) in bulk crystalline silicon at very high magnetic fields ($B_0>8.5\mathrm{T}$) and low temperatures ($T=2.8\mathrm{K}$) is presented. We find that the spin-dependent capture and reemission of highly polarized ($>95\%$) conduction electrons by equally highly polarized ${}^{31}\mathrm{P}$ donor electrons introduces less decoherence than other mechanisms for spin-to-charge conversion. This allows the electrical detection of spin coherence times in excess of $100\mu \mathrm{s}$, 50 times longer than the previous maximum for electrically detected spin readout experiments.

Figure 1

(a) 240 GHz electrically detected magnetic resonance spectrum of phosphorus donors in crystalline silicon. The two large resonances are separated by 4.2 mT, a signature of the hyperfine interaction with a phosphorus nuclear spin. The inset is a schematic of our experiment, shown in more detail in Fig. 1 of Ref. 17. (b) The spin of an excess electron in the conduction band is initially aligned with the applied field so the Pauli exclusion principle means it avoids the coaligned phosphorus spin. (c1) ESR flips the phosphorus spin. (c2) The conduction electron is trapped, reducing the current. (c3) An electron is reemitted, leaving the electron that remains in the opposite spin state.

Figure 2

Comparison of electrical and millimeter-wave ESR detected spin readouts: the plots show an ESR-induced current response (dark data) and the ESR-measured inversion recovery (lighter data). In both experiments, a short (480 ns) pulse of 240 GHz radiation excites the silicon sample. On resonance, the current is strongly reduced, exponentially returning towards equilibrium with a decay time of $2.5\pm 0.1\mathrm{ms}$. The millimeter-wave detected spin-lattice ($T_1$) relaxation time measured with the “inversion recovery” pulse sequence [24] is the same: $2.5\pm 0.1\mathrm{ms}$.

Figure 3

(a) An electrically detected spin echo observed using the pulse sequence illustrated in the inset. (b) Comparison of electrically detected (dark data) and radiation-detected (lighter data) spin-echo decays which reveals the same value for $T_2$. The smooth decay curves are fits with the function $\exp (-2\tau /T_2-8{\tau }^3/T_{\mathrm{S}}{}^3)$ which has previously [3, 25] been used to describe Si:P with naturally occurring ${}^{29}\mathrm{Si}$. $T_2$ is the intrinsic spin coherence time, and the dephasing due to ${}^{29}\mathrm{Si}$ nuclear spins is characterized by $T_{\mathrm{S}}$. Three electrically detected echoes are shown with their time axes expanded by a factor of 20 for clarity and with their $y$-axis units equal (but arbitrary).