NMR study of optically hyperpolarized phosphorus donor nuclei in silicon

We use above-band-gap optical excitation, via a 1047-nm laser, to hyperpolarize the ${}^{31}\mathrm{P}$ spins in low-doped ($N_D=6\times {10}^{15}{\mathrm{cm}}^{-3}$) natural abundance silicon at 4.2 K and 6.7 T, and inductively detect the resulting NMR signal. The 30-kHz spectral linewidth observed is dramatically larger than the 600-Hz linewidth observed from a ${}^{28}\mathrm{Si}$-enriched silicon crystal. We show that the broadening is consistent with previous electron-nuclear double-resonance results showing discrete isotope mass effect contributions to the donor hyperfine coupling. A secondary source of broadening is likely due to variations in the local strain, induced by the random distribution of different isotopes in natural silicon. The nuclear spin $T_1$ and the buildup time for the optically induced ${}^{31}\mathrm{P}$ hyperpolarization in the natural abundance silicon sample were observed to be $178\pm 47$ and $69\pm 6$ s, respectively, significantly shorter than the values previously measured in ${}^{28}\mathrm{Si}$-enriched samples under the same conditions. We measured the $T_1$ and hyperpolarization buildup time for the ${}^{31}\mathrm{P}$ signal in natural abundance silicon at 9.4 T to be $54\pm 31$ and $13\pm 2$ s, respectively. The shorter buildup and nuclear spin $T_1$ times at high field are likely due to the shorter electron spin $T_1$, which drives nuclear spin relaxation via nonsecular hyperfine interactions. At 6.7 T, the phosphorus nuclear spin $T_2$ was $16.7\pm 1.6$ ms at 4.2 K, a factor of 4 shorter than in ${}^{28}\mathrm{Si}$-enriched crystals. This was observed to shorten to $1.9\pm 0.4$ ms in the presence of the infrared laser.

Figure 1

Schematic representation of (a) a uniform ${}^{28}\mathrm{Si}$-enriched crystal, and (b) a natural silicon lattice containing ${}^{28}\mathrm{Si}$, ${}^{29}\mathrm{Si}$, and ${}^{30}\mathrm{Si}$ atoms. The 2-nm Bohr radius of the shallow ${}^{31}\mathrm{P}$ donor electron extends over a large number of silicon lattice sites. The main plot below shows normalized ${}^{31}\mathrm{P}$ NMR spectra from ${}^{28}\mathrm{Si}$ (red) and natural silicon (blue) samples, measured at 6.7 T and 4.2 K. A 1-kHz exponential line broadening has been applied to the spectrum from the natural silicon sample and a 100-Hz line broadening to the spectrum from the ${}^{28}\mathrm{Si}$ sample. The left inset shows a comparison of the observed NMR spectrum for natural silicon (shown in blue) and a simulation of the line shape (shown in black) expected from the mass effect model [15]. The inset also shows the four largest relative contributions from $M_{\text{NN}}\approx 28$ (orange), $M_{\text{NN}}\approx 28.25$ (green), $M_{\text{NN}}\approx 28.5$ (pink), and $M_{\text{NN}}\approx 28.75$ (red). The right inset shows the result of an NMR hole-burning experiment on the ${}^{28}\mathrm{Si}$ sample, with a 10-s-long saturation pulse using a weak 3-Hz Rabi frequency, indicting the inhomogeneous nature of the spectral line. The width of the spectral hole is about 200 Hz.

Figure 2

(a) Buildup of the hyperpolarized ${}^{31}\mathrm{P}$ signal at 9.4 T (black diamonds) and 6.7 T (black circles) in natural silicon as a function of illumination time ($\tau$) using a 1047-nm laser. The normalized data were fit to the function $1-exp\left(\tau /T_b\right)$, to find the characteristic buildup times $T_b^{9.4\text{T}}=13\pm 2$ s, and $T_b^{6.7\text{T}}=69\pm 6$ s. (b) Decay of the optically hyperpolarized ${}^{31}\mathrm{P}$ signal in natural silicon at 9.4 T (black diamonds) and 6.7 T (black circles), yielding $T_1$ relaxation times of $T_1^{9.4\text{T}}=54$ s and $T_1^{6.7\text{T}}=178$ s, respectively. For both subplots, the maximum signal at the two magnetic fields has been normalized to have a value of one since our experiments did not provide the magnitude of spin polarization.

Figure 3

${}^{31}\mathrm{P}$ nuclear spin coherence time $T_2$ in natural silicon measured with the Hahn echo at 4.2-K temperature, 6.7-T field. For the black circles the laser was kept on during acquisition, $T_2=1.9\pm 0.4$ ms, while for the black diamonds the laser was turned off during the acquisition, $T_2=16.7\pm 1.6$ ms. All data were measured with the Hahn echo, with 150 s of optical polarization provided by a 1047-nm, 150-mW, above-gap laser.