Dynamic nuclear polarization of ${}^{29}\text{S}\text{i}$ nuclei in isotopically controlled phosphorus doped silicon

Dynamic nuclear polarization (DNP) of ${}^{29}\text{S}\text{i}$ nuclei in isotopically controlled silicon single crystals with the ${}^{29}\text{S}\text{i}$ isotope abundance $f_{29\text{Si}}$ varied from 1.2% to 99.2% is reported. It was found that both the DNP enhancement and ${}^{29}\text{S}\text{i}$ nuclear spin-lattice relaxation time under saturation of the electron paramagnetic resonance transitions of phosphorus donors increase with the decrease in the ${}^{29}\text{S}\text{i}$ abundance. A remarkably large steady-state DNP enhancement, $E^{\text{ss}}=2680$ which is comparable to the theoretical upper limit of 3310, has been achieved through the “resolved” solid effect that has been identified clearly in the $f_{29\text{Si}}=1.2\%$ sample. The DNP enhancement depends not only on the ${}^{29}\text{S}\text{i}$ abundance but also on the electron spin-lattice relaxation time that can be controlled by temperature and/or illumination. The linewidth of ${}^{29}\text{S}\text{i}$ NMR spectra after DNP shows a linear dependence on $f_{29\text{Si}}$ for $f_{29\text{Si}}\le 10\%$ and changes to a square-root dependence for $f_{29\text{Si}}\ge 50\%$. Comparison of experimentally determined nuclear polarization time with nuclear spin diffusion coefficients indicates that the rate of DNP is limited by the polarization transfer rather than by spin diffusion.

Figure 1

Dependences of the DNP enhancement $E$ and DNP degree $P_{\text{N}}$ on the saturation time $t$ in ${}^{29}\text{S}\text{i-}5\%\left({10}^{15}\right)$. The dotted line is a single exponential fitting to the experimental data (squares). The inset shows observed ${}^{29}\text{S}\text{i}$ NMR signals. EPR saturation was performed with a modulation amplitude $B_{\text{m}}=0.2\text{mT}$ at 12 K in dark.

Figure 2

Comparison of the EPR spectrum (solid curves) and the ${}^{29}\text{S}\text{i}$ NMR signal amplitude (squares) for samples (a) ${}^{29}\text{S}\text{i-}1\%$, (b) ${}^{29}\text{S}\text{i-}100\%$, (c) ${}^{29}\text{S}\text{i-}5\%\left({10}^{15}\right)$, and (d) ${}^{29}\text{S}\text{i-}5\%\left({10}^{17}\right)$. The EPR spectrum for (d) ${}^{29}\text{S}\text{i-}5\%\left({10}^{17}\right)$ is integrated. The NMR signal amplitudes are plotted as a function of the deviation of the magnetic field $B$ from the electron paramagnetic resonant magnetic field $B_0\approx 320\text{mT}$, $B-B_0$. The positive sign of the ${}^{29}\text{S}\text{i}$ NMR signal amplitude corresponds to the dynamic polarization opposite to the equilibrium ${}^{29}\text{S}\text{i}$ nuclear polarization. The up and down arrows in (a)–(c) indicate the magnetic fields $B_0-B_{\text{N}}$ and $B_0+B_{\text{N}}$ corresponding to the flip-flip and flip-flop transitions of the spin packet placed at $B_0$, respectively.

Figure 3

Dependences of the DNP enhancement $E^{\text{ss}}/E_{\text{max}}$ corrected for the equal concentration of the phosphorus donors (squares) and the inverse EPR PPLW $1/\Delta B_{\text{pp}}$ (circles) on the ${}^{29}\text{S}\text{i}$ abundance $f_{29\text{Si}}$ for ${}^{29}\text{S}\text{i-}1\%$, ${}^{29}\text{S}\text{i-}5\%\left({10}^{15}\right)$, ${}^{29}\text{S}\text{i-}10\%$, ${}^{29}\text{S}\text{i-}50\%$, and ${}^{29}\text{S}\text{i-}100\%$. $E^{\text{ss}}/E_{\text{max}}$ and $1/\Delta B_{\text{pp}}$ are normalized by the values of ${}^{29}\text{S}\text{i-}5\%\left({10}^{15}\right)$, respectively.

Figure 4

The DNP enhanced ${}^{29}\text{S}\text{i}$ NMR spectra detected in isotopically controlled silicon single crystals for orientation of the magnetic field approximately along the [111] crystal axis. The horizontal axis is offset by ${}^{29}\text{S}\text{i}$ nuclear Larmor frequency of 60 MHz and the vertical axis is in an arbitrary unit. The thermal equilibrium signal in a ${}^{29}\text{S}\text{i-}5\%\left({10}^{15}\right)$ is also shown (horizontal axis is arbitrarily shifted). The dotted curves in the ${}^{29}\text{S}\text{i-}50\%$ and ${}^{29}\text{S}\text{i-}100\%$ indicate the components of absorption curves obtained by fitting it with multiple Gaussian curves. The total area under the NMR spectra is normalized to be unity but multiplied to present their shapes clearly.

Figure 5

Dependence of the NMR linewidth due to the dipole-dipole interaction, $\Delta {\nu }_{\text{dd}}$, on the ${}^{29}\text{S}\text{i}$ abundance $f_{29\text{Si}}$ for ${}^{29}\text{S}\text{i-}1\%$, ${}^{29}\text{S}\text{i-}5\%\left({10}^{15}\right)$, ${}^{29}\text{S}\text{i-}10\%$, ${}^{29}\text{S}\text{i-}50\%$, and ${}^{29}\text{S}\text{i-}100\%$. The dashed lines show the linear and square-root dependences, respectively.

Figure 6

Variation in the phosphorus EPR spectrum with temperature in (a) ${}^{29}\text{S}\text{i-}5\%\left({10}^{16}\right)$ and (b) ${}^{29}\text{S}\text{i-}5\%\left({10}^{17}\right)$. The microwave power was fixed at 1 mW for all the measurements.

Figure 7

Temperature dependence of the EPR line intensity in (a) ${}^{29}\text{S}\text{i-}5\%\left({10}^{16}\right)$ and (b) ${}^{29}\text{S}\text{i-}5\%\left({10}^{17}\right)$. The intensities of the EPR line detected in dark (squares), under illumination with Nd:YLF-laser power of 750 mW (circles), and 425 mW (triangles) are shown. The microwave power was fixed at 1 mW in all the measurements.

Figure 8

Temperature dependence of the steady-state DNP enhancement $E^{\text{ss}}$ in (a) ${}^{29}\text{S}\text{i-}5\%\left({10}^{16}\right)$ and (b) ${}^{29}\text{S}\text{i-}5\%\left({10}^{17}\right)$. $E^{\text{ss}}$ in the dark (squares), under illumination with Nd:YLF-laser power of 750 mW (circles), and 425 mW (triangles) are shown. The left and right axes in (a) correspond to $E^{\text{ss}}$ under illumination and in the dark, respectively.

Figure 9

Dependences of the nuclear polarization rate $1/T_{1\text{N}}^{\text{p}}$ scaled to be the value at the donor concentration $N_{\text{d}}={10}^{15}{\text{cm}}^{-3}$ (squares), and the nuclear polarization rate assuming complete saturation and the absence of extraneous nuclear relaxation (circles). The latter rate is scaled to have the same value as the former rate at $f_{29\text{Si}}=1.2\%$.