Nuclear magnetic resonance linewidth and spin diffusion in ${}^{29}\text{S}\text{i}$ isotopically controlled silicon

A nuclear magnetic resonance (NMR) study was performed with $n$-type silicon single crystals containing ${}^{29}\text{S}\text{i}$ isotope abundance $f$ ranges from 1.2% to 99.2%. The nuclear spin diffusion coefficient $D$ has been determined from the linewidth of significantly enhanced ${}^{29}\text{S}\text{i}$ NMR signals utilizing a developed dynamic nuclear polarization (DNP) method. The ${}^{29}\text{S}\text{i}$ NMR linewidth depends linearly on $f$, at least when $f<10\%$, and approaches $\propto f^{1/2}$ dependence when $f>50\%$. The estimated ${}^{29}\text{S}\text{i}$ nuclear spin diffusion time $T_{\text{sd}}$ between phosphorus atoms used for DNP is more than ten times shorter than the nuclear polarization time $T_1^p$ of ${}^{29}\text{S}\text{i}$ nuclei around phosphorus. Therefore, the regime of “rapid spin diffusion” is realized in the DNP experiments.

Figure 1

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 [111] crystal axis. The horizontal axis is offset by ${}^{29}\text{S}\text{i}$ nuclear Larmor frequency of 60 MHz; the vertical axis is arbitrary. The thermal equilibrium signal in a ${}^{29}\text{S}\text{i-}5\%$ sample is also shown (horizontal axis is arbitrarily shifted). The dotted curves in the ${}^{29}\text{S}\text{i-}50\%$ and 100% samples indicate the components of absorption curve 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 2

Dependence of the NMR linewidth $\Delta \nu$ determined by Eq. (5) (squares) and FWHM (circles) on the ${}^{29}\text{S}\text{i}$ isotope abundance $f$.

Figure 3

Dependence of the NMR linewidth due to the dipole-dipole interaction, $\Delta {\nu }_{\text{dd}}$, determined by Eq. (5) (squares) and FWHM (circles) on the ${}^{29}\text{S}\text{i}$ isotope abundance $f$. The dashed lines show the linear and square-root dependences.

Figure 4

Dependence of the ${}^{29}\text{S}\text{i}$ nuclear-spin-diffusion coefficient $D$ on the ${}^{29}\text{S}\text{i}$ isotope abundance $f$.