Temperature-dependent NMR study of the impurity state in heavily doped Si:P

Abstract

We report $^{31}\mathrm{P}$ (impurity) and $^{29}\mathrm{Si}$ (host) nuclear magnetic resonance (NMR) data for heavily doped Si:P over a wide temperature range $(100--500\phantom{\rule{0.3em}{0ex}}\mathrm{K})$ for samples with nominal doping levels between $4\ifmmode\times\else\texttimes\fi{}{10}^{18}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$ and $8\ifmmode\times\else\texttimes\fi{}{10}^{19}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$. The data include resonance shifts, linewidths, and spin-lattice relaxation rates for both host and impurity nuclei. The NMR parameters for $^{31}\mathrm{P}$ exhibit complex dependences on temperature and dopant concentration that are distinct from those of the host $^{29}\mathrm{Si}$ nuclei indicating that the hyperfine fields at the impurity are determined by local characteristics of the impurity electronic state. For nominal carrier concentrations up to about $1\ifmmode\times\else\texttimes\fi{}{10}^{19}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$, the impurity NMR properties are inconsistent with expectation for fully ionized dopants with carriers exclusively occupying states in the conduction band. A simple impurity band model yields numerical simulations of the resonance shifts and relaxation rates that reproduce the qualitative features and are in semi-quantitative agreement with the $^{31}\mathrm{P}$ data. These results imply that free carriers in Si:P are in dynamic exchange with residual impurity states at concentrations as high as ${10}^{19}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$ and at temperatures well above room temperature.