Dynamics of negative muonium in<b><i>n</i></b>-type silicon

Abstract

Temperature-dependent diamagnetic amplitudes from radio-frequency muon spin-resonance data on two moderately to heavily doped n-type silicon samples require the presence of ${\mathrm{Mu}}_{T}^{\ensuremath{-}}.$ We determine the ${\mathrm{Mu}}_{T}^{\ensuremath{-}}$ to ${\mathrm{Mu}}_{T}^{0}$ ionization energy to be $0.56\ifmmode\pm\else\textpm\fi{}0.03 \mathrm{eV}$ for silicon, considerably higher than the ${\mathrm{Mu}}_{\mathrm{BC}}^{0}$ to ${\mathrm{Mu}}_{\mathrm{BC}}^{+}$ ionization energy of $0.21\ifmmode\pm\else\textpm\fi{}0.01 \mathrm{eV}.$ Thus muonium will be a negative-$U$ impurity only if the energy difference between the ${\mathrm{Mu}}_{T}^{0}$ and ${\mathrm{Mu}}_{\mathrm{BC}}^{0}$ configurations is less than 0.35 eV. The $\mathrm{Mu}(0/+)$ thermodynamic level correlates well with results for monatomic hydrogen, but the $\mathrm{Mu}(\ensuremath{-}/0)$ level is estimated to be shallower than that claimed for $\mathrm{H}(\ensuremath{-}/0).$ The muonium data show a complicated set of transitions active during the muon lifetime, and involving four separate muonium states. Similar rapid transitions should be considered when interpreting data on isolated hydrogen centers.