We discuss the vibrational dynamics of bond-centered protons $({\mathrm{H}}_{\mathrm{BC}}^{+})$ and deuterons $({\mathrm{D}}_{\mathrm{BC}}^{+})$ in monoisotopic ($^{28}\mathrm{Si}$, $^{29}\mathrm{Si}$, and $^{30}\mathrm{Si}$) silicon crystals, based on joint infrared absorption measurements and ab initio modeling studies. Protons and deuterons have been implanted at temperatures below $20\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, and in situ--type infrared absorption measurements have subsequently been performed at $8\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. A major absorption line is observed at $1998\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ after proton implantation, which has previously been ascribed to a local mode of ${\mathrm{H}}_{\mathrm{BC}}^{+}$. We find that the ${\mathrm{H}}_{\mathrm{BC}}^{+}$ mode at $1998\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ displays an anomalous (positive) frequency shift when the Si isotope mass is increased, unlike the analogous ${\mathrm{D}}_{\mathrm{BC}}^{+}$ mode at $1448\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$, which shows a negative shift. This effect cannot be described with a purely harmonic model. We show that the mode frequencies are accurately accounted for with a simple model based on a linear $\mathrm{Si}\text{\ensuremath{-}}\mathrm{H}\text{\ensuremath{-}}\mathrm{Si}$ structure when anharmonicity, volumetric effects due to the host-isotope mass, and the coupling of the $\mathrm{Si}\text{\ensuremath{-}}\mathrm{H}\text{\ensuremath{-}}\mathrm{Si}$ unit to the lattice are taken into account. Interstitial oxygen $({\mathrm{O}}_{i})$ atoms in silicon, also located at the bond-center site, are as well investigated in a parallel way. The relative contributions of the different terms of the vibrational model to the mode frequency of ${\mathrm{H}}_{\mathrm{BC}}^{+}$ and ${\mathrm{O}}_{i}$ are compared. The anomalous (positive) isotope shift of ${\mathrm{H}}_{\mathrm{BC}}^{+}$ results from mixing via anharmonicity of ${A}_{2u}$ and ${A}_{1g}$ modes of the $\mathrm{Si}\text{\ensuremath{-}}\mathrm{H}\text{\ensuremath{-}}\mathrm{Si}$ unit, which shows that a reliable vibrational model has to take into consideration the local structure of the defect. The mode frequency of the ${\mathrm{O}}_{i}$ defect exhibits the normal (negative) isotope shift, because the relatively modest contribution of anharmonicity diminishes the importance of the mode mixing. The effect of the defect-lattice coupling on the stretch-mode frequencies of ${\mathrm{H}}_{\mathrm{BC}}^{+}$ and ${\mathrm{O}}_{i}$ is also discussed.
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