Dynamics and Reactivity of Positively Charged Muonium in Heavily Doped Si:B and Comparisons with Hydrogen

The detailed dynamics of the positively charged muonium (${\mathrm{Mu}}^{+}$) in heavily doped $p$-type Si:B is reported. Below 200 K, ${\mathrm{Mu}}^{+}$ is static and isolated, and is located in a stretched Si-Si bond. Above $\approx 200\mathrm{K}$, ${\mathrm{Mu}}^{+}$ diffuses incoherently. At temperatures higher than 300 K, the ${\mathrm{Mu}}^{+}\mathrm{\text{−}}{\mathrm{B}}^{-}$ complex is formed while above 520 K, it starts to dissociate. There is significant enhancement of the diffusion of ${\mathrm{Mu}}^{+}$ in Si compared to ${\mathrm{H}}^{+}$ and ${\mathrm{D}}^{+}$—this is attributed to its smaller mass.

Figure 1

Time-dependent muon polarization spectra at 290 K (triangles) and 11 K (circles). The solid red (gray) curves are fits to the static Kubo-Toyabe function, while the solid green (light gray) curve is the fit to the 11 K data as described in the text. The inset is a schematic of the ${\mathrm{Mu}}^{+}$ in the Si-Si bond, which is stretched by $\approx 29\%$.

Figure 2

Temperature dependence of the muon relaxation rate $\Delta$ obtained from fitting the $\mu \mathrm{SR}$ data to the static Kubo-Toyabe function. The inset shows schematically the tunneling of ${\mathrm{Mu}}^{+}$ around the B.

Figure 3

Temperature dependence of the diffusion coefficients in Si for ${\mathrm{Mu}}^{+}$ compared to ${\mathrm{H}}^{+}$ and ${\mathrm{D}}^{+}$ obtained by Herring et al. [10]. The inset shows the temperature dependence of the ${\mathrm{Mu}}^{+}$ hop rate in Si. The solid lines are fits to an Arrhenius law (see text).