Figure 1

(a) The transient bleaching signal $S_b$ decays exponentially with a time constant $T_1=12.2\pm 0.8\mathrm{ps}$ for the bending mode of $\mathrm{H}_2{}^{*}$ in Si. The structure of $\mathrm{H}_2{}^{*}$ is shown in the inset. (b), (c) show the IR absorbance spectra of $e$-irradiated, H- and D-containing Si, respectively.Reuse & Permissions

Figure 2

(a) Temperature dependence of $T_1$ of the $817{\mathrm{cm}}^{-1}$ mode of $\mathrm{H}_2{}^{*}$ obtained by transient bleaching spectroscopy. The dashed and solid lines are theoretical predictions for decay into three phonons $\{517,150,150\}$ and two phonons $\{460,357\}{\mathrm{cm}}^{-1}$, respectively. (b) Two-phonon density of states in Si. The $\mathrm{H}_2{}^{*}$ bending mode at $817{\mathrm{cm}}^{-1}$ coincides with $\mathrm{LA}+\mathrm{TO}$ phonons, whereas the $\mathrm{D}_2{}^{*}$ bending mode at $588{\mathrm{cm}}^{-1}$ lies in the $\mathrm{TA}+\mathrm{TO}$ phonon band.Reuse & Permissions

Figure 3

Vibrational lifetimes of H-related bending modes via decay order in different hosts. The line is a fit of Eq. (4) with two parameters: $A=0.15\mathrm{ps}$ and $B=2.01$. Tight-binding molecular dynamics simulations predict a lifetime of 0.3–0.5 ps for Si-D at $460{\mathrm{cm}}^{-1}$ in Si ($N=1$) and 5–6 ps for Si-H at $640{\mathrm{cm}}^{-1}$ ($N=2$) [9]. The linewidth of the Si-H bending mode in Si-doped GaAs at $896{\mathrm{cm}}^{-1}$ is $\sim 0.02{\mathrm{cm}}^{-1}$ [23], which corresponds to a lifetime of $\sim 260\mathrm{ps}$. Since the maximum phonon frequency in GaAs is at $290{\mathrm{cm}}^{-1}$, there must be at least 4 phonons involved in the decay process. The linewidth of the Si-H bending mode at $890{\mathrm{cm}}^{-1}$ in Si-doped AlAs is $0.07{\mathrm{cm}}^{-1}$ [24], which corresponds to a lifetime of $\sim 75\mathrm{ps}$. The maximum phonon frequency of AlAs is $402{\mathrm{cm}}^{-1}$, which leads to $N=3$. The linewidth of Si-D in GaAs at $641{\mathrm{cm}}^{-1}$ is around $0.13{\mathrm{cm}}^{-1}$, corresponding to $T_1=40\mathrm{ps}$ and $N=3$ [25]. S(Se,Te)-H modes have almost the same frequencies with linewidths of $0.045–0.09{\mathrm{cm}}^{-1}$ corresponding to $T_1=55–110\mathrm{ps}$ and $N=3$ [26], whereas the linewidths of the corresponding D modes are broader in the range $0.3–0.6{\mathrm{cm}}^{-1}$ ($T_1=8–16\mathrm{ps}$) due to their lower-order decay process ($N=2$).Reuse & Permissions