Isotope Dependence of the Lifetime of the $1136\mathrm{\text{−}}{\mathrm{cm}}^{-1}$ Vibration of Oxygen in Silicon

By simply changing the isotopes of the Si atoms that neighbor an oxygen ${\mathrm{O}}_{\mathrm{i}}$ atom in crystalline silicon, the measured decay rate $\tau$ of the asymmetric-stretch vibration (${\nu }_3=1136{\mathrm{cm}}^{-1}$) of oxygen (${\mathrm{O}}_{\mathrm{i}}$) in silicon changes by a factor of $\sim 2.5$. These data establish that ${\nu }_3$ decays by creating one ${\nu }_1$ symmetric-stretch, local-vibrational mode of the $\mathrm{Si}\mathrm{\text{−}}{\mathrm{O}}_{\mathrm{i}}\mathrm{\text{−}}\mathrm{Si}$ structure. If the residual energy (${\nu }_3-{\nu }_1$) is less than the maximum frequency ${\nu }_m$ of the host lattice, as for ${}^{28}\mathrm{Si}\mathrm{\text{−}}{}^{16}\mathrm{O}\mathrm{\text{−}}{}^{28}\mathrm{Si}$ in natural silicon, then it is emitted as one lattice mode, and $\tau$ depends on the density of one-phonon states at ${\nu }_3-{\nu }_1$. If $({\nu }_3-{\nu }_1)>{\nu }_m$, as for ${}^{16}\mathrm{O}$ in single-isotope ${}^{30}\mathrm{Si}$ silicon, two lattice modes are created in addition to ${\nu }_1$, increasing $\tau$. Prediction of $\tau$ for a particular defect clearly requires a detailed knowledge of that defect.

Figure 1

The solid curves shows the one-phonon density of states, and the dotted lines the two-phonon densities, for natural silicon (upper panel) and for single-isotope ${}^{30}\mathrm{Si}$ (lower panel). The vertical lines show the differences $\Delta \nu ={\nu }_3-{\nu }_1$ for the isotope combinations, identified by the decay times shown in Table . The broken line is for ${}^{28}\mathrm{Si}\mathrm{\text{−}}{}^{18}\mathrm{O}\mathrm{\text{−}}{}^{28}\mathrm{Si}$, ${\tau }_m=11\mathrm{ps}$, $\Delta \nu =473{\mathrm{cm}}^{-1}$; see text.

Figure 2

Calculated energies of the three most active modes in the decay of ${\nu }_3$, labeled (a). The curves labeled (b) and (c) are ${\nu }_1$ and an optic phonon at $524{\mathrm{cm}}^{-1}$, respectively. The 10 ps lifetime shown is the average of five MD runs (see text).

Figure 3

The decay rate of the ${\nu }_3$ transient signal in ${}^{30}\mathrm{Si}$ as a function of $T$: points are measured data, the line is Eq. (1).