Nonlocal host isotope effect in silicon: High-resolution spectroscopy of the 29 cm${}^{-1}$ oxygen vibrational line

To investigate a possible host isotope effect on the local-mode-coupled low-energy two-dimensional motion of interstitial oxygen in silicon, we have measured the resonance parameters of the lowest transition of the $29{\mathrm{cm}}^{-1}$ band of the Si-O-Si complex in three samples of natural silicon (${}^{\mathrm{nat}}$Si) and in isotopically enriched ${}^{28}$Si and ${}^{30}$Si at temperatures between 5 and 50 K by means of coherent-source terahertz spectroscopy. At 5 K the resonance frequencies are $29.220\pm 0.003$, $29.240\pm 0.003$, and $28.820\pm 0.006{\mathrm{cm}}^{-1}$ and the line widths are $0.11\pm 0.01$, $0.10\pm 0.01{\mathrm{cm}}^{-1}$, and $0.07\pm 0.01{\mathrm{cm}}^{-1}$ for ${}^{\mathrm{nat}}$Si, ${}^{28}$Si, and ${}^{30}$Si, respectively; samples with similar oxygen content. The frequency of the resonance maximum in ${}^{\mathrm{nat}}$Si is clearly downward shifted from that of ${}^{28}$Si, though 85.2$\%$ of the Si-O-Si in ${}^{\mathrm{nat}}$Si consist of ${}^{28}$Si pairs. From this observation and the fact that not only the lines in the isotopically enriched samples but also in ${}^{\mathrm{nat}}$Si can be fitted by single Lorentzians we conclude that shift and width of the ${}^{\mathrm{nat}}$Si-resonance is not due to the Si isotopes in the Si-O-Si complex but to an average effect of the isotopically inhomogeneous lattice.

Figure 1

(a) Transmission spectra through plane-parallel silicon samples of natural ${}^{\mathrm{nat}}$Si (sample 3), qmi ${}^{28}$Si, and qmi ${}^{30}$Si at $T=5$ K. Interference of the radiation within the plane-parallel samples leads to broad oscillations in the background. The deep (note the logarithmic scale) minima are caused by the transition from the ground state to the next excited state of the 29 cm${}^{-1}$ band. The dots correspond to experimental data; the lines represent the least square fits using Eq. (1), as described in the text. (b) For comparison the transmission through the ${}^{\mathrm{nat}}$Si-samples 1 and 3 (i.e., with lowest and highest oxygen concentration) are shown. In the latter case, the temperature evolution of the resonance could be seen up to approximately 30 K but above about $T=22$ K it was not possible to reliably register it. At 50 K no resonance could be identified in the transmission of sample 3.

Figure 2

(a) Spectra of the imaginary part of the dielectric susceptibility of the qmi ${}^{28}$Si and ${}^{30}$Si as well as of ${}^{\mathrm{nat}}$Si sample 2 at 5 K. The center frequency of the latter resonance is slightly downshifted relative to ${}^{28}$Si by $\Delta {\nu }_0=0.02$ cm${}^{-1}$ and it is considerably broader. For the ${}^{28}$Si sample two spectra at higher temperatures are given showing broadening and shift of the resonance. The spectra are obtained by fitting the optical transmission by expression (3) as presented in Fig. 1 and described in the text. (b) The three spectra of the ${}^{\mathrm{nat}}$Si samples 1, 2, and 3 demonstrate that in this range of oxygen concentration there is no significant variation of position and line width of the resonance.

Figure 3

Temperature dependencies of parameters of the 29 cm${}^{-1}$-resonance of interstitial oxygen in ${}^{28}$Si, ${}^{30}$Si, and ${}^{\mathrm{nat}}$Si: (a) and (b) eigenfrequency ${\nu }_0$, (c) damping parameter $\gamma$, and (d) effective oscillator strength ${\phi }_{12}$.

Figure 4

Spectra of the imaginary part of the dielectric susceptibility of the qmi ${}^{28}$Si and ${}^{\mathrm{nat}}$Si. The broken line is calculated with the assumption that the shifts of the ${}^{28}$Si and ${}^{30}$Si resonances are determined by a local host isotope effect resulting from the anharmonic coupling of the 2D LEAE mode to A${}_{2u}$. The two humps indicated by arrows would then be the 28-29 and 28-30 resonances to appear in ${}^{\mathrm{nat}}$Si.