Vibrational relaxation pathways in porous silicon: A time-resolved infrared spectroscopic study

We have used a free electron laser to measure the picosecond vibrational dynamics of the SiH, $\mathrm{Si}{\mathrm{H}}_2$, and ${\mathrm{O}}_3\mathrm{Si}\mathrm{H}$ stretching modes in porous silicon. A three beam pump-probe technique has been employed to make temperature dependent measurements of the population relaxation times. We demonstrate that both bending modes and scissors modes play important roles as does the vibrational bath provided by the pore walls themselves. Using a forward box, two beam photon echo technique we have measured the homogeneous dephasing times of all modes which have dynamic linewidths in the range $0.6–1.2{\mathrm{cm}}^{-1}$. The inferred pure dephasing rates are dominated by the elastic scattering of acousticlike Si-Si vibrations.

Figure 1

Infrared transmission spectrum of a free-standing $p\text{−}\mathrm{Si}$ layer. The spectral positions of the SiH, $\mathrm{Si}{\mathrm{H}}_2$, and ${\mathrm{O}}_3\mathrm{Si}\mathrm{H}$ mode are highlighted. The sharp lines observed on the high energy side of the spectrum are due to $\mathrm{C}{\mathrm{O}}_2$ absorption.

Figure 2

Decay of the pump-probe signals at a temperature of $10\mathrm{K}$ when resonantly exciting the SiH stretch mode at (a) $4.73\mu \mathrm{m}$, the $\mathrm{Si}{\mathrm{H}}_2$ stretch mode at (b) $4.80\mu \mathrm{m}$, and the oxygen backbonded SiH stretch mode at (c) $4.42\mu \mathrm{m}$. The solid lines are fits of single-exponential decay in cases (a) and (c), while in case (b) a biexponential fit is used. The lifetimes of the respective modes, obtained through these fits, are indicated.

Figure 3

Temperature dependence of the population relaxation rate $1∕T_1$ of (a) the SiH stretch mode, (b) the $\mathrm{Si}{\mathrm{H}}_2$ stretch mode, and (c) the ${\mathrm{O}}_3\mathrm{Si}\mathrm{H}$ mode. The circles are the measured lifetimes while the lines are fits of Eq. (1) in which either three-, four-, or five-phonon anharmonic decay with appropriate choices of Si-Si vibrational energy are used. In case (a) (Si-H) the best fit is the unbroken line, which represents four-phonon decay into two bending modes $\left(625{\mathrm{cm}}^{-1}\right)$, and two Si-Si vibrations at $530{\mathrm{cm}}^{-1}$ and $334{\mathrm{cm}}^{-1}$. For case (b) $\left(\mathrm{Si}\text{−}{\mathrm{H}}_2\right)$, there are two equally plausible decay pathways, shown as the unbroken and dashed line. The unbroken line assumes four-phonon decay into one scissors mode $\left(906{\mathrm{cm}}^{-1}\right)$ and three bulk vibrations having energies of $530{\mathrm{cm}}^{-1}$, $370{\mathrm{cm}}^{-1}$, and $275{\mathrm{cm}}^{-1}$. The dashed curve also assumes four-phonon decay with the accepting modes being two bending modes $\left(660{\mathrm{cm}}^{-1}\right)$ and two Si-Si vibrations having energies of $530{\mathrm{cm}}^{-1}$ and $233{\mathrm{cm}}^{-1}$. In the last case (c) $\left({\mathrm{O}}_3\mathrm{Si}\text{−}\mathrm{H}\right)$ the best fit is the unbroken line and assumes four-phonon decay into one bending mode $\left(625{\mathrm{cm}}^{-1}\right)$ and three equal energy $461{\mathrm{cm}}^{-1}$ vibrations. Full details of the various energy conserving phonon decay pathways are given in the text.

Figure 4

Decay of the photon echo signals at a temperature of $10\mathrm{K}$ when resonantly exciting (a) the SiH stretch mode at $4.73\mu \mathrm{m}$, (b) the $\mathrm{Si}{\mathrm{H}}_2$ stretch mode at $4.80\mu \mathrm{m}$, and (c) the oxygen backbonded SiH stretch mode at $4.42\mu \mathrm{m}$. In cases (a) and (c) the lines are single-exponential fits to the measured decay of the echo. In case (b) a biexponential fit is used. The respective dephasing times of each mode are displayed in the corner of each plot.

Figure 5

Temperature dependence of the pure dephasing rate of (a) the SiH stretch mode, (b) the $\mathrm{Si}{\mathrm{H}}_2$ stretch mode, and (c) the ${\mathrm{O}}_3\mathrm{Si}\mathrm{H}$ mode. The dashed line is a least-squares fit to Eq. (2) and the solid line is a least-squares fit to Eq. (3).