Intrinsic coherent acoustic phonons in the indirect band gap semiconductors Si and GaP

We report on the intrinsic optical generation and detection of coherent acoustic phonons at (001)-oriented bulk Si and GaP without metallic phonon transducer structures. Photoexcitation by a 3.1-eV laser pulse generates a normal strain pulse within the $\sim 100$-nm penetration depth in both semiconductors. The subsequent propagation of the strain pulse into the bulk is detected with a delayed optical probe as a periodic modulation of the optical reflectivity. Our theoretical model explains quantitatively the generation of the acoustic pulse via the deformation potential electron-phonon coupling and detection in terms of the spatially and temporally dependent photoelastic effect for both semiconductors. Comparison with our theoretical model reveals that the experimental strain pulses have finite buildup times of 1.2 and 0.4 ps for GaP and Si, which are comparable with the time required for the photoexcited electrons to transfer to the lowest X valley through intervalley scattering. The deformation potential coupling related to the acoustic pulse generation for GaP is estimated to be twice as strong as that for Si from our experiments, in agreement with a previous theoretical prediction.

Figure 1

Schematic of the experiment. (a) Pump light generates an acoustic pulse at the surface ($z=0)$ at $t=0$. (b) The acoustic pulse propagates into the bulk at the speed of sound $v$. The probe light is reflected by the acoustic pulse, which is positioned at $z=vt$ for $t>0$, as well as by the surface. The incident angle of the probe light in the lower panel is exaggerated for clarity.

Figure 2

Schematic band structures of GaP (a) and Si (b) near the fundamental band gaps [33, 34]. Solid and broken arrows indicate the major transitions with 3.1-eV photons and the relaxation pathways discussed in the text.

Figure 3

(a,b) Reflectivity changes of (001)-oriented GaP and Si pumped and probed at 3.1 eV (400 nm). Pump densities are 30 and 90 $\mu \mathrm{J}$/${\mathrm{cm}}^2$ for GaP and Si. Parts (a) and (b) show identical traces with different vertical and horizontal scales. (c) Fourier-transformed spectra of the reflectivity changes after $t=0.1$ ps. Broken lines indicate the frequencies $f_B^{\mathrm{GaP}}$ and $f_B^{\mathrm{Si}}$ given by Eq. (1) for GaP and Si.

Figure 4

(a,b) Oscillatory parts of the reflectivity changes pumped at 3.1 eV and probed at different wavelength $\lambda$, for GaP (a) and Si (b). Pump densities are 80 and 200 $\mu \mathrm{J}$/${\mathrm{cm}}^2$ for GaP and Si. Traces are offset for clarity. (c) Frequencies $f$ of reflectivity modulation divided by twice the refractive index, $2n$, as a function of the probe light wave number ${\lambda }^{-1}$. The solid lines represent $f/\left(2n\right)=v{\lambda }^{-1}$ with the LA phonon velocity $v$.

Figure 5

Amplitude of the experimental reflectivity oscillation as a function of the probe photon energy $E=\hslash ck$ (symbols). The pump photon energy is 3.1 eV, and pump densities are 80 and 200 $\mu \mathrm{J}$/${\mathrm{cm}}^2$ for GaP and Si. Solid curves represent the theoretical amplitudes $A_{\mathrm{osc}}$ scaled to the experimental ones at $E\simeq 2.0$ eV.

Figure 6

Depth profile of the elastic strain calculated with Eq. (7) at different times $t$ after photoexcitation with a 3.1-eV optical pulse. The plots are generic for both GaP and Si.

Figure 7

Theoretical reflectivity changes, pumped at 3.1 eV and probed at different wavelength $\lambda$, calculated using Eq. (16): for GaP (a,b) and Si (c,d). Traces are offset for clarity.

Figure 8

Experimental and calculated reflectivity changes for GaP (a) and Si (b) pumped and probed with 10-fs pulses at 3.1 eV. Experimental pump densities are 30 and 90 $\mu \mathrm{J}$/${\mathrm{cm}}^2$ for GaP and Si. The calculated reflectivity traces are scaled to the experimental ones and offset for clarity. Vertical lines show the positions for the oscillation maxima.