Effect of diffusion on acoustic deformation potential characterization through coherent acoustic phonon dynamics

Ultrafast spectroscopy of coherent acoustic phonon (CAP) dynamics has recently been proposed as a method to characterize acoustic deformation potential (ADP), a key standard to quantify carrier–acoustic phonon coupling in semiconductors. In this Letter, we illustrate the importance of addressing the diffusion effect in ADP characterization by this method, using Ge as the demonstration system. It is found that the ADP mechanism and the thermoelastic effect have comparable contributions to CAP generation in Ge. Due to the different dependences on pump photon energies, the roles of these two mechanisms were assessed by varying pump wavelengths, based on which the ADP coupling constant of Ge was obtained. The analysis reveals that the carrier diffusion has a considerable impact on the shape of the CAP wave packet and must be processed cautiously for the ADP characterization for Ge.

Figure 1

(a) The transient reflectivity signal with an 800-nm pump at the fluence of $0.5\mathrm{mJ}/\mathrm{c}{\mathrm{m}}^2$ and a 730-nm probe. The inset shows the schematic for CAP generation and detection: a CAP wave packet (a bipolar-shape strain wave, the blue curve) is excited by the pump and propagates into the sample at the longitudinal acoustic velocity; the strain alters the dielectric constant, forming a moving optical interface (the dashed line); the probe (the red arrow) is reflected partially at the surface and partially at the traveling interface; and the interference of the two parts of reflection causes oscillation in the transient reflectivity signal. (b) The oscillation parts of the transient reflectivity signals probed at 625, 730, and 920 nm, with the 800-nm pump at the fluence of $0.5\mathrm{mJ}/\mathrm{c}{\mathrm{m}}^2$. The dots represent the experimental data and the solid lines are the fitting curves based on Eq. (1), which are offset for clarity. (c) The relationship between $f$/($2n$) and $1/{\lambda }_{\mathrm{pr}}$. The squares represent $f$/($2n$) with $f$ extracted experimentally. The error bars do not exceed the size of the symbols and are not shown. The red line represents the linear fitting function.

Figure 2

(a) The CAP signals under pump wavelengths of 650, 680, and 800 nm, at the fluence of $0.315\mathrm{mJ}/\mathrm{c}{\mathrm{m}}^2$, probed at 740 nm. The empty dots represent the experimental results and the solid curves represent the fittings with Eq. (1). (b) The oscillation amplitude as a function of the pump fluence from 0.157 to $1.57\mathrm{mJ}/\mathrm{c}{\mathrm{m}}^2$. The solid lines represent the linear fit of the first four values for each pump wavelength. The data points for 650 and 680 nm are shifted up by $4\times {10}^{–3}$ and $2\times {10}^{–3}$ in (a), and $1\times {10}^{–3}$ and $0.5\times {10}^{–3}$ in (b) for clarity.

Figure 3

The spatial distributions of the strain in Ge at (a) 25 ps and (b) 120 ps with carrier diffusion coefficients 0.1, 1, 10, and $100\mathrm{c}{\mathrm{m}}^2/\mathrm{s}$. The curves are shifted vertically for clarity, and the strain at the distance of 1.1 μm is zero for all cases.

Figure 4

(a) The calculated damping oscillation signals with pump wavelengths 650, 680, and 800 nm at the fluence of $0.315\mathrm{mJ}/\mathrm{c}{\mathrm{m}}^2$. Extraction of the ADP coupling constant by fitting the experimental normalized amplitudes as functions of $E_{\mathrm{pu}}$ assuming different carrier diffusion coefficients (b) $4.2\mathrm{c}{\mathrm{m}}^2/\mathrm{s}$, (c) $6\mathrm{c}{\mathrm{m}}^2/\mathrm{s}$, (d) $8\mathrm{c}{\mathrm{m}}^2/\mathrm{s}$, (e) $10\mathrm{c}{\mathrm{m}}^2/\mathrm{s}$, and (f) $0\mathrm{c}{\mathrm{m}}^2/\mathrm{s}$. The blue curves correspond to the best fit while the black dashed curves illustrate exemplary deviating fitting by improper ADP coupling constants.