Coherent acoustic phonon dynamics facilitating acoustic deformation potential characterization of ${\mathrm{Mg}}_3{\mathrm{Sb}}_2$

Acoustic deformation potential (ADP) quantifies carrier-acoustic phonon coupling and is essential for dissecting transport physics in thermoelectrics. Herein, we report the use of ultrafast spectroscopy of coherent acoustic phonons (CAPs) to characterize the ADP of thermoelectric materials, using ${\mathrm{Mg}}_3{\mathrm{Sb}}_2$ as an example. The photon energy-dependent amplitudes of the CAP-induced oscillatory reflectance were used to determine the ADP coupling constant, agreeing well with that from first-principles calculations. This method relies on the transient Coulombic interaction between carriers and acoustic phonons, free of influence from other scattering channels. It is shown that the method is particularly feasible for the study of thermoelectric materials, because their common features of strong phonon anharmonicity and small band gaps make the measurement insensitive to the uncertainty of carrier diffusion coefficients, ensuring its accuracy.

Figure 1

(a) The schematic of the ultrafast spectroscopy system. (b) The transient reflectance signal with pump photon energy 3.1 eV and probe photon energy 1.55 eV. The pump fluence was $0.3\mathrm{mJ}/\mathrm{c}{\mathrm{m}}^2$. The inset illustrates the origin of the oscillatory signal. (c) The extracted oscillatory components of the transient reflectance signals for different probe photon energies with the same pump conditions as those in (b). (d) The oscillation period and the real part of the refractive index of ${\mathrm{Mg}}_3{\mathrm{Sb}}_2$ versus the probe photon energy.

Figure 2

(a) The oscillatory components of the transient reflectance signals for different $E_{\mathrm{pump}}$ (offset for clarity) when the probe photon energy was 1.55 eV and the pump fluence was $0.3\mathrm{mJ}/\mathrm{c}{\mathrm{m}}^2$. (b) Theoretically predicted and measured $A_{\mathrm{osc}}\text{−}{E}_{\mathrm{pump}}$ relations normalized by the amplitudes at 1.8 eV. The red and blue lines represent the cases when the ADP mechanism and the TE effect dominates, respectively. The purple line represents the best fitting. The error bar corresponds to the standard deviation $\left(\times 3\right)$ of three measurements. The calculated strain fields (c) and oscillatory transient reflectance signals (d) for $E_{\mathrm{pump}}=1.94$, 2.96, and 3.10 eV.

Figure 3

The strain components generated by the ADP mechanism (a), by the TE effect (b), and the total strain by both the mechanisms (c) with or without diffusion considered. $E_{\mathrm{pump}}=3.18$ eV and $t=20$ ps.

Figure 4

(a) The extracted CAP-induced oscillatory components of the transient reflectance signals for different fluence with the same pump photon energy 3.1 eV. (b) The variation of the oscillation amplitude as a function of the pump fluence.

Figure 5

(a) The band structure without pressurization. (b) The variation of the band-edge energies relative to those at zero pressure (left) and the band gap versus pressure (right). The circles and lines represent the calculated values and the fitting curves, respectively.

Figure 6

The electron-scattering rates by LA phonons predicted by the ADP theory and first-principles calculations.