Speed of Sound in Single Crystals of Lead-Free Iodide Perovskites Measured by Femtosecond Transient Reflectivity

Coherent acoustic phonons are ultrasonic strain pulses with frequencies ranging from GHz to THz, and are generated through the photoexcitation of semiconductors. They have been studied in various materials because understanding the interaction between light and lattice vibrations is crucial for advancing the field of ultrafast optoelectronics.
Lead-halide perovskites (HPs) have emerged as active materials in solar cells, light-emitting diodes, and photodetectors. However, due to the toxicity of lead, it is important to find alternative, environmentally friendly, elements that may replace Pb²⁺ in the crystalline lattice of HPs. Among them, bismuth and antimony are promising candidates.
In this work, we investigate the intrinsic generation and detection of coherent acoustic phonons in single crystals (SCs) of the indirect band gap iodide perovskites Cs₃Bi₂I₉, MA₃Bi₂I₉, and MA₃Sb₂I₉. Using femtosecond transient reflectivity (FTR), we were able to extract the sound speed for these three materials providing new insights into the interplay between electronic structure, phonon dynamics, and optical properties.
The SCs were grown by hydrothermal methods [1]. FTR was performed using a pump energy of 4.5 eV and a probe in the 1.5−3.5 eV energy range.
The excitonic energies found with transient reflectivity are in very good agreement with the results obtained by spectroscopic ellipsometry and the Elliot fit reported by Valastro et al. [1]. Beyond the spectral features, the intensity of the FTR spectra of all materials shows periodic oscillations with a period of tens of picoseconds in the 1.5-2.4 eV energy range of the probe, where no spectral feature related to the band structure is observed. The oscillations are due to the modulation of the probe light propagation into the material by the strain field induced by the coherent acoustic phonons directly generated by the pump, that move with the velocity (v) of the longitudinal acoustic phonons. The intensity of the oscillations is fitted as follows:
ΔA=(a₁x+offset)+A cos (2π(t-t₀)/τ + Θ
Where (a₁x+offset) is a straight line fitting the background dynamics, A is the amplitude of the oscillation, τ is the oscillation period, θ is the phase, and t₀ is the initial time of the oscillation (approximately 20 ps). We point out that the oscillation intensity does not decay in the temporal window of our experiment (-1 to 300 ps) because the acoustic pulse acts on the probe propagation up to its penetration depth, which is expected to be in the micrometer range because of the indirect character of the bandgap of the investigated materials.
On the other hand, the temporal dynamics follow a sinusoidal behavior, whose period, in the case of samples thicker than the light penetration depth, as in the case of our SCs, decreases with decreasing probe wavelength. The oscillation period is given by the following formula:
1/τ=2n(λ)v/λ
where n is the refractive index, λ is the probe wavelength in air and v is the phonon velocity.
The speeds of sound extracted by the analysis of our measurements are: 1995 m/s for Cs₃Bi₂I₉, 2036 m/s for MA₃Sb₂I₉, and 2260 m/s for MA₃Bi₂I₉, indicating that the cation type has a strong influence on the value of the speed of sound. We note that our results on the inorganic Cs₃Bi₂I₉ are in good agreement with acousto-optic measurements [2], while they represent the first measurement of the speed of sound in the hybid MA₃Sb₂I₉ and MA₃Bi₂I₉.

[1] S. Valastro et al., Adv. Optical Mater. 12, 2302397 (2024)
[2] A.V. Zamkov et al., Inorganic Materials 37, 82 (2001)