Fig. 2: The analysis of thermal properties of MAPbI₃.

a The mechanism of the optoacoustic transducers. The blue rectangle is the perovskite film and the pink part represents the thermal expansion material. b Measured specific heat capacity of perovskites and other representative absorbers. The double-walled carbon nanotube, carbon black, carbon nanofiber, candle soot particles, and MAPbI₃ are labeled as cyan rectangle, red circle, light green triangle, the brown inverted triangle, and blue diamond, respectively. c Measured thermal diffusion coefficient of different light absorption materials. The red star, blue hexagon, dark red rectangle, green circle, and pink triangle represent MAPbI₃, carbon black, carbon nanofiber, double-walled carbon nanotube, and multi-walled carbon nanotube, respectively. d Schematic illustration of the heat generation process within MAPbI₃. Here, the acronyms of CB and VB represents conduction band and valence band, respectively. The physical meaning of vertical axis is the energy levels. Specifically, the arrows of ①–⑤ represent the process of carrier relaxation. ①: The generation of optical phonons by the relaxation of high energy electrons in the conduction band; ②: The excited optical phonons decay to acoustic modes; ③: the propagation of acoustic phonons within the crystal lattice; ④: The phonon up-transition process (acoustic phonons → optical phonons) due to the energy overlap between the two modes; ⑤: The charge carriers are reheated by the recycled thermal energy. e Calculated phonon spectrum of MAPbI₃. The blue curve represents optical phonon spectrum and the red curve represents acoustic phonon spectrum. f Density of states of the phonon spectrum.