Phase diagram and thermoelectric performance of lead-free perovskite using machine learning potentials and density functional theory

Compared to traditional silicon cells, emerging lead-free perovskite cells are of great significance in solving existing energy and environmental problems due to their advantages such as high conversion efficiency, low cost, and flexibility. However, the issue of phase stability has become a challenge that limits their industrialization. An efficient machine learning potential (MLP) is trained through a neural network with natural evolution strategies, also known as the neuroevolution potential (NEP). NEP-based molecular dynamics (MD) simulation is implemented in a supercell, including 16,000 atoms, which can eliminate size effects during the density functional theory (DFT) simulation. As the temperature increases, a clear phase transition in the order of $\gamma \to \beta \to \alpha$ can be observed on ${\mathrm{CsSnBr}}_3$ and ${\mathrm{CsSnI}}_3$. The X-ray diffraction (XRD) spectrum confirms that the phase transitions are consistent with experimental measurements, which reveal the applicability of MLP in material design. A phase diagram on pressure-temperature (P-T) is explored. Surprisingly, it is observed from the phase diagram that they can maintain the stability of the phase $\gamma$ under high pressure. At P $=$ 3 GPa, the soft mode in phonon dispersion disappears, confirming the dynamic stability. The underlying physical mechanism governing the phase transition associated with pressure suppression has been elucidated. We also explore their thermoelectric performance at P $=$ 3 GPa and T $=$ 400 K. ${\mathrm{CsSnI}}_3$ exhibits a higher figure of merit ($ZT$) than ${\mathrm{CsSnBr}}_3$. The highest value $ZT$ for n-type doping ${\mathrm{CsSnI}}_3$ is 0.184, which is in agreement with experimental measurements of 0.08–0.21.