Quantifying Spatiotemporal Signal in Photothermal Heterodyne Imaging of Metal-Halide Perovskites

Resonant pump-probe spectroscopies like photothermal heterodyne imaging have emerged as promising approaches to selectively measure the distribution of chemical species with high spatial and temporal resolution. In photothermal heterodyne imaging, a pump resonant with an electronic or vibrational transition of the species of interest heats the sample, and a higher energy probe measures differential reflectance (or transmittance) due to heating. For materials research, pump-probe photothermal spectroscopies thus offer an attractive and unique tool to evaluate the spatial distribution of “dark” species including, <i>e.g.</i> defects or molecules without significant radiative transitions. However, the conditions under which signal is optimized in thin films, including metal-halide perovskites, is not well understood, and approximations are frequently used to describe to differential reflectance or transmittance signal. Here, we develop a multiphysics simulation implemented with a finite-difference method to quantify transient photothermal heating and the resulting differential reflectance signal. Using this approach, we investigate the conditions that optimize spatiotemporal resolution in alloyed methylammonium and formamidinium metal-halide perovskite thin films and evaluate these simulations experimentally. Combining these results, we identify key figures of merit to optimize spatiotemporal resolution in thin films and find that significant information about spatial distribution is buried within the temporal signal.