Improved Methods for Measuring Charge Carrier Transport Parameters from Microscopy Data

Time-resolved microscopy techniques are frequently used to measure the transport of excited charge carriers and excitons in semiconducting materials. Typically, parameters such as diffusivity are extracted by generating a spatially localized population of excited charge carriers, then measuring the spatial growth of the population profile over time. However, commonly used analysis techniques are highly sensitive to the shape of the initial charge carrier profile, and can result in large errors for even small deviations from an assumed profile shape. Additionally, these measurements may be significantly affected by shot noise under common experimental conditions. Here, we propose a new analysis algorithm that uses convolutions of Gaussian functions with the measured charge carrier spatial profiles to both smooth the effects of shot noise and to measure the growth of the spatial profiles. Using simulated data sets of charge carrier transport, we demonstrate that the diffusivity values obtained from this algorithm are less impacted by shot noise and are almost completely insensitive to the shape of the initial charge carrier spatial profile for one-dimensional transport. Within this framework, we quantify how physical phenomena such as nonlinear recombination terms and multi-dimensional diffusion can skew the extracted diffusivity parameters. To mitigate some of these effects, we introduce strategies for extending our algorithm to measure diffusion in two dimensions, which additionally allows for accurate measurements of anisotropic diffusion. Finally, we validate our algorithm by using it to analyze time-resolved photoluminescence microscopy experiments on exciton diffusion in two-dimensional perovskites.