(174c) Properties of Photovoltaic Materials from Bayesian Analysis of Optoelectronic Measurements

Quantifying rates of charge carrier recombination is an important step in the development of solar cells with high power conversion efficiencies. The rate of production of new photovoltaic devices can be greatly enhanced if rapid and reliable screening of candidate materials can be incorporated into the development cycle. Optoelectronic measurements, particularly time-resolved ones such as TRPL (time-resolved photoluminescence) and TRTS (time-resolved terahertz spectroscopy), contain a rich information content that can be extracted by rapid measurements on slices of materials. Moreover, the underlying physical processes giving rise to these measurements are well understood in terms of fundamental models of carrier transport and recombination. However, recovering characteristic parameters such as carrier mobility, doping concentration, and recombination rate constants is hindered by the interplay of coupled (and frequently non-linear) recombination mechanisms. Most analysis of optoelectronic measurements relies on analytical approximations in limiting regimes, where simplifications can be applied to decouple and linearize the transport and recombination physics. Unfortunately these analytic approximations, while highly useful and insightful, discard much of the information content of the experimental measurements.

Computer simulations of carrier transport and recombination are frequently used to assist in the analysis of optoelectronic measurements, but only relatively recently in terms of an automated process without significant human intervention [1]. Bayesian inference (BI) is a means of solving an inverse problem by fitting model predictions with particular parameters to experimental data sets. Because additional data generally leads to improved predictions, BI is sometimes considered a form of machine learning. In contrast to other optimization techniques, BI does not aim for a single solution, but rather a distribution of likely possibilities. It is therefore more robust to experimental uncertainties and errors in the physics models than, for example, a maximum likelihood estimation. In addition, the inference provides quantitative measures of uncertainty and correlations between different parameters. We have recently shown that by incorporating simulations of the complete carrier physics into a Bayesian analysis, previously unrecoverable material parameters, such as carrier mobility and doping level, can be determined from TRPL measurements [1].

In the first part of this talk I will summarize a recent case study of TRPL from a MAPI (methyl-ammonium lead iodide) absorber. Our methodology was validated by simulating TRPL data sets using the best values of the absorber parameters obtained from a number of different experiments [2]. This enables us to check that the inferred parameter values match closely with the inputs. From a three-fluence power scan, Bayesian inference extracts values of the (ambipolar) carrier mobility, free carrier density, and rate constants for the three-carrier Auger and two-carrier radiative recombination mechanisms. We also obtain an effective lifetime for the sum of defect-assisted nonradiative recombination, which can be decomposed further into bulk and surface recombination mechanisms by introducing data from an additional sample thicknesses. Further experiments separate the front and back surface recombination velocities and can also distinguish between the electron and hole mobilities. A direct inference of the experimental TRPL data yields similar parameter values to an analytic analysis, but with significantly reduced uncertainties. Ultimately, Bayesian inference enables a significant increase in the information yield from TRPL measurements.

Bayesian inference proceeds by sampling parameter sets from a multidimensional space (typically 8-10 dimensions) spanning 1-2 orders of magnitude around our initial estimates of each parameter. A likelihood is assigned to each parameter set, based on the deviations of the predicted TRPL decay from the experimental data set (or from the simulated ones in the validation study). After a large number of samples, we construct marginalized distributions from which we can determine the most probable value of each parameter, along with quantitative measures of the uncertainties, and information about cross correlations between different parameters. The rich information content has been used to suggest additional experiments to separate coupled contributions to TRPL decay.

The large number of simulations required to sample the parameter space creates a substantial computational burden. We first sought to mitigate this by extensive parallelization, making use of a recently acquired GPU-based supercomputer at the University of Florida. I will outline the key considerations in our development of a custom GPU based code for the prediction of TRPL decay. We were able to achieve reductions in processing time by factors of 2500 over a single CPU by using 8 A-100 GPUs. A simulation of two sample thicknesses with 3 fluences (6 data sets in all) could then be analyzed in about 30 hours. However, the computational inefficiency of random sampling necessitates access to high-performance computing resources, limiting a widespread applicability of the approach. Our recent work has focused on increasing the sampling efficiency by introducing an importance sampling algorithm (Metropolis Monte Carlo), which reduces the computational requirements by 2-3 orders of magnitude.

In the second part of the talk I will outline an application of Metropolis Monte Carlo (MMC) to Bayesian inference. Starting from an initial guess of the parameters, a Markov chain of states (parameter sets) is generated with a probability for each state that, at some point, will sample the posterior distribution representing the experimental data. In practice, convergence is quite quick – of the order of 10⁴ Monte Carlo steps, which represents a reduction in computational requirements by factors of several hundred. Unfortunately MMC is inherently serial, as the outcome of a trial move depends on the current state. The processing time is actually similar to the GPU-based random algorithm, although the hardware requirements are much less. The MMC method is more complicated to implement than random sampling and I will briefly mention some of the insights obtained in the course of this work that can be used to improve the efficiency and robustness of the method.

[1] C. Fai, Anthony J.C. Ladd and Charles J. Hages, Machine learning for enhanced semiconductor characterization from time-resolved photoluminescence, Joule (2022) https://doi.org/10.1016/j.joule.2022.09.002

[2] F. Staub et al.. Beyond Bulk Lifetimes: Insights into Lead Halide Perovskite Films from Time-Resolved Photoluminescence, Phys. Rev. Appl (2016) https://link.aps.org/doi/10.1103/PhysRevApplied.6.044017