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Machine Learning with Knowledge Constraints for Process Optimization of Open-Air Perovskite Solar Cell Manufacturing
Zhe Liu, Nicholas Rolston, Austin C. Flick, Thomas W. Colburn, Zekun Ren, Reinhold H. Dauskardt, Tonio Buonassisi
TL;DR
Scalable perovskite manufacturing requires optimizing many process parameters, while existing sequential-learning approaches have limited integration of prior studies and researcher feedback. This paper develops an ML-guided sequential-learning framework for RSPP and achieves 18.5% efficiency after screening 100 conditions, including 10 conditions exceeding 17% efficiency.
Problem
Scalable perovskite manufacturing involves many parameters to co-optimize, while existing sequential-learning methods poorly incorporate prior studies and qualitative researcher feedback.
Method
The framework combines Latin hypercube initialization, Gaussian-process regression, Bayesian optimization, and knowledge constraints for sequential process selection.
Results
18.5% efficiency was achieved after five rounds screening 100 conditions, including 10 conditions producing devices exceeding 17% efficiency.
Takeaways & Limitations
Bayesian optimization reached near-optimal performance quickly within a small experimental budget, outperforming one-variable-at-a-time sampling during the first 100 conditions.
Takeaways & Limitations
The decreasing improvement rate of Bayesian optimization suggests that adaptive acquisition strategies may be needed for further gains.
Abstract
from arXiv · showhide
Perovskite photovoltaics (PV) have achieved rapid development in the past decade in terms of power conversion efficiency of small-area lab-scale devices; however, successful commercialization still requires further development of low-cost, scalable, and high-throughput manufacturing techniques. One of the critical challenges of developing a new fabrication technique is the high-dimensional parameter space for optimization, but machine learning (ML) can readily be used to accelerate perovskite PV scaling. Herein, we present an ML-guided framework of sequential learning for manufacturing process optimization. We apply our methodology to the Rapid Spray Plasma Processing (RSPP) technique for perovskite thin films in ambient conditions. With a limited experimental budget of screening 100 process conditions, we demonstrated an efficiency improvement to 18.5% as the best-in-our-lab device fabricated by RSPP, and we also experimentally found 10 unique process conditions to produce the top-performing devices of more than 17% efficiency, which is 5 times higher rate of success than the control experiments with pseudo-random Latin hypercube sampling. Our model is enabled by three innovations: (a) flexible knowledge transfer between experimental processes by incorporating data from prior experimental data as a probabilistic constraint; (b) incorporation of both subjective human observations and ML insights when selecting next experiments; (c) adaptive strategy of locating the region of interest using Bayesian optimization first, and then conducting local exploration for high-efficiency devices. Furthermore, in virtual benchmarking, our framework achieves faster improvements with limited experimental budgets than traditional design-of-experiments methods (e.g., one-variable-at-a-time sampling).
1. Introduction:
Open-air perovskite manufacturing offers scalable, low-cost potential but presents a high-dimensional process-optimization challenge. The study develops a sequential-learning framework that combines Bayesian optimization with probabilistic constraints from prior data and visual film-quality assessments, reaching 18.5% efficiency in five experimental iterations.
- Motivation: High-dimensional co-optimization of precursor composition, speed, temperature, nozzle height, and curing methods complicates process control, reproducibility, and estimation of manufacturing potential.For scalable processes such as RSPP, achieving module-scale control and reproducibility can take months to years.
- Motivation: Classical Bayesian optimization lacks direct incorporation of previous relevant studies and flexible integration of researchers’ qualitative feedback.These limitations can force models to relearn information already apparent to researchers and discourage materials-science researchers from using sequential learning.
- Method: Probabilistic constraints allow acquisition functions to incorporate previous experimental data and domain knowledge during experimental planning.The framework also uses visual assessments of film thickness, color, and structural defects to avoid unnecessary device fabrication for visibly low-quality films.
- Contributions: 18.5% efficiency was achieved in five experimental iterations while optimizing six key RSPP input variables for the perovskite absorber layer.The study targeted performance exceeding the best PCE previously obtained in the laboratory with RSPP.
2. Methods:
The study optimized RSPP perovskite fabrication using six process variables and a sequential-learning framework based on Gaussian-process regression, Bayesian acquisition, and probabilistic constraints. The process overview used spray deposition onto a heated substrate followed by nitrogen-plasma afterglow exposure for rapid solidification.
- RSPP fabrication: RSPP fabrication deposited precursor solution onto a heated glass substrate and exposed it briefly to nitrogen-plasma afterglow to rapidly solidify a polycrystalline thin film.The process overview also included a ~20 nm NiOx layer deposited by spin coating on ITO-coated glass.
- Process optimization inputs: Six RSPP process variables were optimized: substrate temperature, nozzle linear speed, precursor spray flow rate, plasma gas flow rate, plasma-nozzle height, and plasma duty cycle.The target output was solar-cell power conversion efficiency.
- Process optimization inputs: Optimization bounds were defined from historical data covering more than 300 process conditions, with expert judgment balancing experimental feasibility and parameter-space breadth.The less-explored plasma duty cycle was assigned a relatively broad range.
- Sequential learning: Sequential learning comprised five steps: initial sampling, regression, prediction, evaluation, and acquisition.Initial sampling used pseudo-random Latin hypercube sampling, while the surrogate model was Gaussian Process regression with anisotropic Matern52.
- Sequential learning: The acquisition function combined an upper confidence bound objective with probabilistic constraints and local penalization for selecting batches of new experiments.Local penalization generated an envelope function that reduced acquisition values in selected regions.
- Knowledge-constrained acquisition: Two probabilistic constraints incorporated film-quality observations and relevant prior-experiment data, reducing sampling in regions associated with poor films or low PCE.Constraint Function 2 was softened to a range of 0.8 – 1, and current data were weighted 5 times more than prior data.
3. Results and Discussion:
Sequential learning with probabilistic knowledge constraints optimized open-air RSPP manufacturing, achieving high-efficiency devices within 100 screened conditions. Virtual benchmarking showed Bayesian optimization accelerated early improvement, while later stages benefited from adaptive local or exploitative search.
- Experimental optimization: 10 process conditions exceeded 17% PCE among 85 BO-guided conditions, while 45 conditions exceeded 15% PCE.The analysis defined top performers as devices above 17% PCE and good performers as devices exceeding 15% PCE.
- Experimental optimization: 18.5% best-in-our-lab RSPP device efficiency was achieved in fewer than 100 conditions, exceeding the 18% ceiling of prior LHS and previous experiments.The champion process condition produced the device; champions from LHS and previous experiments had never reached 18% PCE.
- Knowledge-constrained learning: All devices fabricated from visually low-quality films had PCE below 13.5%, averaging 7.8%, validating film-quality screening as a probabilistic constraint.This validation supports skipping device fabrication for low-quality films and incorporating film ratings into the regression model.
- Adaptive acquisition: Five experimental rounds used LHS initialization, BO-guided rounds 1–3, and final-round local optimization around the regression model’s best predicted condition.The probabilistic constraint affected acquisition from Round 1, while particle swarm optimization located the best condition in the final local-search window.
- Virtual benchmarking: 50 conditions reached the top 1 percentile mark at normalized PCE 0.8 with both BO methods, compared with 19 for OVATS and fewer than 5 for LHS and FS-PGS.These comparisons used a limited experimental budget of 100 process conditions.
- Virtual benchmarking: After 50 conditions, BO methods reached normalized PCE 0.9, versus 0.85 for LHS and below 0.8 for OVATS and FS-PGS; after 120 conditions, OVATS overtook BO.Beyond 160 conditions, knowledge-constrained BO surpassed regular BO, reaching above 0.98 normalized PCE by 300 conditions versus above 0.96 for regular BO.
4. Conclusions:
The study concludes that Bayesian optimization with knowledge constraints can efficiently optimize perovskite solar-cell manufacturing by combining prior experimental data with researchers’ film-quality evaluations. In open-air RSPP processing, the framework reached 18.5% efficiency within 100 screened conditions and showed faster early improvement than conventional sampling methods.
- Framework: Bayesian optimization with knowledge constraints incorporated preliminary experimental data and researchers’ visual evaluations of perovskite film quality.The workflow was designed to mimic conventional iterative optimization while flexibly incorporating multiple information sources.
- Experimental outcome: 18.5% efficiency was achieved in open-air RSPP after optimizing six deposition variables across 5 experimental rounds and 100 process conditions.This was reported as the highest PCE achieved to date with RSPP, using only a small fraction of more than 40k grid-search combinations.
- Virtual benchmarking: Within the first 100 process conditions, both Bayesian optimization methods significantly outperformed one-variable-at-a-time sampling, which overtook them afterward.The comparison indicates that Bayesian optimization approaches the optimum quickly under a small experimental budget, while later-stage adaptive acquisition strategies may be needed.
- Broader applicability: The framework could be applied broadly to perovskite PV process optimization and materials screening across spin coating, blade coating, slot-die coating, and thermal evaporation.Knowledge constraints can also incorporate quantitative film-quality measurements, including light-beam induced current mapping, photoluminescence imaging, and quasi-fermi level splitting mapping.
Supplementary Information · 1. Sequential Learning Framework to Guide Iterative Learning Cycles · 2. Apply the Sequential Learning to RSPP Experiments
The supplementary information presents a sequential-learning framework, applies it to RSPP experiments, and compares sequential learning with design-of-experiment approaches for device optimization.
- Supplementary Information: The supplementary information includes a section on sequential learning for guiding iterative learning cycles.
- 1. Sequential Learning Framework to Guide Iterative Learning Cycles: The framework is organized around iterative learning cycles.
- 2. Apply the Sequential Learning to RSPP Experiments: A dedicated section applies sequential learning to RSPP experiments.
- 3. Compare Sequential Learning vs. Design of Experiment for Device Optimization: The supplementary material compares sequential learning with design-of-experiment methods for device optimization.
- 3.4 Design of Experiment Method 3: Factorial Sampling in Progressive Grid Division (FS-PGS): Factorial Sampling in Progressive Grid Division is identified as a design-of-experiment method.
- 3.3 Design of Experiment Method 2: One Variable at a Time Sampling (OVATS): One Variable at a Time Sampling is identified as another design-of-experiment method.
- 3.5 Benchmarking: the BO Methods vs Model-Free Design of Experiment Methods: Benchmarking compares Bayesian optimization methods with model-free design-of-experiment methods.
1. Sequential Learning Framework to Guide Iterative Learning Cycles
The framework guides iterative process optimization through sequential experimental cycles beginning with broad Latin-hypercube sampling and incorporating manufacturing measurements. It combines visual film-quality assessment as a probabilistic constraint with an upper-confidence-bound acquisition strategy balancing exploration and exploitation.
- Sequential learning cycle: Each iterative cycle contains five sequential steps, including experimental planning, RSPP device fabrication, and PCE measurement.The supplied framework summary identifies five steps per cycle and specifies LHS for initial planning.
- Initial sampling strategy: Latin-hypercube sampling provides broad initial coverage of the process-parameter space with relatively few experiments.The method is intended to maximize early information because experiments are expensive.
- Knowledge-constrained acquisition: Visual inspection supplies a probabilistic constraint for acquisition decisions by distinguishing porous, nonuniform films from uniform, good-quality films.Poor crystallization is indicated by pale-gray edges, nonuniformity, and large holes.
- Knowledge-constrained acquisition: None of the devices made from visually assessed low-quality films exceeded 15% efficiency.This device test validated visual assessment as an indicator of low-efficiency films.
- Upper Confidence Bound: The upper confidence bound acquisition function balances exploration and exploitation better than expected improvement for the process-efficiency relation.UCB is used as the utility function for selecting acquisition decisions.
2. Apply the Sequential Learning to RSPP Experiments
Sequential learning was applied across five experimental batches of 20 process conditions, using global Latin hypercube sampling initially and local region search finally. Batch size, model updating, top-device characterization, and non-uniformity analysis supported the experimental optimization.
- Experimental design: Five experimental batches of 20 process conditions used global LHS initially and local region search in the final round.Relative humidity was tracked as a potential variability source, although RSPP device PCEs were fairly independent of ambient RH.
- Experimental design: Batch size 20 balanced feedback speed against per-substrate time cost because thermal evaporation accommodated up to 20 substrates per batch.Average time per substrate diminished quickly as batch size increased, while batch time to feedback also had to be considered.
- Model updating: After every experimental batch, new data were added to the training dataset to revise the regression model and compare predictions with measured PCEs.Prediction uncertainty was represented by error bars corresponding to a 68.2% confidence interval.
- Device outcomes: 10 top-performing devices achieved PCE ≥17%, including an 18.5% champion device fabricated under process condition 89.The top performers’ process conditions and I-V characteristics were documented, with their distributions and curves separately shown.
- Device characterization: Non-uniformity affected both light-beam-induced-current maps and optical images, with thickness variation and carrier collection reflected in the LBIC maps.The analysis used reflection-mode optical microscopy and LBIC mapping for samples from the same batch as the best-performing cells.
3. Compare Sequential Learning vs. Design of Experiment for Device Optimization
The comparison examines sampling strategies for exploring and optimizing a high-dimensional process space. Full-factorial sampling is exhaustive but experimentally burdensome, whereas sequential and pseudo-random approaches reduce sampling demands through space reduction or stratification.
- Sampling the optimization space: 100,000 random samples and 41,580 full-factorial samples produced very similar predicted-efficiency distributions, with only minor differences in the 10–13% range.The random-sample analysis also identified approximate normalized-PCE thresholds for the top 5%, 1%, and 0.1% of conditions.
- Sampling the optimization space: Latin hypercube sampling stratifies each parameter into m levels and samples each parameter level once, while retaining pseudo-random choices among unoccupied hypercubes.Different random seeds can produce different samples, but repeated runs converge statistically toward random sampling.
- Sequential design strategies: One-variable-at-a-time sampling fixes previously optimized variables while exploring levels of another variable, with the variable sequence determined randomly.Each round samples all levels in one variable while the remaining variables use randomly selected values.
- Sequential design strategies: Full-factorial sampling requires m^n conditions for m levels across n variables, making experimental sampling infeasible as dimensionality increases.For example, 5 levels across 6 variables require 15,625 conditions.
- Sequential design strategies: Progressive two-level factorial sampling starts with 2^n conditions, repeatedly narrows the space toward the best condition, and expands it when the best-device location stops changing.The described implementation begins with high and low conditions in every variable, then iteratively reduces and later broadens the sampled region.