Pc1d example problem
![pc1d example problem pc1d example problem](https://media.springernature.com/lw685/springer-static/image/art%3A10.1007%2Fs11468-017-0563-8/MediaObjects/11468_2017_563_Fig8_HTML.gif)
For other secondary process variables, for example, precursor type and carrier gas flowrate, the physical relation between process variables and material properties is unclear and likely tool specific, 27 we can replace the physics-based parametrization in the first layer of the Bayesian network inference with a machine-learning model with higher capacity, such as kernel ridge regression. 26 Therefore, we use the growth temperature as the key optimization variable. These process parameters are closely related, and the relationship can be approximated using the Ideal Gas Law in the kinetic epitaxy process. 24, 25 Other important process parameters include precursor flowrate and growth pressure. 24, 25 Previous studies showed that the growth temperature has an impact on the film’s growth rate, surface morphology, dopant incorporation, and defect formation. Growth temperature is one of the most important and challenging parameters to optimize in III–V film deposition. In this contribution, we consider the optimization of the synthesis temperature profile of a gallium arsenide (GaAs) solar cell using a metal organic chemical vapor deposition (MOCVD) reactor. 14 Furthermore, recently, the combination of physical insights with machine-learning models have shown good promise in development of energy materials. In contrast, recently, Bayesian inference coupled to a physics-based forward model and rapid, light-dependent and temperature-dependent, current–voltage measurements were shown to offer a statistically rigorous approach to identify the root cause(s) of underperformance in early-stage photovoltaic devices. Furthermore, insights into the root causes of underperformance are severely limited, often requiring secondary characterization methods or batches composed of combinatorial variations of the base samples.
![pc1d example problem pc1d example problem](https://thumbs.static-thomann.de/thumb/orig/pics/bdb/440487/13272636_800.jpg)
6, 7, 8, 9, 10, 11, 12, 13 However, traditional black-box optimization approaches have limitations: the maximum achievable performance improvement is limited by the designer’s choice of variables and their ranges, artificially constraining the parameter space. These methods have shown potential for inverse design of materials and systems in a cost-effective manner, and are usually postulated as ideal methods for future self-driving laboratories. Often, process optimization is done using black-box optimization methods (e.g., Design of Experiments, 1 Grid Search, 2 Bayesian Optimization, 3, 4 Particle Swarm Optimization, 5 etc.), in which selected variables are modified systematically within a range and the system’s response surface is mapped to reach an optimum. This is especially relevant for photovoltaic devices, as numerous process variables can influence their performance. Process optimization is essential to reach maximum performance of novel materials and devices. As a demonstration of our method, in only five metal organic chemical vapor depositions, we identify a superior growth temperature profile for the window, bulk, and back surface field layer of a GaAs solar cell, without any secondary measurements, and demonstrate a 6.5% relative AM1.5G efficiency improvement above traditional grid search methods.
![pc1d example problem pc1d example problem](https://iiif.elifesciences.org/lax/58942%2Felife-58942-fig10-v2.tif/full/617,/0/default.jpg)
With the trained surrogate model and only a small number of experimental samples, our approach reduces significantly the time-consuming intervention and characterization required by the experimentalist. For this purpose, we combine a Bayesian inference framework with a neural network surrogate device-physics model that is 100× faster than numerical solvers. Our Bayesian network approach links a key GaAs process variable (growth temperature) to material descriptors (bulk and interface properties, e.g., bulk lifetime, doping, and surface recombination) and device performance parameters (e.g., cell efficiency).
#Pc1d example problem windows
Herein, we demonstrate that embedding physics domain knowledge into a Bayesian network enables an optimization approach for gallium arsenide (GaAs) solar cells that identifies the root cause(s) of underperformance with layer-by-layer resolution and reveals alternative optimal process windows beyond traditional black-box optimization.
![pc1d example problem pc1d example problem](https://www.coursehero.com/thumb/6e/09/6e09725ef90441229500ba2f27114c14c5da4019_180.jpg)
#Pc1d example problem full
Process optimization of photovoltaic devices is a time-intensive, trial-and-error endeavor, which lacks full transparency of the underlying physics and relies on user-imposed constraints that may or may not lead to a global optimum.