Forward and Backward Machine Learning for Modeling Copper Diffusion in Cadmium Telluride Solar Cells

To optimize solar cell performance, it is necessary to properly design the doping profile in the absorber layer of the solar cell. For CdTe solar cells, Cu is used for providing p-type doping. Hence, having an estimator that, given the diffusion parameter set (time and Temperature) and the doping concentration at the junction, gives the junction depth of the absorber layer, is essential in the design process of CdTe solar cells (and other cell technologies). In this work it is called a forward (direct) estimation process. The backward (inverse) problem then is the one in which, given the junction depth and the desired concentration of Cu doping at the CdTe/CdS heterointerface, the estimator gives the time and/or the Temperature needed to achieve the desired doping profiles. This is called a backward (inverse) estimation process. Such estimators, both forward and backward, do not exist in the literature for solar cell technology. To train the Machine Learning (ML) estimator, it is necessary to first generate a large set of data that are obtained by using the PVRD-FASP Solver, which has been validated via comparison with experimental values. Note that this big dataset needs to be generated only once. Next, one uses Machine Learning (ML), Deep Learning (DL) and Artificial Intelligence (AI) to extract the actual Cu doping profiles that result from the process of diffusion, annealing, and cool-down in the fabrication sequence of CdTe solar cells. Two deep learning neural network models are used: (1) Multilayer Perceptron Artificial Neural Network (MLPANN) model using a Keras Application Programmable Interface (API) with TensorFlow backend, and (2) Radial Basis Function Network (RBFN) model to predict the Cu doping profiles for different Temperatures and durations of the annealing process. Excellent agreement between the simulated results obtained with the PVRD-FASP Solver and the predicted values is obtained. It is important to mention here that it takes a significant amount of time to generate the Cu doping profiles given the initial conditions using the PVRD-FASP Solver, because solving the drift-diffusion-reaction model is mathematically a stiff problem and leads to numerical instabilities if the time steps are not small enough, which, in turn, affects the time needed for completion of one simulation run. The generation of the same with Machine Learning (ML) is almost instantaneous and can serve as an excellent simulation tool to guide future fabrication of optimal doping profiles in CdTe solar cells.