Towards a fully differentiable digital twin for solar cells

TL;DR

The paper introduces Sol(Di)^2T, a fully differentiable digital twin that unifies material morphology, optical response, electrical transport, and climate-location effects to predict and optimize energy yield (EY) of solar cells. By embedding phase-field BHJ morphology, ML surrogates for optics and drift-diffusion, and a differentiable EY calculator, it enables gradient-based inverse design from material to deployment location. Demonstrated on PM6:Y6 organic solar cells, the framework identifies optimal photoactive-layer thickness and tilt angles across locations, and provides open-source code for broader adoption and extension to other PV technologies. The work strengthens the link between nanoscale morphology and macroscopic EY, offering a scalable tool for location-specific PV optimization and accelerated design iterations.

Abstract

Maximizing energy yield (EY) - the total electric energy generated by a solar cell within a year at a specific location - is crucial in photovoltaics (PV), especially for emerging technologies. Computational methods provide the necessary insights and guidance for future research. However, existing simulations typically focus on only isolated aspects of solar cells. This lack of consistency highlights the need for a framework unifying all computational levels, from material to cell properties, for accurate prediction and optimization of EY prediction. To address this challenge, a differentiable digital twin, Sol(Di)$^2$T, is introduced to enable comprehensive end-to-end optimization of solar cells. The workflow starts with material properties and morphological processing parameters, followed by optical and electrical simulations. Finally, climatic conditions and geographic location are incorporated to predict the EY. Each step is either intrinsically differentiable or replaced with a machine-learned surrogate model, enabling not only accurate EY prediction but also gradient-based optimization with respect to input parameters. Consequently, Sol(Di)$^2$T extends EY predictions to previously unexplored conditions. Demonstrated for an organic solar cell, the proposed framework marks a significant step towards tailoring solar cells for specific applications while ensuring maximal performance.

Figures (7)

• Figure 1: (a) Overview of the digital twin framework $\text{Sol}(\text{Di})^2\text{T}$ for energy yield (EY) optimization, comprising five simulation stages: material morphologies, optical properties, electrical properties, EY calculation framework, and optimization and machine learning (ML). (b) Device architecture of the studied cell. The different thicknesses are not drawn to scale. The exact stack thicknesses are 150 of ITO, 30 of ZnO, 200 of PM6:Y6, 50 of PEDOT:PSS, a layer of 10 of Ag, and finally a layer of 140 of PEDOT:PSS. The yellow arrow represents the incoming light.
• Figure 2: Detailed framework of the forward-pass of the digital twin $\text{Sol}(\text{Di})^2\text{T}$. The different sub-structures are given the same colors as in Figure \ref{['fig:figure1']}: material morphologies (blue), optical properties (green), electrical properties (orange), and the energy yield calculation framework (red). The input quantities (in circles) are material (M), process conditions (PC), design (D), and placement (P). Material (M) encompasses material properties and experimental knowledge of the material. Process conditions (PC) include temperature and drying conditions. Design (D) is defined by the details of the layer stack of the solar cell. Placement (P) includes the location and orientation of the solar cell. Squared boxes, framed in black, are methods, and rounded, unframed patches are (intermediate) results.
• Figure 3: Morphology module results. The top part shows the BHJ morphology of PM6:Y6 from PF simulations. The volume fraction and crystalline order parameter are depicted for both the donor and acceptor material. The volume fraction and crystalline order parameter spread from 0 or low values (dark blue) to 1 or higher values (dark red). The bottom part shows the morphology mapping we attain from the donor (PM6) and acceptor (Y6) material. It illustrates the four coexisting phases in the BHJ, which are listed in Table \ref{['tab:phasetype']}. The phases are: donor crystal phase (dark grey), acceptor crystal phase (medium grey), amorphous mixed phase (light grey), and amorphous donor phase (black).
• Figure 4: Optics module results. (a) The considered finite-sized molecular model of PM6:Y6. (b) The optical properties of the two molecules obtained from TD-DFT calculations. (c) The absorbance of the material mixture PM6:Y6 calculated via homogenization of the molecular optical properties. (d) The charge generation rate, where different colors indicate the different layers of the stack. The lime green color indicates the photoactive material PM6:Y6.
• Figure 5: Electrical module results. (a) Open-circuit voltages for different light intensities as a function of temperature. The spheres represent experimental data and the squares the corresponding fits. (b) Fill factors for different light intensities as a function of temperature. The spheres represent experimental data and the squares the corresponding fits. (c) The obtained bimolecular recombination coefficient $k_\mathrm{rec}$ as a function of temperature. (d) The obtained mobility $\mu$ as a function of temperature.