Holistic yield modeling, top-down loss analysis, and efficiency potential study of thin-film solar modules

The study addresses how to accurately predict and analyze the real-world performance and energy yield of thin-film photovoltaic modules under non-standard operating conditions. While single-cell laboratory measurements and standard testing conditions do not capture field-relevant effects, the authors aim to develop a holistic modeling framework that links semiconductor device physics, optical behavior, and module-scale electrical transport. This approach enables allocation and quantification of all loss mechanisms from the Shockley–Queisser limit down to actual module power, supports reverse inference of difficult-to-measure material parameters from module data, and informs optimization priorities to close the cell-to-module gap. The work demonstrates the model on a commercial 1.2 × 0.6 m² CIGS module with 144 monolithically integrated cells and a specified layer stack.

Prior work has examined thin-film solar devices via electrical simulations and drift-diffusion models, but predominantly at the cell level. Studies emphasize the need to consider entire modules in the field to guide development toward higher net energy yields. The Shockley–Queisser model sets an upper efficiency bound, yet practical losses arise from non-radiative recombination, optical reflection and parasitic absorption, geometrical dead areas, and electrical transport effects such as ohmic losses, shunts, and local MPP mismatches. Existing models typically handle subsets of these mechanisms or single dimensions, leaving a gap between cell-scale simulation and system-level performance tools. This work integrates an electronic drift-diffusion model, a modified transfer-matrix approach with partially incoherent interference, and a quasi-three-dimensional finite-element Poisson solver to capture the full chain of physical processes at module scale. It builds upon literature optical constants, semiconductor parameters, and prior finite-element and TMM approaches, adding a reverse engineering fitting routine to infer material parameters from module I–V data.

The authors develop a three-level, linked simulation framework for thin-film modules: (1) a one-dimensional finite-element drift-diffusion model of the p–n junction solving the van Roosbroeck system (Poisson’s equation and carrier continuity equations) to capture electronic recombination and junction behavior; (2) a modified generalized transfer-matrix method (TMM) accounting for coherent/partially incoherent interference due to rough interfaces, internal and back-side reflections, and wavelength-dependent absorption (Lambert–Beer-like) using measured or literature refractive indices; and (3) a quasi-three-dimensional finite-element Poisson solver on a Delaunay-triangulated mesh to simulate lateral current collection and transport, including contact layer conductivities, series/shunt pathways, and monolithic interconnects (P1/P2/P3). The model is parameterized with measured geometries (layer thicknesses, lateral dimensions), optical constants (ellipsometry/transmittance for most layers; CIGS from literature), measured sheet/specific resistivities (e.g., AZO and Mo), and literature semiconductor parameters. A Reverse Engineering Fitting (REF) routine uses a gradient-free downhill simplex algorithm to minimize a weighted mean-squared error between simulated and measured I–V curves, fitting difficult-to-measure parameters (e.g., background doping densities and carrier mobilities in CIGS and CdS). Standard testing conditions (1000 W m−2, 25 °C, AM1.5G) are used to evolve the baseline digital twin. For field yield simulations, measured plane-of-array irradiance and rear-glass module temperature (time-resolved) are fed into the TMM and drift-diffusion models, respectively; temperature-dependent junction I–V curves serve as inputs to the 3D transport solver. The framework enables time-resolved top-down loss allocation across four categories: semiconductor (recombination), optical (reflection, parasitic absorption, incomplete absorption), geometrical (edge, interconnect dead area), and electrical (ohmic in contacts and interconnect paths, shunts across P1/P3, local MPP mismatches). The module under study is a NICE Solar Energy N-G1000E105 CIGS module (144 cells), with a stack: 400 nm Mo / 2100 nm CIGS (GGI graded 0.2–0.4) / 50 nm CdS / 50 nm i-ZnO / 800 nm AZO / 750 µm encapsulant / 3.2 mm low-iron AR-coated glass. Module geometry includes edge areas and 265 µm interconnect widths; active area is 6695 cm². REF-derived parameters include background doping levels and mobilities (e.g., higher-than-typical CIGS electron mobility ≈ 200 cm² V−1 s−1 and characteristic doping densities on the order of 10¹⁵–10¹⁷ cm−3). The coefficient of determination R² is used to assess I–V fits. Field data were recorded at ZSW Widderstall (south-facing, 40° tilt) with 1-minute I–V scans and MPP tracking; irradiance measured by a secondary standard pyranometer and temperature by a PT1000 at the rear glass.

• The stacked model reproduces the STC module I–V with high fidelity: R² = 0.997 versus measurements. The STC power conversion efficiency (PCE) is approximately 14.27% (14.3% reported in Fig. 1 caption).
• Sequential loss inclusion shows: from the Shockley–Queisser limit to semiconductor level, Voc drops due to non-radiative recombination; TMM reduces jsc and slightly Voc via reflection and parasitic/incomplete absorption; geometrical losses (edges, interconnects) reduce power; 3D transport introduces series/shunt effects and local MPP mismatches lowering fill factor and jsc.
• Temperature dependences: simulated coefficients Voc ≈ −2.0 mV K−1 and FF ≈ −0.06% K−1, matching measured values (≈ −2.1 mV K−1 and −0.05% K−1) and within theoretical expectations.
• Daily yield prediction for a clear day (Sept 9, 2020): simulated energy 698.9 Wh vs measured 698.7 Wh; time-resolved Voc, jsc, and FF trajectories closely match measurements, including morning tree shading effects and noon FF dip due to higher temperature and higher current-induced ohmic drops.
• Shockley–Queisser PCE limit varies with irradiance and temperature (about 29%–34% over the day). Actual module PCE falls more at low light (shunt influence) and during heating (temperature coefficients), consistent with model and measurements.
• Largest single source of loss is recombination at the semiconductor level; optical losses comprise reflection, incomplete and parasitic absorption; geometrical losses come from edges and interconnects; electrical losses arise from ohmic resistances, shunts, and local MPP mismatches.
• Reverse Engineering Fitting recovers otherwise hard-to-measure parameters: background doping densities (e.g., CdS donor ~1×10¹⁷ cm−3; CIGS on the order of ~10¹⁵ cm−3) and notably high CIGS electron mobility (~200 cm² V−1 s−1), implying longer diffusion lengths.
• Sensitivity/efficiency potential at STC: achieving a +0.65% absolute PCE gain (to 14.92%) can be met by any of: lowering TCO sheet resistance from 25 Ω/sq to 7.75 Ω/sq; or reducing front TCO parasitic absorption by ~26%; or eliminating encapsulant absorption; or shrinking edge area from ~505 cm² (7%) to ~190 cm² (2.6%); or reducing interconnect width from 265 µm to 100 µm (with optimized cell width). Implementing all listed improvements yields a projected module PCE of 17.9% without altering the CIGS absorber process.

The integrated, three-level model successfully addresses the core challenge of connecting fundamental device physics to module-scale, real-world performance. By accurately predicting time-resolved Voc, jsc, FF, PCE, and daily energy with near-perfect agreement to measurements, the approach validates that physical loss mechanisms across optics, semiconductor recombination, geometry, and lateral transport are captured and correctly apportioned. The top-down loss analysis quantifies the contribution of each mechanism, highlighting recombination as the dominant intrinsic loss and identifying significant optical and transport-related penalties. The model further explains deviations between the Shockley–Queisser limit and actual module PCE under varying irradiance and temperature, attributing low-light departures to shunts and midday degradation to temperature coefficients and ohmic drops. The reverse fitting capability enables extraction of key material parameters directly from module I–V data, providing practical insight where direct measurements are difficult. Sensitivity analyses translate material and design changes (e.g., TCO conductivity/absorption, encapsulant transparency, edge and interconnect areas) into efficiency gains, guiding R&D priorities toward impactful module-level improvements.

This work presents, to the authors’ knowledge for the first time, a linked three-stage simulation of thin-film solar modules that spans drift-diffusion semiconductor physics, modified transfer-matrix optics, and quasi-3D electrical transport with geometrical corrections. The holistic model accurately reproduces STC behavior and non-STC, time-resolved field performance, enables comprehensive top-down loss allocation, and supports bottom-up sensitivity analyses. Reverse Engineering Fitting allows inference of critical, hard-to-measure parameters (e.g., background doping and carrier mobilities), improving understanding and enabling targeted optimization. The framework identifies recombination as the largest loss and quantifies how optical, geometrical, and electrical improvements can raise module efficiency, projecting up to 17.9% PCE with combined module-level enhancements. Future research could incorporate spatially resolved thermal modeling, extend to other thin-film and wafer-based technologies, and integrate year-long meteorological datasets and degradation effects to assess lifetime yield and reliability.

• Thermal modeling is simplified: a spatially distributed thermal model is not included, and a uniform equilibrium temperature is assumed across the module. Rear-glass temperature measurements may differ from junction temperature by up to ~2 K, potentially impacting accuracy in transient or highly non-uniform conditions.
• The REF optimization uses a gradient-free simplex with practical limits of ~4–6 free parameters to ensure convergence time; expanding parameter sets may challenge robustness or runtime.
• Optical and electrical parameterizations rely partly on literature data and fitted values; uncertainties in optical constants, especially for CIGS, are mitigated by thickness and band-gap matching but still introduce model dependence.
• The approach is demonstrated on a homogeneous thin-film module; while adaptable, wafer-based technologies and modules with pronounced inhomogeneities, hotspots, or defects may require additional modeling refinements.
• Field validation shown for specific days; broader climatological generalization (e.g., annual yield, degradation over time) is not covered in this study.