Researchers from Northwestern University, University of Cádiz, and University of Arizona have developed new formulae for analyzing optical thin films that outperform traditional models by accounting for complex geometries and absorbing substrates. These advances offer more precise ultraviolet-visible-near-infrared (UV-vis-NIR) spectroscopic analysis of film materials used in critical modern technologies.
A Modern Upgrade to Thin-Film Optics
Thin films, which are microscopically thin layers used in everything from smartphones and solar panels to high-performance electronics, are notoriously challenging to analyze using UV-vis-NIR spectroscopy with high precision (1–3). Now, a new study published in Measurement Science and Technology offers a significant move forward in the field of thin-film optical analysis.
Led by Manuel Ballester (Northwestern University), along with Emilio Marquez (University of Cádiz), John Bass, Christoph Würsch, Florian Willomitzer, and Aggelos K. Katsaggelos (Northwestern University and University of Arizona), the team has developed new mathematical expressions that more accurately model the transmittance and reflectance of thin films, particularly those with wedge-shaped profiles on absorbing substrates. Their work not only reviews and tests legacy formulae but also introduces powerful new tools that promise greater accuracy, even under non-ideal sample conditions (1).
Chemical vapor deposition (CVD) machine creating an optically thin film coating © Your Hand Please-chronicles-stock.adobe.com
Rethinking Traditional Assumptions
Historically, the optical analysis of thin films assumed idealized sample structures, namely, thin, flat films deposited on completely transparent, non-absorbing substrates. “These simplifications made the math easier,” Ballester said, “but they didn’t reflect the actual samples found in real-world applications” (1).
Many previous formulae in reflectance and transmittance spectroscopy also assumed negligible wedge angles and ignored the complexity of absorption by the substrate (1–3). In contrast, the new study challenges both of these assumptions. The authors present a framework that accommodates thick, absorbing substrates and films with significant wedge angles, helping address a longstanding gap in optical thin-film characterization (1).
Precision Across Spectral Ranges
The study focuses on calculating two key optical properties: the refractive index (n₁(λ)) and the extinction coefficient (κ₁(λ))—both as functions of wavelength in the UV-vis-NIR regions. These values are crucial for engineers and scientists designing optical components or semiconductors (1).
The team’s enhanced formulae are particularly effective for samples with complex topographies or those analyzed over broad spectral ranges that include regions of strong absorption. For example, when the wedge parameter Δd exceeds λ/(4n) or when both the film and the substrate exhibit significant absorption, the new methods show clear superiority over widely used approximations like the Swanepoel model (1).
Spectroscopy Reimagined
A cornerstone of this research is the integration of these new formulae into open-source tools coded in Python and MATLAB. These computational tools include both traditional and newly derived expressions, making it easier for researchers to select the most appropriate model based on sample type and desired accuracy. The team emphasizes a critical trade-off: simpler models like Swanepoel’s require less computing time but at the cost of precision, while their new formulae demand more computation but offer sharper accuracy (1).
To ensure rigorous analysis, the team numerically and analytically tested each formula against multiple use cases, summarizing their findings in a detailed comparison table. This enables users to make informed decisions when analyzing thin films with varying structural and optical complexities (1).
Looking Ahead
The implications of this work extend far beyond academic theory. Thin-film technologies are integral to displays, sensors, photovoltaics, and semiconductor devices. With this new framework, engineers and material scientists can better characterize layered materials during the research and development phase, potentially accelerating innovations in optics and electronics.
Future research aims to expand these methods to include multilayer films with tilted geometries and rough surfaces, further aligning theory with industrial realities. The team also plans to experimentally validate the models against real-world measurements, enhancing their practical utility (1).
References
(1) Ballester, M.; Marquez, E.; Bass, J.; Würsch, C.; Willomitzer, F.; Katsaggelos, A. K. Review and Novel Formulae for Transmittance and Reflectance of Wedged Thin Films on Absorbing Substrates. Meas. Sci. Technol. 2025, 36 (2), 025502. DOI: 10.1088/1361-6501/ada305
(2) Dhruv, S. D.; Sharko, S. A.; Solanki, P.; Vala, M.; Thakker, I. T.; Kataria, B.; Dhruv, D. K. Optical Characterization of Semiconducting Thin Films Using UV-VIS-NIR Spectroscopy: A Review. Solid State Phenom. 2023, 350, 115–124. DOI: 10.4028/p-YADdi5
(3) Minkov, D.; Angelov, G.; Nikolov, D.; Rusev, R.; Marquez, E.; Fernandez, S. Method for Superior Denoising of UV/Vis/NIR Transmittance Spectra of Thin Films. Opt. Express 2024, 32 (19), 33758–33778. DOI: 10.1364/OE.528917
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