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| Solar Panels |
Background and Literature Review
Solar cells require the use of anti-reflection coatings (ARC) that consist of one or more thin films carefully chosen for their thicknesses and refractive indexes in order to minimise reflection losses caused by common solar cell materials such as silicon, which suffers an approximate 30% loss without the use of ARC due to its high refractive index (n ≈ 3.5 – 4, in typical operation range of 400 to 1100 nm)[1],[7]. Existing ARC materials (e.g. silicon nitride, silicon oxide) are mostly oxide-based (except silicon nitride) and are prone to premature aging, UV-induced degradation, and the added complexity and cost associated with requiring protective encapsulation of such materials [2].
Hexagonal boron nitride (h-BN) is deemed a suitable alternative ARC material as h-BN is a wide-bandgap (~6.2 eV) [3] 2D material with a refractive index of approximately 2.23 [4], along with high chemical/thermal stability, and excellent mechanical robustness [5],[6]. Therefore, these properties shows that low-temperature deposition (<200°C) of polycrystalline h-BN films are suitable for both terrestrial and space solar cell applications [6]. Furthermore, the refractive index of h-BN is close to the ideal value for a single-layer quarter-wave ARC on silicon (≈2.02) [7], which allows effective destructive interference and low reflectance at the design wavelength while providing broadband transparency. Experimental studies have demonstrated that boron nitride thin films can reduce reflection losses to below 5% over wide solar windows when used in single- or double-layer configurations on Silicon and Gallium arsenide (GaAs)- based cells [8].
In this work, a single-layer h-BN ARC is designed on a traditional crystalline silicon (c-Si) solar cell substrate, which attempts to investigate and simulate the optical response for this coating and evaluate its efficiency and capability to minimise reflection losses and operating in a wide-angle range.
Schematic Diagrams
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| Figure 1 - Cross-section schematic of the single-layer h-BN antireflection coating implemented on a standard silicon solar cell |
Figure 1 shows the cross section of the schematic of the example implementation of the single-layer h-BN antireflection coating on top of a standard silicon solar cell. The structure consists of 4 main regions: The air medium (refractive index n≈1 [9]), the n and p-type silicon substrates (n≈4.0767 [10]) with conventional thickness of 0.5 and 180μm respectively, and the h-BN ARC layer (n≈2.2256 [11]) of thickness d of 62nm, which is designed with the wavelength λ of 550nm, which is the midpoint of the visible spectrum (400–700nm), ensuring the coating is operational and functional across the full visible range.
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| Figure 2 – Operations of ARC illustrated on cross-section of solar cell |
The h-BN ARC operates on the principle of destructive interference, as shown in Figure 2. When incident light (the incoming sunlight) arrives at the ARC layer, one reflection forms immediately (Reflection Wave 1), and when the wave continues into the ARC and towards the silicon substrate, another reflection forms at the h-BN-Si interface and hence reflects back into the air (Reflection Wave 2). As both reflections occur at a junction going from a lower to a higher refractive index (n_Air < n_ARC< n_Si), both rays have an equal phase shift of π. The h-BN thickness of exactly 62nm is chosen so that the path length travelled by reflection wave 2 through the coating equals half a wavelength, which induces an extra phase difference of π. Therefore, the path-length induced phase difference of π yields the two reflected waves to be out of phase by π, resulting in destructive interference, hence suppressing and minimising the total net reflected energy.
Equations and Theory
When light arrives at the h-BN ARC layer at angle θi, it refracts into the coating at angle θt, which relationship is described by Snell's law, n1sinθi =n2sinθt, where n1=n_Air and n2=n_ARC. As reflection wave 2 travels an additional length of 2n2cosθt, for destructive interference, this must equal half a wavelength, i.e. 2dn_ARCcosθt = λ/2, At normal incidence, θt = 0, hence the equation can be rewritten as d=λ/(4n_ARC), which for a design λ of 550nm, d = (550×10^(-9))/((4)(2.2256)) = 61.7811nm, therefore resulting in a thickness of 62nm. In order to achieve optimal destructive interference of the two reflection waves, it’s required to satisfy the equation nARC = √(n_substrate n_incident ), where n_substrate = n_si = 4.0767, and n_incident = n_air = 1, resulting √((4.0767)(1)) ≈ 2.0191, which is relatively close to n_ARC = 2.2256.
For the full reflection and transmission values, the transfer matrix method is used. For a single layer of ARC with refractive index nARC and thickness d, the transfer matrix can be written as:
Therefore, the optimal ARC index can be obtained by:
Results
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| Figure 3 - Plot of reflection and transmission functions across the visible light range for normal incidence of light. |
From figure 3, it is observed that at the design wavelength of 550nm, the TMM predicts a reflectance of approximately 0.6% for the h-BN coated cell, compared to 37.8% for bare silicon without any ARC applied, which is a reduction of over 37.2%. This is consistent with the quarter-wave destructive interference condition derived theoretically in the section above. However, the reflectance minimum is not exactly zero because n_ARC=2.2256 is still different from the ideal value of n_Si=2.019, resulting a small residual reflection amplitude. The transmittance correspondingly peaks at around 99.4% at 550nm, confirming the high transmission percentage at the design wavelength. Furthermore, reflectance rises symmetrically when approaching towards the edges of the visible spectrum (400nm and 700nm), which is expected as at wavelengths away from 550nm, it weakens the destructive interference condition.
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| Figure 4 - Plot of reflectance vs wavelength and angle |
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| Figure 5 - Plot of transmittance vs wavelength and angle |
Figure 4 and 5 shows the coating maintains low reflectance across a wide range before performance reduces. For angles up to roughly 40–50°, the reflectance at 550 nm remains below approximately 5%, indicating a practically optimal operational window that applies to most real-world solar illumination angles throughout the day. Beyond roughly 60°, the reflectance is observed to increase significantly and approaches 100%, which is within expectations. It is also observed that 550 nm wavelength sustains the lowest reflectance at all angles due to it being the design wavelength. As for transmittance, the plot (figure 5) demonstrates a corresponding inverse relationship with reflectance, peaking near 99.4% at the design wavelength and normal incidence, and decreasing significantly as both angle of incidence and wavelength deviate further from their optimal values. At angles approaching 90°, transmittance falls toward zero across all wavelengths, consistent with near-total reflection under such conditions.
Therefore, from the figures above, it is evident that the h-BN ARC demonstrates strong antireflection performance across the visible spectrum at normal and near-normal incidence, which aligns with theoretical expectations hence achieving the primary design objective. However, it’s worth noting that efficiency limitations are present. The most significant limitation is the refractive index mismatch between h-BN and the ideal value, as mentioned in previous sections, however close the value may be for h-BN, the condition of n_ARC = √(n_substrate n_incident ) is still unsatisfied. Comparing with silicon nitride (Si₃N₄), which is the industrial standard for antireflection coatings, which does have a nARC of approximately 2.0523 [12] which yields a value much closer to the ideal value. As a result, Si₃N₄ can achieve near-zero reflectance at its design wavelength. However, h-BN holds several significant advantages that existing materials, such as Si₃N₄, does not offer. As a 2D material, h-BN is chemically and thermally stable, and resistant to moisture and oxidation, properties that are critical for long-term outdoor deployment where degradation of the ARC layer directly reduces cell efficiency over time. Si₃N₄, while does match the ideal refractive index values, suffers from UV-induced degradation, and requires high-temperature manufacturing techniques, whereas h-BN can be transferred or grown at lower temperatures, making it more compatible with temperature-sensitive cell architectures such as heterojunction silicon-based cells. Therefore, h-BN is not the optimal choice purely from a refractive index standpoint, but its combination of optical performance, physical stability, and process compatibility positions it as a compelling candidate particularly for next-generation and flexible solar cell technologies where conventional ARC materials face degradation challenges.
The second limitation of this design is that it’s single layer only, which inherently limits the spectral bandwidth and angular tolerance compared to more advanced and sophisticated multi-layer implementations. A double-layer (or above) ARC could broaden the reflectance minimum further into the ultraviolet and near-infrared levels and sustain lower reflectance at higher angles of incidence. Hence, the potential of multi-layered h-BN ARC layers can be considered for future developments. Regardless, for a single-layer solution, the h-BN ARC represents an effective and practically constructable alternative to traditional ARC materials, with trade-offs between optical performance, fabrication simplicity, and material compatibility, making it a strong candidate for integration into standard silicon solar cell manufacturing processes with further research and development.
Code Availability
The underlying code for this study is not publicly available but may be made available to qualified researchers/students on reasonable request from the author.
References
[1] PV Education, Optical Properties of Silicon. Available at: https://www.pveducation.org/pvcdrom/materials/optical-properties-of-silicon
[2], [3], [5] A. Alemu, A. Freundlich, N. Badi, C. Boney, A. Bensaoula, Low temperature deposited boron nitride thin films for a robust anti-reflection coating of solar cells. Available at: https://www.sciencedirect.com/science/article/pii/S0927024809004528
[4], [11] Refractiveindex.info, Optical constants of BN (Boron nitride), (2024). Available at: https://refractiveindex.info/?shelf=main&book=BN&page=Lee
[6] Anna A. Popkova, Ilya M. Antropov, Johannes E. Fröch, Sejeong Kim, Igor Aharonovich, Vladimir O. Bessonov, Alexander S. Solntsev, and Andrey A. Fedyanin, Optical Third-Harmonic Generation in Hexagonal Boron Nitride Thin Films, ACS Photonics 2021. Available at: https://pubs.acs.org/doi/10.1021/acsphotonics.0c01759
[7] PV Education, Anti-Reflection Coatings. Available at: https://www.pveducation.org/pvcdrom/design-of-silicon-cells/anti-reflection-coatings
[8] Nacer Badi, Alex Freundlich, Abdelhak Bensaoula, Andenet Alemu, Boron nitride anti-reflection coatings and methods, U.S. Patent US9318626B2, Apr. 19, 2016. [Online]. Available: https://patents.google.com/patent/US9318626B2/en
[9] Refractiveindex.info, Optical constants of Air. Available at: https://refractiveindex.info/shelf=other&book=air&page=Borzsoyi
[10] Refractiveindex.info, Optical constants of Si (Silicon). Available at: https://refractiveindex.info/shelf=main&book=Si&page=Wang-25C
[12] Refractiveindex.info, Optical constants of Si3N4, SiN (Silicon nitride). Available at: https://refractiveindex.info/shelf=main&book=Si3N4&page=Luke
Author Information
H. Ryan Wong - Undergraduate, Faculty of Environment, Science and Economy, University of Exeter, Exeter EX4 4QF, United Kingdom; Email: ryanwongstudios@proton.me
Additional Information
This is a student case study submitted for academic assessment. It is published here solely for educational reference and discussion purposes. While this work received a fairly good mark, it remains student-level work and may contain limitations, simplifications, or areas that could be improved. Readers who wish to use any part of this document as a reference or example do so entirely at their own risk. The author does not claim that this represents the best possible approach, nor should it be treated as authoritative or model solution for submission.
Correspondence and any requests for relevant materials should be addressed to the author, H. Ryan Wong by emailing: ryanwongstudios@proton.me
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