Vibro-electrical performance of nickel-clustered monocrystalline-silicon photovoltaic cells: A data-informed analytical modal study

Elyor Saitov
University of Tashkent for Applied Sciences, 1 Gavkhar Street, Chilanzar District, Tashkent 100149, Uzbekistan
Nurullo Zikrillaev
Tashkent State Technical University named after Islam Karimov, University Street 2, Tashkent 100095, Uzbekistan
Abdusalom Umarov
University of Tashkent for Applied Sciences, 1 Gavkhar Street, Chilanzar District, Tashkent 100149, Uzbekistan; Tashkent State Transport University, 1 Temiryulchilar Street, Tashkent 100167, Uzbekistan
Khayrulla Zikrillaev
Tashkent State Technical University named after Islam Karimov, University Street 2, Tashkent 100095, Uzbekistan
Sayfillo Nasriddinov
Tashkent regional branch of Astrakhan State Technical University. Tashkent region.100164, Republic of Uzbekistan
Khikmat Makhmudov
Uzbek National Institute of Metrology, Farobiy Street, 333A, 333B, Tashkent 100174, Uzbekistan
Nigora Usmanova
Tashkent State Technical University named after Islam Karimov, University Street 2, Tashkent 100095, Uzbekistan

Article ID: 4833

Keywords: modal analysis; plate vibration; photovoltaic cells; Mindlin-Reissner plate theory; inclusion homogenization; harmonic response; thermal annealing

Abstract

Dynamic mechanical loading can initiate cracks, interconnect damage, and power loss in crystalline-silicon photovoltaic assemblies, yet the local vibration consequences of metallic impurity clusters inside a cell remain poorly quantified. This study combines previously published electrical and microstructural measurements for nickel-clustered monocrystalline-silicon cells [7] with a reproducible plate-vibration model. The records cover 600-1100 ℃ additional annealing, reported cluster-size intervals of 1-30 µm, open-circuit voltages of 480-506 mV, and short-circuit current densities of 20.2-45.7 mA cm^-2. A 10 × 5 × 0.38 mm coupon was represented as a simply supported Kirchhoff-Love plate, with the unreported crystal orientation bracketed by silicon Young's moduli of 130-169 GPa. An independent Mindlin-Reissner eigenvalue calculation, including transverse shear and rotary inertia, predicted a first frequency 1.26% below the Kirchhoff-Love value. Pure-Ni inclusions and Reuss-Voigt stiffness bounds were retained as a conservative homogenization envelope. The Kirchhoff-Love first local bending frequency was 67.05-76.45 kHz. For the 900 ℃ condition with the highest UocJsc proxy calculated from the published data, the proxy was 2.190 times the control value, while the model predicted a first-mode shift of -0.0037% to -0.0040% for the midpoint morphology and -0.0006% to -0.0127% across its stated lower-upper morphology bounds. The maximum predicted reduction over the full feasible morphology domain was 3.051%. These calculations predict a small coupon-level modal effect under the stated geometry, support, and homogenization assumptions; they do not constitute experimental evidence of modal performance, fatigue resistance, or module-level vibration reliability.

Published

2026-11-12

How to Cite

Saitov, E., Zikrillaev, N., Umarov, A., Zikrillaev, K., Sayfillo Nasriddinov, Khikmat Makhmudov, & Nigora Usmanova. (2026). Vibro-electrical performance of nickel-clustered monocrystalline-silicon photovoltaic cells: A data-informed analytical modal study. Sound & Vibration, 60(6). https://doi.org/10.59400/sv4833

Download Citation

Issue

Vol. 60 No. 6 (2026): In Progress

Section

Article

This work is licensed under a Creative Commons Attribution 4.0 International License.

References

[1].International Electrotechnical Commission. IEC TS 62782:2016: Photovoltaic (PV) Modules—Cyclic (Dynamic) Mechanical Load Testing. International Electrotechnical Commission; 2016.

[2].Kajari-Schröder S, Kunze I, Eitner U, Köntges M. Spatial and orientational distribution of cracks in crystalline photovoltaic modules generated by mechanical load tests. Solar Energy Materials and Solar Cells. 2011, 95(11): 3054–3059. doi: 10.1016/j.solmat.2011.06.032

[3].Luo B, Gallas S, Micallef C, et al. Experimental and finite element modal analysis of photovoltaic modules for the design of next-generation vehicle-integrated PV applications. Solar Energy Materials and Solar Cells. 2025, 290: 113683. doi: 10.1016/j.solmat.2025.113683

[4].Bergmann S, Hassani F, Javanbakht Z, Aßmus M. On a fast analytical approximation of natural frequencies for photovoltaic modules. Technische Mechanik—European Journal of Engineering Mechanics. 2020, 40(2): 191–203. doi: 10.24352/UB.OVGU-2020-025

[5].Lindroos J, Fenning DP, Backlund DJ, et al. Nickel: A very fast diffuser in silicon. Journal of Applied Physics. 2013, 113(20): 204906. doi: 10.1063/1.4807799

[6].Abdurakhmanov BA, Bakhadirkhanov MK, Ayupov KS, et al. Formation of clusters of impurity atoms of nickel in silicon and controlling their parameters. Nanoscience and Nanotechnology. 2014, 4(2): 23–26. doi: 10.5923/j.nn.20140402.01

[7].Bakhadyrkhanov MK, Valiev SA, Zikrillaev NF, et al. Silicon photovoltaic cells with clusters of nickel atoms. Applied Solar Energy. 2016, 52(4): 278–281. doi: 10.3103/S0003701X1604006X

[8].Bakhadyrkhanov MK, Kenzhaev ZT. Optimal conditions for nickel doping to improve the efficiency of silicon photoelectric cells. Technical Physics. 2021, 66(7): 851–856. doi: 10.1134/S1063784221060049

[9].Kenzhaev ZT, Iliev HM, Ismailov KA, et al. Physical mechanisms of gettering properties of nickel clusters in silicon solar cells. Physical Sciences and Technology. 2024, 11(1–2): 13–22. doi: 10.26577/phst2024v11i1a2

[10].Leissa AW. Vibration of Plates. NASA SP-160. National Aeronautics and Space Administration; 1969.

[11].Hopcroft MA, Nix WD, Kenny TW. What is the Young’s modulus of silicon? Journal of Microelectromechanical Systems. 2010, 19(2): 229–238. doi: 10.1109/JMEMS.2009.2039697

[12].Ledbetter HM, Reed RP. Elastic properties of metals and alloys, I: Iron, nickel, and iron-nickel alloys. Journal of Physical and Chemical Reference Data. 1973, 2(3): 531–617. doi: 10.1063/1.3253127

[13].Huang M, Yang C, Cai K, et al. Modal analysis of flexible photovoltaic support system using multi-source data. Journal of Civil Structural Health Monitoring. 2025, 15: 3321–3343. doi: 10.1007/s13349-025-00992-0

[14].Castellini P, Martarelli M, Tomasini EP. Laser Doppler vibrometry: Development of advanced solutions answering to technology’s needs. Mechanical Systems and Signal Processing. 2006, 20(6): 1265-1285. doi: 10.1016/j.ymssp.2005.11.015

[15].Mindlin RD. Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates. Journal of Applied Mechanics. 1951, 18(1): 31-38. doi: 10.1115/1.4010217

Editor-in-Chief

Prof. Jun Yang

Institute of Acoustics, Chinese Academy of Sciences, China

ISSN

1541-0161 (Print)

2693-1443 (Online)

Publication Frequency

Bi-monthly

Indexing

Web of Science Coverage

Emerging Sources Citation Index (IF 4.2, Q1)

Elsevier Solutions

Scopus (2025 CiteScore 2.0);

Portico, etc.

About the Publisher

Academic Publishing insists on taking academic exchange and publication as the main line, carrying out comprehensive management based on science and technology, and fully exploring excellent international publishing resources. Within 5 years, it will form a strategic framework and scale with science (S), technology (T), medicine (M), education (E), and humanities and arts (H) as the main publishing fields. Academic Publishing is headquartered in Singapore and based in Malaysia, with the United States and China providing the main scientific and academic resources. At the same time, it has established long-term good cooperative relations with other publishing companies, scientific research communities, and academic organizations in more than a dozen countries and regions. Academic Publishing uses English and Chinese as its main publishing languages, mainly publishing books, journals, and conference papers in print and online. The vast majority of publications follow the international open access policy, providing stable and long-term quality and professional publications. With the joint efforts of the expert team and our professional editorial team, our publications will gradually be indexed by international databases in stages to provide convenient and professional retrieval for various scholars. At the same time, manuscripts we accept will be subject to the peer review principle, and cutting-edge and innovative research articles will be preferentially accepted for peer reference and discussion. All kinds of our publications are welcome for peer to contribute, access, and download.

more

Member of ASC

Volume Arrangement

Featured Articles

New scaling of critical damping and reduced frequency for mechanically excited systems

This paper introduces a universal framework for understanding the vibration responses of systems subjected to harmonic excitation. By examining a simplified cylinder-spring-damper model, the study refurbishes traditional scaling methods for the excitation frequency ratio and critical damping ratio. The findings indicate that in damped systems, the maximum amplitude of vibration does not align with the natural frequency. This observation leads to the introduction of a new scaling method for reduced frequency. This new approach aligns resonance peaks at the new reduced velocity of 1.0 across different damping ratios, providing a consistent characterization of vibration behavior. A new critical damping ratio of 0.707 is identified for an excited system as opposed to the traditional damping ratio of 1.0 for an unexcited system. Key properties such as maximum amplitude, phase lag, bandwidth, and quality factor are analyzed, demonstrating that the proposed reduced frequency and critical damping ratio effectively capture the dynamics of both damped and undamped excited systems. The findings offer significant insights for practical applications in engineering and various scientific fields.

Ultrasonic wave velocity as a universal metric for defect detection in timber structures: A case study on Japanese cedar wood (Cryptomeria japonica)

This study makes significant contributions to the field of ultrasonic testing (UT) by offering a novel approach to the identification of artificially introduced defects within Japanese cedar wood (Cryptomeria japonica). The findings are of particular relevance for the heritage conservation and construction sectors, where non-invasive defect detection is paramount. The study establishes a robust framework for assessing the structural integrity of timber by correlating ultrasonic wave velocity reductions with defect size and distribution. Big-sized defects led to more substantial decreases in wave velocity. The study establishes a robust framework for assessing the structural integrity of historical timber by correlating ultrasonic wave velocity reductions with defect size and distribution. This framework has the potential to be applicable to diverse wood species and defect types.

Vehicle structural road noise prediction based on an improved Long Short-Term Memory method

The control of vehicle interior noise has become a critical metric for assessing noise, vibration, and harshness (NVH) in vehicles. During the initial phases of vehicle development, accurately predicting the impact of road noise on interior noise is essential for reducing noise levels and expediting the product development cycle. In recent years, data-driven methods based on machine learning have gained significant attention due to their robust capability in navigating complex data mapping relationships. Notably, surrogate models have demonstrated exceptional performance in this domain. Numerous researchers have integrated diverse intelligent algorithms into the study of vehicle noise, leveraging advantages such as the elimination of precise modeling requirements, extensive solution space exploration, continuous learning from data, and robust algorithmic versatility. However, in NVH engineering applications, data-driven models face inherent limitations, particularly in interpretability and stability. To address these issues, this paper introduces an improved Long Short-Term Memory (LSTM) network that combines knowledge and data. Inspired by the physical information neural network concept, this approach incorporates values calculated through empirical formulas into the neural network as constraints. Comparative assessments with traditional LSTM networks highlight the advantages of this deep learning model. By integrating empirical formulas constraints, the model not only enhances interpretability but also achieves robust generalization with fewer data samples. The proposed method is validated on a specific vehicle model, showing significant improvements in prediction accuracy and efficiency.