The Effect of Temperature on the Energetic Position of the Fermi Level in Porous Silicon

Keywords: Fermi level, Amorphous silicon, Porous silicon, Bandgap, Density of states, Gaussian distribution, Electrical conductivity

Abstract

This paper presents the theoretical investigation of the temperature-dependent shift of the Fermi level in porous silicon (por-Si). The study is based on the charge-state distribution model originally proposed for hydrogenated amorphous silicon (a-Si:H), with consideration of the unique physical and chemical properties of porous silicon (por-Si). The temperature dependence of the parameters in the charge-state density within the bandgap is accounted for in both simplified and advanced models. For each model, the Fermi-level shift behavior was calculated using numerical methods based on integral-differential equations. The results are presented in graphical form, and the physical mechanisms underlying the Fermi level shift across different temperature ranges are discussed. The conclusions obtained can be applied to explain carrier transport processes, reduce surface recombination, and improve the efficiency of por-Si/c-Si heterostructure-based solar cells.

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References

M. Taguchi, K. Kawamoto, and S. Tsuge, “HIT cells—high-efficiency crystalline Si cells with novel structure,” Prog. Photovolt. Res. Appl. 8(5), 503–513 (2000). https://doi.org/10.1002/1099-159x(200009/10)8:5%3C503::aid-pip347%3E3.0.co;2-g

M.L. Scherff, et al., “Efficiency for amorphous/crystalline heterojunction solar cells on flat p-type silicon wafers,” in: Proceedings of PV in Europe 2002, (Rome, Italy, 2002), pp. 216–219.

B. Liang, X. Chen, X. Wang, H. Yuan, A. Sun, Z. Wang, L. Hu, et al., “Progress in crystalline silicon heterojunction solar cells,” Journal of Materials Chemistry A, 13, 2441–2477 (2025). https://doi.org/10.1039/D4TA06224H

M. Schmidt, L. Korte, A. Laades, R. Stangl, Ch. Schubert, H. Angermann, E. Conrad, and K.V. Maydell, “Physical aspects of a Si:H/c-Si heterojunction solar cells,” Thin Solid Films, 515(19), 7475–7480 (2007). https://doi.org/10.1016/j.tsf.2006.11.087

Yu.V. Kryuchenko, A.V. Sachenko, A.V. Bobyl, V.P. Kostylyov, E.I. Terukov, A.S. Abramov, E.V. Mal’chukova, and I.O. Sokolovskyi, “Simulation of the natural characteristics of vertical a-Si:H/μc-Si:H tandem solar cells. I. General relations,” Semiconductors, 49(5), 683–692 (2015). https://doi.org/10.1134/S1063782615050097

Y.M. Huang, Q.L. Ma, M. Meng, and B.G. Zhai, “Porous silicon based solar cells,” Materials Science Forum, 663–665, 836 840 (2010). https://doi.org/10.4028/www.scientific.net/MSF.663-665.836

H. Kwon, J. Lee, M. Kim, and S. Lee, “Investigation of antireflective porous silicon coating for solar cells,” International Scholarly Research Network ISRN Nanotechnology, 2011, 16409 (2011). https://doi.org/10.5402/2011/716409

H. Lin, M. Yang, X. Ru, G. Wang, S. Yin, F. Peng, C. Hong, et al., “Silicon heterojunction solar cells with up to 26.81% efficiency achieved by electrically optimized nanocrystalline-silicon hole contact layers,” Nature Energy, 8, 789–799 (2023). https://doi.org/10.1038/s41560-023-01255-2

S.P. Zimin, “Classification of electrical properties of porous silicon,” Semiconductors, 34(3), 353–357 (2000). https://doi.org/10.1134/1.1187985

Y. Wang, and D. Wang, “Advances in porous silicon materials for sensing, energy storage, and microelectronics,” Nanomaterials, 16, 257 (2026). https://doi.org/10.3390/nano16040257

Yu.V. Kryuchenko, A.V. Sachenko, A.V. Bobyl, V.P. Kostylyov, P.N. Romanets, I.O. Sokolovskyi, A.I. Shkrebtii, et al., “Efficiency a-Si:H solar cell. Detailed theory,” Semiconductor Physics, Quantum Electronics & Optoelectronics, 15(2), 91-116 (2012). https://doi.org/10.15407/spqeo15.02.091

M.J. Powell, and S.C. Deane, “Improved defect-pool model for charged defects in amorphous silicon,” Physical Review B, 48(15), 10815–10827 (1993). https://doi.org/10.1103/PhysRevB.48.10815

C. Longeaud, J.A. Schmidt, and R.R. Koropecki, “Determination of semiconductor band gap state parameters from photoconductivity measurements. II. Experimental results,” Physical Review B, 73(23), 235317 (2006). https://doi.org/10.1103/PhysRevB.73.235317

N. Wang, F. Meng, L. Zhang, Z. Liu, and W. Liu, “Light soaking of hydrogenated amorphous silicon: a short review,” Carbon Neutrality, 3, 18 (2024). https://doi.org/10.1007/s43979-024-00093-9

S. De Wolf, A. Descoeudres, Z.C. Holman, and C. Ballif, “High-efficiency silicon heterojunction solar cells: A review,” Green, 2, 7–24 (2012). https://doi.org/10.1515/green-2011-0018

H. Fritzsche, “Development in understanding and controlling the Staebler–Wronski effect in a-Si:H,” Annual Review of Materials Research, 31, 47–79 (2001). https://doi.org/10.1146/annurev.matsci.31.1.47

Published
2026-06-10
Cited
How to Cite
Babakhodzhaev, U., Usmanov, M., Vokhobjonov, I., & Shamsiddinova, S. (2026). The Effect of Temperature on the Energetic Position of the Fermi Level in Porous Silicon. East European Journal of Physics, (2), 187-190. https://doi.org/10.26565/2312-4334-2026-2-19