Reflection Coefficient Calculation of a Structure Including a Porous Silicon Layer with Transfer Matrix Method and FDTD

Abstract

Porous silicon is an important material for a variety of application area such as anti-reflective coating for solar cells. Today, solar cell market is mostly dominated by silicon based solar cells. Porous silicon thin films are easy to fabricate and it is compatible with silicon technology. Designing porous silicon anti-reflective coating layers is a critical issue to enhance silicon based solar cell performance. There are several methods to calculate reflection coefficient of porous silicon thin layers. In this study, transfer matrix method and finite-difference time-domain method are used to calculate reflection coefficient of porous silicon thin layers. Because finite-difference time-domain method gives more accurate results, the results obtained with finite-difference time-domain method are used to control the results obtained with transfer matrix method. In transfer matrix method, refractive indices of the porous silicon layers are calculated with Bruggeman effective medium approximation.

Keywords

• Anti-Reflective Coating
• Solar Cell
• Reflection Coefficient
• TMM
• FDTD.

References

1. Basu, S. (Ed.). (2011). Crystalline Silicon: Properties and Uses. BoD–Books on Demand.
2. Dubey, R. S., & Gautam, D. K. (2011). Porous silicon layers prepared by electrochemical etching for application in silicon thin film solar cells. Superlattices and Microstructures, 50(3), 269-276.
3. Karbassian, F. (2018). Porous silicon. In Porosity-Process, Technologies and Applications. IntechOpen.
4. Zhao, M., Balachandran, R., Allred, J., & Keswani, M. (2015). Synthesis of porous silicon through interfacial reactions and measurement of its electrochemical response using cyclic voltammetry. RSC advances, 5(96), 79157-79163.
5. Wilkins, M. M., Boucherif, A., Beal, R., Haysom, J. E., Wheeldon, J. F., Aimez, V., ... & Hinzer, K. (2013). Multijunction solar cell designs using silicon bottom subcell and porous silicon compliant membrane. IEEE Journal of Photovoltaics, 3(3), 1125-1131.
6. Ariza-Flores, D., Pérez-Huerta, J. S., Kumar, Y., Encinas, A., & Agarwal, V. (2014). Design and optimization of antireflecting coatings from nanostructured porous silicon dielectric multilayers. Solar energy materials and solar cells, 123, 144-149.
7. Jimenéz-Vivanco, M. R., García, G., Carrillo, J., Morales-Morales, F., Coyopol, A., Gracia, M., ... & Lugo, J. E. (2020). Porous Si-SiO2 UV Microcavities to modulate the responsivity of a broadband photodetector. Nanomaterials, 10(2), 222.
8. Deinega, A. V., Konistyapina, I. V., Bogdanova, M. V., Valuev, I. A., Lozovik, Y. E., & Potapkin, B. V. (2010). Optimization of an anti-reflective layer of solar panels based on ab initio calculations. Russian Physics Journal, 52(11), 1128.

9. Min-Dianey, K. A. A., Zhang, H. C., Brohi, A. A., Yu, H., & Xia, X. (2018). Optical spectra of composite silver-porous silicon (Ag-pSi) nanostructure based periodical lattice. Superlattices and Microstructures, 115, 168-176.
10. Najar, A., Al-Jabr, A. A., Slimane, A. B., Alsunaidi, M. A., Ng, T. K., Ooi, B. S., ... & Anjum, D. H. (2013, April). Effective antireflection properties of porous silicon nanowires for photovoltaic applications. In 2013 Saudi International Electronics, Communications and Photonics Conference (pp. 1-4). IEEE.
11. Burham, N., Hamzah, A. A., & Majlis, B. Y. (2017). Self-adjusting electrochemical etching technique for producing nanoporous silicon membrane. New Research on Silicon-Structure, Properties, Technology.
12. Yaakob, S., Bakar, M. A., Ismail, J., Bakar, N. H. H. A., & Ibrahim, K. (2012). The formation and morphology of highly doped N-type porous silicon: effect of short etching time at high current density and evidence of simultaneous chemical and electrochemical dissolutions. J. Phys. Sci, 23(2), 17-31.
13. Vázsonyi, É., Battistig, G., Horváth, Z. E., Fried, M., Kádár, G., Pászti, F., ... & Poortmans, J. (2000). Pore Propagation Directions in P+ Porous Silicon. Journal of Porous Materials, 7(1), 57-61.
14. Khardani, M., Bouaïcha, M., & Bessaïs, B. (2007). Bruggeman effective medium approach for modelling optical properties of porous silicon: comparison with experiment. physica status solidi c, 4(6), 1986-1990.
15. Birge, J. R., & Kärtner, F. X. (2006). Efficient analytic computation of dispersion from multilayer structures. Applied optics, 45(7), 1478-1483.
16. Pérez, E. X. (2008). Design, fabrication and characterization of porous silicon multilayer optical devices. Universitat Rovira i Virgili.
17. Hossain, M. F., & Noushin, T. (2016, December). Sensitivity enhancement of porous silicon waveguide sensor using graphene by FDTD with Lumerical software. In 2016 2nd International Conference on Electrical, Computer & Telecommunication Engineering (ICECTE) (pp. 1-4). IEEE.
18. Pickering, T., Shanks, K., & Sundaram, S. (2021). Modelling technique and analysis of porous anti-reflective coatings for reducing wide angle reflectance of thin-film solar cells. Journal of Optics, 23(2), 025901.
19. Elsherbeni, A. Z., & Demir, V. (2009). The finite-difference time-domain method for electromagnetics with MATLAB simulations. Raleigh, NC: SciTech Pub.