Abstract
This study presents an analytical model of the reflectance of flat and textured silicon substrates. The model was used to study the reflection behavior of textured silicon surfaces under non-normal incidence. By characterizing the incident light and facets of the silicon wafer with vector geometry, dot products and Phong’s reflection model (https://cs.oberlin.edu/~bob/cs357.08/VectorGeometry/VectorGeometry.pdf) were used to determine the reflection angles between incident light rays and pyramidal facets. The possible optical interactions are considered for a wide range of pyramidal geometries and light incidence angles that are relevant to the exposure of textured silicon surfaces to incident sunlight. Furthermore, the model was used to investigate the possibility of secondary reflection, for the full range of incidence angles to the substrate. The textured silicon surfaces were found to reduce the reflection angles more effectively than flat substrates at lower angles of incidence. Secondary reflection was also found to be experienced or guaranteed, for all pyramid heights, when the angle of incidence to the substrate was less than 19.4°. The predictions are validated with experimental measurements of reflectance from (001)-textured silicon surfaces. The implications of the results are then discussed for the development of micropyramids for improved photoconversion in silicon solar cells.
Similar content being viewed by others
References
H. Chung, C. Chen, and H. Chu: Analysis of pyramidal surface texturization of silicon solar cells by molecular dynamics simulations. Int. J. Photoenergy 2008, 1–6 (2008).
J.M. Gee, R. Gordon, and H.F. Laing: Optimization of textured-dielectric coatings for crystalline-silicon solar cells. In Proceedings of the 25th IEEE Photovoltaic Specialists Conference, Washington DC, 1996; pp. 733–736.
J.D. Hylton, A.R. Burgers, and W.C. Sinke: Alkaline etching for reflectance reduction in multicrystalline silicon solar cells. J. Electrochem. Soc. 151 (6), 408–427 (2004).
C.R. Tellier and A. Brahim-Bounab: Anisotropic etching of silicon crystals in KOH solution. J. Mater. Sci. 29 (22), 5953–5971 (1994).
M. Shikida, K. Sato, K. Tokoro, and D. Uchikawa: Differences in anisotropic etching properties of KOH and TMAH solution. Sens. Actuators, A 80, 179–188 (1999).
H. Seidal, L. Csepregi, A. Henberger, and H. Baumgartel: Anisotropic etching of crystalline silicon in alkaline solutions. J. Electrochem. Soc. 137 (11), 116–125 (1990).
P. Kilpinen, E. Haimi, and V.K. Lindroos: The etch rate variations of p+ silicon wafers in aqueous KOH solutions as a function of processing conditions. MRS Proc. 605, 293 (1999). doi:10.1557/PROC-605-293.
H. Seidal, L. Csepregi, A. Henberger, and H. Baumgartel: Anisotropic etching of crystalline silicon in alkaline solution: Orientation dependence and behavior of passivation layers. J. Electrochem. Soc. 137 (11), 612–626 (1996).
K. Sato, M. Shikida, T. Yamashiro, M. Tsunekawa, and S. Ito: Roughening of single-crystal silicon surface etched by KOH water solutions. Sens. Actuators, A 73, 122–130 (1999).
L.E. Kassel: KOH-etch related defects on processed silicon wafers. MRS Proc. 259, 187 (1992). doi:10.1557/PROC-259-187.
C. Yang, P. Chen, Y. Chiou, and R. Lee: Effects of mechanical agitation and surfactant additive on silicon anisotropic etching in alkaline KOH solution. Sens. Actuators, A 119, 263–270 (2005).
I. Zubel and M. Kramkowska: The effect of isopropyl alcohol on etching rate and roughness of (100) Si surface etched in KOH and TMAH solutions. Sens. Actuators, A 93, 138–147 (2001).
V. Moroz, J. Huang, K. Wijekoon, and D. Tanner: Experimental and theoretical analysis of the optical behavior of textured silicon wafers. In Proceedings of the 37th IEEE Photovoltaic Specialists Conference. (IEEE, Seattle, WA, 2011); pp. 2900–2905.
X. Zhu, L. Wang, and D. Yang: Investigations of random pyramid texture on the surface of single-crystalline silicon for solar cells. In Proceedings of the ISES Solar World Congress, Beijing, China, (Springer-Verlag, Berlin Heidelberg, Germany, 2007); pp. 1126–1130.
P. Campbell and M.A. Green: Light trapping properties of pyramidally textured surfaces. J. Appl. Phys. 62 (1), 243–249 (1987).
S.C. Baker-Finch and K.R. McIntosh: Reflection distributions of textured monocrystalline silicon: Implications for silicon solar cells. Prog. Photovoltaics Res. Appl. 21 (5), 960–971 (2013). DOI: 10.1002/pip.2186.
S.C. Baker-Finch and K.R. McIntosh: Reflection of normally incident light from silicon solar cells with pyramidal texture. Prog. Photovoltaics Res. Appl. 19 (4), 406–416 (2011). DOI: 10.1002/pip.1050.
W.C. O’Mara, R.B. Herring, and L.P. Hunt: Handbook of Semiconductor Silicon Technology (William Andrew Inc., Norwich, NY, 1990); pp. 349–352.
D.L. King and M.E. Buck: Experimental optimization of an anisotropic etching process for random texturization of silicon solar cells. In Proceedings of the 22nd IEEE Photovoltaic Specialists Conference, 1991; pp. 303–308.
A. Parretta, A. Sarno, P. Tortora, H. Yakubu, P. Maddalena, J. Zhao, and A. Wang: Angle dependent reflectance measurements on photovoltaic materials and solar cells. Opt. Commun. 172 (1–6), 139–151 (1999).
J.A. Dziuban: Bonding in Microsystem Technology (Springer, Science & Business Media, 2007); p. 16.
S.C. Baker-Finch: Rules and tools for understanding, modelling and designing textured silicon solar cells. Ph.D. Thesis, Australia National University, 2012.
B. Geitz: Vector Geometry for Computer Graphics. e-Publishing, Part III (2007); pp. 15–16. [Online]. Available: https://cs.oberlin.edu/~bob/cs357.08/VectorGeometry/VectorGeometry.pdf (Accessed August 25, 2013).
K. Wijekoon, T. Weidman, S. Paak, and K. MacWilliams: Production ready novel texture etching process for fabrication of single crystalline silicon solar cells. In Proceedings of the 35th IEEE Photovoltaic Specialists Conference, Honolulu, HI, 2010; pp. 3635–3641.
P.M.M. Bressers, J.J. Kelly, J.G.E. Gardeniers, and M. Elwenspoek: Surface morphology of p-type (100) silicon etched in aqueous alkaline solution. J. Electrochem. Soc. 143 (5), 1744–1750 (1996).
C.J. Wu, P.J. Wei, and J.F. Lin: The reflectivity of an etched silicon surface with pyramids: I. Theoretical model and its predictions. J. Micromech. Microeng. 19, 1–7 (2009).
P.K. Singh, R. Kumar, M. Lal, S.N. Singh, and B.K. Das: Effectiveness of anisotropic etching of silicon in aqueous alkaline solution. Sol. Energy Mater. Sol. Cells 70, 102–113 (2001).
F.L. Pedrotti, L.S. Pedrotti, and L.M. Pedrotti: Introduction to Optics, 3rd ed. (Pearson Prentice Hall, Upper Saddle River, NJ, 2007).
A. Hamel and A. Chibani: Characterization of texture surface for solar cells. J. Appl. Phys. 10 (3), 231–234 (2010).
Z. Xi, D. Yang, W. Dan, C. Jun, X. Li, and D. Que: Texturization of cast multicrystalline silicon for solar cells. Semicond. Sci. Technol. 19 (3), 485–489 (2004).
C. Sethi, V.K. Anand, K. Walia, and S.C. Sood: Optimization of surface reflectance for alkaline textured monocrystalline silicon solar cell. IJCSCT 5 (1), 785–788 (2012).
K.R. McIntosh and S.C. Baker-Finch: OPAL 2: Rapid optical simulation of silicon solar cells. In Proceedings of the 38th IEEE Photovoltaic Specialists Conference, Austin, TX, 2012; pp. 265–271. DOI: https://doi.org/10.1109/PVSC.2012.6317616.
S.C. Baker-Finch and K.R. McIntosh: A freeware program for precise optical analysis of the front surface of a solar cell. In Proceedings of the 35th IEEE Photovoltaic Specialists Conference, Honolulu, HI, 2010; pp. 2184–2187. DOI: https://doi.org/10.1109/PVSC.2010.5616132.
ACKNOWLEDGMENTS
The authors are grateful to thank Prof. Oleg Yordanov, Bruno Dandogbessi, and Uche Opara for useful scientific discussions. Appreciation is also extended to the World Bank STEP-B Program, the World Bank African Centers of Excellence Program, the African Development Bank, the African Capacity Building Foundation (ACBF), and the Nelson Mandela Institute for financial support.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Fashina, A.A., Kana, M.G.Z. & Soboyejo, W.O. Optical reflectance of alkali-textured silicon wafers with pyramidal facets: 2D analytical model. Journal of Materials Research 30, 904–913 (2015). https://doi.org/10.1557/jmr.2015.70
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1557/jmr.2015.70