Optical reflectance of alkali-textured silicon wafers with pyramidal facets: 2D analytical model
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Martiale Gaetan Zebaze Kana Physics Advanced Laboratory, Sheda Science and Technology Complex, PMB 186, Garki, Abuja, Nigeria; and Department of Materials Science and Engineering, Kwara State University, PMB 1530, Malate, Nigeria
Winston Oluwole Soboyejoa) Department of Theoretical and Applied Physics, African University of Science and Technology, PMB 681, Garki, Abuja, Nigeria; Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, USA; and Princeton Institute of Science and Technology of Materials (PRISM), Bowen Hall, Princeton, New Jersey 08544, USA (Received 19 September 2014; accepted 17 February 2015)
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.
I. INTRODUCTION
Surface texturing in solar-based devices is a geometric method of reducing reflection in crystalline silicon substrates.1 It is often achieved by the anisotropic etching of (100)-oriented silicon substrates into square-based pyramidal structures.2 The pyramidal structures are formed by the alkaline etching of (100)-oriented silicon surfaces along crystallographic orientations that expose the {111} planes.3 Potassium hydroxide (KOH) and additive isopropyl alcohol (IPA) are two of the most common alkaline solutions that are used for anisotropic etching of silicon surfaces.4–12 The sizes and uniformities of the resulting pyramids are also traceable to IPA, which acts as a wetting agent, when added to alkaline etchants.11 Furthermore, the pyramidal sizes, heights, and base widths are usually on the order of several micrometers.12,13 Contributing Editor: Winston Schoenfeld a) Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/jmr.2015.70 904
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