Pyramid Surface Texture & Light Trapping Calculator

Why a Textured Wafer Looks Black

Anisotropic etching of a (100) silicon wafer exposes (111) planes and leaves a field of upright pyramids with 54.74° facets. Light that the first facet reflects is aimed at the facet opposite, so most of it gets a second chance to enter the silicon — and the reflectances multiply.

Two Bounces, Not One

A pyramid does not change the Fresnel coefficients; it changes where the ray goes next. At normal incidence a facet inclined by \(\alpha\) is struck at a local angle of incidence \(\alpha\), and the specularly reflected ray leaves rotated by \(2\alpha\) from vertical. For \(\alpha > 45^\circ\) that ray still points downward and meets the opposing facet, where the local angle is smaller and the interface is more transparent. The escaping fraction is the product over the bounces, which is why a texture that reflects 34% per facet reflects only a few percent overall. Below \(45^\circ\) the once-reflected ray already points out of the groove and the texture buys nothing.

Each \(R(\theta_j)\) is a full transfer-matrix solve of air / SiN\(_x\) / Si at that bounce's local angle, so the anti-reflection coating and the texture are accounted for together rather than multiplied as independent factors. The last term is the first-pass path length in the wafer: refraction at the tilted facet sends the ray obliquely, and the absorber sees more silicon than its thickness. Full light trapping — every subsequent internal bounce, up to the \(4n^2\) Lambertian limit \(\approx 60\) for silicon — needs the ray tracer behind the calculator's pyramid finish.

Interactive design tool

This page includes a live transfer-matrix calculator for this design. Adjust the parameters to recompute spectra, layer stack, and performance figures in the browser, then open the design in the full calculator.