We fabricate and measure graded-index “black silicon” surfaces and find the underlying scaling law governing reflectance. Wet etching (100) silicon in HAuCl4, HF, and H2O2 produces Au nanoparticles that catalyze formation of a network of [100]-oriented nanopores. This network grades the near-surface optical constants and reduces reflectance to below 2% at wavelengths from 300 to 1000 nm. As the density-grade depth increases, reflectance decreases exponentially with a characteristic grade depth of about 1/8 the vacuum wavelength or half the wavelength in Si. Observation of Au nanoparticles at the ends of cylindrical nanopores confirms local catalytic action of moving Au nanoparticles.

We study optical effects and factors limiting performance of our confirmed 16.8% efficiency “black silicon” solar cells. The cells incorporate density-graded nanoporous surface layers made by a one-step nanoparticle-catalyzed etch and reflect less than 3% of the solar spectrum, with no conventional antireflection coating. The cells are limited by recombination in the nanoporous layer which decreases short-wavelength spectral response. The optimum density-graded layer depth is then a compromise between reflectance reduction and recombination loss. Finally, we propose universal design rules for high-efficiency solar cells based on density-graded surfaces.

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