Organ pipe radiant modes of periodic micromachined silicon surfaces

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Abstract
In recent studies on small pyroelectric thermal anemometers with roughened surfaces we showed that one of the most widely used heat transfer models1,2 yielded calculated anemometer responses for flow and geometric behaviour that agreed functionally with observations, but were significantly smaller than the experimental data3–5. As the first stage in investigating the role of small structures in heat transfer, we initiated a study of emittance from deep gratings. Here we report measurements at 400 °C of infrared (3 µmλ14 µm), normal, s- and p-polarized spectral emittances of 45 µm deep, near square-wave gratings of heavily phosphorus doped (110) silicon (P content ∼5 × 1019 cm−3). The grating surface repeat scales, Λ, were 10, 14, 18 and 22µm, yielding a range of Λ/λ from 0.14 to 7.33. The s-polarization vector was parallel to the grating slots. Both s and p spectral emittances had pronounced resonant periodicities with a characteristic length of ∼42 µm. A reasonable explanation for this behaviour is the presence of standing waves in the air slots perpendicular to the silicon surface similar to those in an organ pipe. While the resonant amplitude of the s polarization does not depend significantly on Λ it does for the p polarization. No explanation for the Λ dependence of the p polarization is known.