Wavenumber-modulated patterns of transmission through one- and two-dimensional gratings on a silicon substrate

Abstract

The phenomenon of filtering in zero-diffraction order is studied for transmission through one- and two-dimensional periodic structures on a silicon wafer. Our study combines FTIR spectrometry in the range 2.5 to 25 µm, a theoretical insight using scalar diffraction theory and a rigorous full-vector simulation. The phenomenon exhibits itself as `bright' and `dark' bands in the spectra of normal transmission through grating samples, which replace each other quasi-periodically with respect to wavenumber, at wavelengths smaller than the grating period. The transmission modulation ratio is high for two-side polished samples, while it drastically degrades in samples with an unpolished backside. It is shown that the scalar theory, which satisfactorily describes the periodicity of the transmission, is incapable of calculating correctly the transmission modulation depth. To fully account for the experimental data numerical simulations using rigorous electromagnetic diffraction theory are carried out. Good agreement between the rigorous theory and experiment, both in the range of the transmission oscillations and in the region of enhanced absorption, is obtained.