Dynamical diffraction and band structure analysis application to the design of vapor sensors based on porous silicon microcavities

Two different original theoretical approach for the analysis of vapour sensors based on a porous silicon optical microcavity are presented. The devices under analysis are based on a cavity with a high porosity layer of optical thickness lambdaB/2, where lambdaB is the Bragg resonant wavelength. This is enclosed between two distributed Bragg reflectors with seven periods made of alternate low and high porosity layers. When such a porous silicon microcavity is exposed to chemical vapours, a marked red-shift of its resonant peak, ascribed to capillary condensation of vapour in the pores, is observed. According to the first approach, the features of porous silicon microcavities are analyzed looking at the correspondent band structure. In particular, the microcavity structure is viewed as a 1-D photonic crystal with a defect of optical thickness lambdaB/2 giving rise to a narrow resonant transmittance peak at lambdaB in a wide transmittivity stop-band. We then compare the derivation of the band structure with an original approach based on the dynamical diffraction theory, the same widely used in x-ray diffraction. Using this approach we get an analytical expression of the reflectivity, giving the position but also the shape of the resonant peak.