Improved Interference Filter Structures Made of Porous Silicon
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measured under an incidence angle of 80 using s-polarized light. From the reflectance spectra of single porous layers the effective dielectric function of PS was deduced by a fitting procedure (for details see [13]). The etch rate as a function of the anodization current density was determined by a thickness measurement of the PS layer using a scanning electron microscope (SEM). RESULTS AND DISCUSSION For the formation of interference filters the optical thickness do = n •d (n refractive index, d geometrical thickness) must be known. We have investigated both parameters n and d as a function of the anodization current density for single layers on p and p' doped substrates. The refractive indices n were determined by a fit of the reflectance spectra in the range from 9000 up to 25000 cm 1 using effective medium theory. A typical fit is shown in Fig. 1, where the high accuracy of the fit can be seen. For simplicity in Fig. 2a the effective refractive indices are shown only for 12000 cm-1 for both doping levels. The etch rate of these samples determined by SEM is shown in Fig. 2b. 0.30 0.25
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Measurement Simulation
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Wavenumber (cm-') Fig. 1: Fit and measurement of a reflectance spectrum. The porosity of the porous layer on the p-doped substrate was about 71%, the thickness 1pm. For the fit effective medium theory was used. Using these results Bragg reflectors can be formed very easily: Each layer in the Bragg reflector must be of the optical thickness of a quarter of the wavelength that should be reflected. The high refractive layer H corresponds to the lower porosity, the low refractive layer to the high porosity. The computer controlled etch process makes possible the formation of different Bragg reflectors in the visible and infrared range (Fig. 3). For these filters the stack of [HL] layers was repeated 20 times. Disadvantages of the presented Bragg filters are the sidelobes of the Braggreflectors and additional second order peaks. These can be avoided by using more complex filter structures: In contrast to other dielectric filter structures gradual variations of the refractive index with depth can be realized very easily with porous silicon: Knowing the relation of anodization current density and refractive index (see Fig. 2) the continuous variation of the refractive index 644
with depth could be realized by a. continuous variation of the current density. These types of filters are the so called rugate filters. 2.1
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