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Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 6, Iss. 8 — Aug. 26, 2011
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Structural considerations on multistopband mesoporous silicon rugate filters prepared for gas sensing purposes

Tero Jalkanen, Jarno Salonen, Vicente Torres-Costa, Kazuhiro Fukami, Tetsuo Sakka, and Yukio H. Ogata  »View Author Affiliations


Optics Express, Vol. 19, Issue 14, pp. 13291-13305 (2011)
http://dx.doi.org/10.1364/OE.19.013291


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Abstract

Different designs for producing multiple stopband mesoporous silicon rugate filters via electrochemical anodization are compared. The effects of light absorption and dispersion to visible range filter design are investigated. Thermal oxidation is applied for passivating the chemically reactive porous silicon surface, and the response of the passivated structures to ethanol vapor is examined. Differences in gas sensing properties for the various designs are evaluated and possible reasons for the observed differences are discussed. Methods for sidelobe suppression in multipeak filters are discussed and demonstrated, and their effects in gas sensing applications are estimated.

© 2011 OSA

1. Introduction

Optical properties of electrochemically prepared porous silicon (PS) have received a lot of attention since 1990, when Canham [1

1. L. T. Canham, “Silicon quantum wire array fabricated by electrochemical and chemical dissolution of wafers,” Appl. Phys. Lett. 57, 1046–1048 (1990). [CrossRef]

] first reported his findings on visible photoluminescence at room temperature. The discovery was soon followed by reports on electroluminescence [2

2. A. Halimaoui, C. Oules, G. Bomchil, A. Bsiesy, F. Gaspard, R. Herino, M. Ligeon, and F. Muller, “Electroluminescence in the visible range during anodic oxidation of porous silicon films,” Appl. Phys. Lett. 59, 304–306 (1991). [CrossRef]

, 3

3. N. Koshida and H. Koyama, “Visible electroluminescence from porous silicon,” Appl. Phys. Lett. 60, 347–349 (1992). [CrossRef]

], which gave even more promise for using PS in optoelectronic applications. In addition, refractive index of PS had been found dependent on the porosity [4

4. C. Pickering, M. I. J. Beale, D. J. Robbins, P. J. Pearson, and R. Greef, “Optical properties of porous silicon films,” Thin Solid Films 125, 157–163 (1985). [CrossRef]

], which allowed the research to expand to using the material in passive optical components. Optical interference filters based on PS were initially reported in the first half of the 1990’s [5

5. G. Vincent, “Optical properties of porous silicon superlattices,” Appl. Phys. Lett. 64, 2367–2369 (1994). [CrossRef]

, 6

6. M. G. Berger, C. Dieker, M. Thönissen, L. Vescan, H. Lüth, H. Münder, W. Theiss, M. Wernke, and P. Grosse, “Porosity superlattices: a new class of Si heterostructures,” J. Phys. D. 27, 1333–1336 (1994). [CrossRef]

]. The Bragg reflector type filters were soon followed by more complex rugate filters [7

7. M. G. Berger, R. Arens-Fischer, M. Thönissen, M. Krüger, S. Billat, H. Lüth, S. Hilbrich, W. Theiss, and P. Grosse, “Dielectric filters made of PS: advanced performance by oxidation and new layer structures,” Thin Solid Films 297, 237–240 (1997). [CrossRef]

]. In general, PS has been investigated for a wide range of different optical applications [8

8. V. Torres-Costa and R. J. Martín-Palma, “Application of nanostructured porous silicon in the field of optics. A review,” J. Mater. Sci. 45, 2823–2838 (2010). [CrossRef]

].

Large internal surface area of PS makes the material also an attractive choise for gas sensing applications. Some of the first proposed approaches for PS based gas sensing utilized gas adsorption induced changes in electrical [9

9. I. Schechter, M. Ben-Chorin, and A. Kux, “Gas sensing properties of porous silicon,” Anal. Chem. 67, 3727–3732 (1995). [CrossRef]

] and optical [10

10. R. B. Bjorklund, S. Zangooie, and H. Arwin, “Color changes in thin porous silicon films caused by vapor exposure,” Appl. Phys. Lett. 69, 3001–3003 (1996). [CrossRef]

] properties of the material. The concept of using PS optical interference filters for gas sensing was first introduced in 1999 [11

11. P. A. Snow, E. K. Squire, P. St. J. Russell, and L. T. Canham, “Vapor sensing using the optical properties of porous silicon Bragg mirrors,” J. Appl. Phys. 86, 1781–1784 (1999). [CrossRef]

]. Since then research in this area has expanded and several reports on different sensing scenarios have been published [12

12. M. Arroyo-Hernández, R. J. Martín-Palma, V. Torres-Costa, and J. M. Martínez-Duart, “Porous silicon optical filters for biosensing applications,” J. Non-Cryst. Solids 352, 2457–2460 (2006). [CrossRef]

15

15. T. Jalkanen, V. Torres-Costa, J. Salonen, M. Bjorkqvist, E. Mäkilä, J. M. Martínez-Duart, and V.-P. Lehto, “Optical gas sensing properties of thermally hydrocarbonized porous silicon Bragg reflectors,” Opt. Express 17, 5446–5456 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-7-5446. [CrossRef] [PubMed]

]. However, filters displaying just a single reflective band suffer from poor selectivity which may lead to e.g. false positives in sensing applications. The use of PS filters displaying multiple reflective bands has been suggested as a partial remedy for this problem [16

16. A. M. Ruminski, M. M. Moore, and M. J. Sailor, “Humidity-compensating sensor for volatile organic compounds using stacked porous silicon photonic crystals,” Adv. Funct. Mater. 18, 3418–3426 (2008). [CrossRef]

].

Rugate filters displaying multiple reflectance bands have been theoretically predicted at least for some 20 years ago [17

17. B. G. Bovard, “Rugate filter theory: an overview,” Appl. Opt. 32, 5427–5442 (1993). [CrossRef] [PubMed]

]. The first multistopband rugate filters based on PS were demonstrated some years later [7

7. M. G. Berger, R. Arens-Fischer, M. Thönissen, M. Krüger, S. Billat, H. Lüth, S. Hilbrich, W. Theiss, and P. Grosse, “Dielectric filters made of PS: advanced performance by oxidation and new layer structures,” Thin Solid Films 297, 237–240 (1997). [CrossRef]

]. Multipeak rugate filters based on PS have been demonstrated by several research groups since then [14

14. M. S. Salem, M. J. Sailor, K. Fukami, T. Sakka, and Y. H. Ogata, “Sensitivity of porous silicon rugate filters for chemical vapor detection,” J. Appl. Phys. 103, 083516 (2008). [CrossRef]

,16

16. A. M. Ruminski, M. M. Moore, and M. J. Sailor, “Humidity-compensating sensor for volatile organic compounds using stacked porous silicon photonic crystals,” Adv. Funct. Mater. 18, 3418–3426 (2008). [CrossRef]

,18

18. F. Cunin, T. A. Schmedake, J. R. Link, Y. Y. Li, J. Koh, S. N. Bhatia, and M. J. Sailor, “Biomolecular screening with encoded porous-silicon photonic crystals,” Nat. Mater. 1, 39–41 (2002). [CrossRef]

21

21. N. Ishikura, M. Fujii, K. Nishida, S. Hayashi, and J. Diener, “Dichroic rugate filters based on birefringent porous silicon,” Opt. Express 16, 15531–15539 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-20-15531. [CrossRef] [PubMed]

]. Proposed applications include e.g. biomolecular screening [18

18. F. Cunin, T. A. Schmedake, J. R. Link, Y. Y. Li, J. Koh, S. N. Bhatia, and M. J. Sailor, “Biomolecular screening with encoded porous-silicon photonic crystals,” Nat. Mater. 1, 39–41 (2002). [CrossRef]

], and gas sensing [14

14. M. S. Salem, M. J. Sailor, K. Fukami, T. Sakka, and Y. H. Ogata, “Sensitivity of porous silicon rugate filters for chemical vapor detection,” J. Appl. Phys. 103, 083516 (2008). [CrossRef]

, 16

16. A. M. Ruminski, M. M. Moore, and M. J. Sailor, “Humidity-compensating sensor for volatile organic compounds using stacked porous silicon photonic crystals,” Adv. Funct. Mater. 18, 3418–3426 (2008). [CrossRef]

]. However, a comprehensive study comparing the different multipeak filter designs in gas sensing has not been reported.

In the current study, different approaches for producing PS rugate filters displaying multiple reflective peaks are demonstrated and compared, and the resulting structural differences are discussed. The reactive sample surfaces are stabilized with thermal oxidation, and sample responses to ethanol vapor are measured. Differences in sensitivity and response time between different samples are analyzed. Effects of refractive index matching layers [22

22. W. H. Southwell and R. L. Hall, “Rugate filter sidelobe suppression using quintic and rugated quintic matching layers,” Appl. Opt. 28, 2949–2951 (1989). [CrossRef] [PubMed]

] and apodization [23

23. W. H. Southwell, “Using apodization functions to reduce sidelobes in rugate filters,” Appl. Opt. 28, 5091–5094 (1989). [CrossRef] [PubMed]

, 24

24. H. A. Abu-Safia, A. I. Al-Sharif, and I. O. Abu Aljarayesh, “Rugate filter sidelobe suppression using half-apodization,” Appl. Opt. 32, 4831–4835 (1993). [CrossRef] [PubMed]

] to the gas sensing properties of different filter types are also discussed.

2. Experimental

2.1. Sample preparation

Samples were prepared by electrochemical anodization on boron doped p + -type silicon substrate with a 〈100〉 crystal orientation and 0.01-0.02 Ωcm resistivity. The substrate was placed in a teflon cell which left an area of 0.79 cm2 of the substrate surface exposed. A copper plate was placed under the substrate, and used as a current collector for the working electrode. This was preceded by application of InGa alloy on the backside of the substrate in order to ensure an ohmic contact. Electrolyte solution composed of hydrofluoric acid (46-48 wt %) and ethanol in 1:1.7 volumetric ratio was used. The working electrode and a platinum counter electrode were connected to a programmable current source (Keithley 6221), which was used for controlling the anodization process. Several anodization current profiles, with varying current density values below 126.6 mA/cm2, were used to create a variety of porous silicon rugate filters which displayed reflective peaks in the visible range.

After the anodization process, the samples were rinsed with ultrapure water (Millipore, Milli-Q Gradient) and ethanol, and carefully dried with argon gas. In order to stabilize the samples for the gas sensing experiments, thermal oxidation was employed. The dried samples were inserted to a quartz tube, which was placed in a furnace set to 600 °C. 90 minute thermal oxidation treatment was conducted under ambient atmospheric conditions.

2.2. Sample characterization

Reflectance measurements were conducted with a Ocean Optics HR4000CG-UV-NIR spectrometer, coupled to a tungsten halogen light source (LS-1, Ocean Optics). A bifurcated optical fiber was used for illuminating the sample, at normal angle of incidence, and collecting the reflected light to the spectrometer.

Scanning electron microscopy (JEOL JSM-6500FE and Carl Zeiss STM Ultra 55 FE-SEM) was employed for visual examination of single layer and rugate filter structures. The real and imaginary part of the optical refractive index for PS single layers produced with a 88.6 mA/cm2 etching current density, were determined based on sample reflectance spectra, using a self-adaptive evolutionary algorithm designed specifically for this purpose [25

25. V. Torres-Costa, R. J. Martín-Palma, and J. M. Martínez-Duart, “Optical constants of porous silicon films and multilayers determined by genetic algorithms,” J. Appl. Phys. 96, 4197–4203 (2004). [CrossRef]

].

Fourier transform infrared (FTIR) spectrometer (Jasco, FT/IR-460 Plus) was used for confirming the chemical composition of the thermally oxidized PS sample surface.

2.3. Gas sensing set-up

A nitrogen gas line was connected to an atmospheric chamber equipped with an optical window. The total nitrogen flow to the chamber was kept constant at 250 ml/min. Ethanol concentration inside the chamber was controlled by diverting a part of the nitrogen carrier flow through a bubbling chamber filled with liquid phase ethanol. PS rugate filter response to gas concentration inside the atmospheric chamber was recorded through the optical window with a spectrometer (Ocean Optics). Ethanol gas concentrations for different carrier flow ratios were determined with FTIR measurements using the Beer-Lambert law.

3. Results and Discussion

3.1. Preparation of single-line PS rugate filters

Rugate filters can be defined as structures that present a continuous variation of the refractive index perpendicular to the sample surface [17

17. B. G. Bovard, “Rugate filter theory: an overview,” Appl. Opt. 32, 5427–5442 (1993). [CrossRef] [PubMed]

]. In the case of a so-called single-line rugate filter, exhibiting one reflective peak, a refractive index profile consisting of a sine wave is applied. For PS [20

20. E. Lorenzo, C. J. Oton, N. E. Capuj, M. Ghulinyan, D. Navarro-Urrios, Z. Gaburro, and L. Pavesi, “Porous silicon-based rugate filters,” Appl. Opt. 44, 5415–5421 (2005). [CrossRef] [PubMed]

], a good approximation can be achieved by alternating the anodization current density sinusoidally. When the porosity differences are small, this approximately leads to a sinusoidal variation of the PS refractive index as a function of depth. For p-type silicon and HF:ethanol based electrolyte, PS formation rate for higher current densities is somewhat higher than for lower current densities. As a result, slight deviation from the ideal sinusoidal refractive index profile can be observed. This can be accounted for by making appropriate corrections to the sinusoidal current form [26

26. M. S. Salem, M. J. Sailor, T. Sakka, and Y. H. Ogata, “Electrochemical preparation of a rugate filter in silicon and its deviation from the ideal structure,” J. Appl. Phys. 101, 063503 (2007). [CrossRef]

].

Figure 1 shows the measured reflectance spectra for two PS rugate filters prepared with a sinusoidal current density profile oscillating between 49.4 and 89.9 mA/cm2. Sine wave periodicities were 3 s (Fig. 1 (a)) and 5 s (Fig. 1 (b)) with the total anodization times being 180 s and 200 s, respectively. From Fig. 1 one can see that by increasing the duration of the sinusoidal period, the reflective peak can be shifted to longer wavelengths. This is accompanied by an increase in the width of the stopband. The reflective band width Δλ is connected to the optical admittance ratio by the following equation [17

17. B. G. Bovard, “Rugate filter theory: an overview,” Appl. Opt. 32, 5427–5442 (1993). [CrossRef] [PubMed]

]:
Δλλ0=12lnηMηm,
(1)
where λ 0 is the resonant wavelength, and η M and η m are the maximum and minimum optical admittances, respectively. It is worth noting that optical admittance is directly proportional to the complex optical refractive index [27

27. H. A. MacLeod, Thin-film Optical Filters, 2nd. ed. (Adam Hilger Ltd., 1986). [CrossRef]

]. As the anodization current value determines the refractive index of the formed PS layer, the widening of the reflective band can be accounted for by lowering the amplitude of the sinusoidal current profile used for anodization accordingly.

Fig. 1 Reflectance spectra for two PS rugate filters prepared with a sinusoidal anodization current oscillating between 49.4 and 89.9 mA/cm2. The period durations were (a) 3 s and (b) 5 s, with the total preparation times being 180 and 200 s, respectively.

3.2. Dual-peak filters

Fabrication of rugate filters displaying several reflective peaks can be accomplished by at least two distinct methods. Either placing filters on top of each other, i.e. stacking, or by placing them in superposition, i.e. using a refractive index profile that is a linear combination of several sinusoidal waves [17

17. B. G. Bovard, “Rugate filter theory: an overview,” Appl. Opt. 32, 5427–5442 (1993). [CrossRef] [PubMed]

, 28

28. M. Kildemo, O. Hunderi, and B. Drévillon, “Approximation of reflection coefficients for rapid real-time calculation of inhomogenous films,” J. Opt. Soc. Am. A 14, 931–939 (1997). [CrossRef]

]. In this section, a thorough comparison between the two methods will be presented.

Perhaps the more intuitive and straightforward method for obtaining a dual-peak filter is to prepare two single-line rugate filters on top of each other. These type of filters have been produced from PS by different research groups [14

14. M. S. Salem, M. J. Sailor, K. Fukami, T. Sakka, and Y. H. Ogata, “Sensitivity of porous silicon rugate filters for chemical vapor detection,” J. Appl. Phys. 103, 083516 (2008). [CrossRef]

, 16

16. A. M. Ruminski, M. M. Moore, and M. J. Sailor, “Humidity-compensating sensor for volatile organic compounds using stacked porous silicon photonic crystals,” Adv. Funct. Mater. 18, 3418–3426 (2008). [CrossRef]

, 18

18. F. Cunin, T. A. Schmedake, J. R. Link, Y. Y. Li, J. Koh, S. N. Bhatia, and M. J. Sailor, “Biomolecular screening with encoded porous-silicon photonic crystals,” Nat. Mater. 1, 39–41 (2002). [CrossRef]

]. In practice, these structures are formed by first applying a sinusoidal anodization current to produce a single-line PS rugate filter for a certain wavelength. This is followed by generating a second filter displaying a reflective peak in a differing wavelength range, below the first filter. Figure 2 compares the reflectance spectra of two stacked dual-peak PS rugate filters. Figures 2 (a) and (b) display the measured reflectance spectra for stacked rugate samples, which were formed by anodizing two filters, with formation parameters identical to samples in Fig. 1 (a) and (b), on top of each other. For the sample in Fig. 2 (a) the filter displaying a reflectance peak around 500 nm is on top and the filter with a peak at longer wavelengths is situated on the bottom. As for the sample shown Fig. 2 (b), the stacking order is reversed. For Fig. 2 (a) the reflectance peak from the lower filter is clearly visible, but an interference pattern originating from the interfaces between the surrounding medium, the filter surfaces, and silicon substrate is transferred to the lower filter reflective peak. This phenomenon is also predicted by theoretical calculations for stacked rugate filters [28

28. M. Kildemo, O. Hunderi, and B. Drévillon, “Approximation of reflection coefficients for rapid real-time calculation of inhomogenous films,” J. Opt. Soc. Am. A 14, 931–939 (1997). [CrossRef]

]. As for Fig. 2 (b) the reflectance peak from the lower filter is not visible in the measured spectrum. This is attributed to PS light absorption in the lower wavelength range. The presence of the filter is only seen in the sidelobe fringe pattern, which is similar to the one seen in Fig. 2 (a), and clearly different from the regular patterns observed in Fig. 1 (a) and (b). Light absorption for the lower wavelength range can be verified by examining the imaginary part of PS refractive index (Fig. 3), which was determined for PS samples prepared with a 88.6 mA/cm2 anodization current density for 15 s.

Fig. 2 Reflectance spectra for two distinct dual-peak PS rugate filters prepared by stacking two filters similar to the ones shown in Fig. 1 on top of each other. (a) A filter prepared with similar parameters as the one shown in Fig. 1 (a) is on top, and a filter shown in Fig. 1 (b) is at the bottom. (b) The stacking order for the filters is reversed. The reflective peak originating from the bottom filter is completely invisible due to light absorption at the lower wavelength range. Existence of the lower filter only manifests irregularities in the sidelobe fringe pattern.
Fig. 3 Imaginary part of the porous silicon refractive index determined for an as-anodized sample produced with 88.6 mA/cm2 anodization current density. The extinction coefficient for lower wavelengths increases considerably. This behaviour is analogous to crystalline silicon refractive index.

The optical constants were determined based on PS sample reflectance spectra, using a self-adaptive evolutionary algorithm designed specifically for this purpose [25

25. V. Torres-Costa, R. J. Martín-Palma, and J. M. Martínez-Duart, “Optical constants of porous silicon films and multilayers determined by genetic algorithms,” J. Appl. Phys. 96, 4197–4203 (2004). [CrossRef]

]. The extinction coefficient shown in Fig. 3 shows similar behaviour to bulk silicon, which explains the increased light absorption for wavelengths below 500 nm. The numerical values presented here should be understood as effective extinction coefficient values, also including losses from diffraction, sample impurities etc. Based on Fig. 3 and Fig. 2 (b) it can be concluded that filters displaying peaks in wavelength ranges with high absorption should be placed on top in stacked filter structures. This problem can also be avoided by designing the filters for infrared range, where light absorption for PS is negligible [29

29. J. Salonen, K. Saarinen, J. Peura, J. Viinikanoja, I. Salomaa, E. Laine, and J. Kauppinen, “Dispersive Fourier transform spectroscopy of free-standing porous silicon films,” Mater. Res. Soc. Symp. Proc. 486, 323–327, (1998). [CrossRef]

].

The second method for preparing filters with m reflective peaks (m ∈ ℤ+) is to use an anodization current density profile composed of a linear combination of m sinusoidal waveforms [17

17. B. G. Bovard, “Rugate filter theory: an overview,” Appl. Opt. 32, 5427–5442 (1993). [CrossRef] [PubMed]

]. In this case the anodization current density profile J(t) has the following form:
J(t)=Joff+i=1mAisin(2πtpi+ϕi),
(2)
where J off is the offset current density, A is amplitude for an individual sine wave, t is anodization time, p is sine wave period length, and ϕ is the phase shift term which was set as zero for all the filters presented in this work. Preparation of these types of PS rugate filters has also been demonstrated before [7

7. M. G. Berger, R. Arens-Fischer, M. Thönissen, M. Krüger, S. Billat, H. Lüth, S. Hilbrich, W. Theiss, and P. Grosse, “Dielectric filters made of PS: advanced performance by oxidation and new layer structures,” Thin Solid Films 297, 237–240 (1997). [CrossRef]

, 19

19. S. O. Meade, M. S. Yoon, K. H. Ahn, and M. J. Sailor, “Porous silicon photonic crystals as encoded microcarriers,” Adv. Mater. 16, 1811–1814 (2004). [CrossRef]

21

21. N. Ishikura, M. Fujii, K. Nishida, S. Hayashi, and J. Diener, “Dichroic rugate filters based on birefringent porous silicon,” Opt. Express 16, 15531–15539 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-20-15531. [CrossRef] [PubMed]

].

Measured reflectance spectrum for a dual-peak PS rugate filter produced with an anodization current composed of two superimposed sine waves is shown in Fig. 4 (a). The parameters used for the anodization process are shown in Table 1 (sample S1). Figure 4 (b) shows a stacked structure obtained with similar parameters (sample S2 in Table 1) by anodizing the single-line rugate filters on top of each other. By comparing the spectra, it is obvious that both samples display reflective peaks in same wavelength regions. However, in contrast to the stacked sample the superimposed sample S1 does not display an interference fringe pattern on either of the stopbands. This can be attributed to the absence of a filter-filter interface.

Fig. 4 Rugate filters displaying two reflective peaks produced with different current profiles ((a) linear combination of two sine waves, (b) successive sine waves with different periodicity, (c) successive sine waves with different periodicity and offset level). The insets display schematic profiles for the anodization current density J. Solid and dashed lines represent the measured reflectance spectra before and after thermal oxidation, respectively.

Table 1. Anodization parameters for the PS rugate filters shown in Fig. 4

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The observed blueshift caused by the thermal oxidation is a well-known phenomenon, which is caused by a decrease in the effective refractive index of PS [29

29. J. Salonen, K. Saarinen, J. Peura, J. Viinikanoja, I. Salomaa, E. Laine, and J. Kauppinen, “Dispersive Fourier transform spectroscopy of free-standing porous silicon films,” Mater. Res. Soc. Symp. Proc. 486, 323–327, (1998). [CrossRef]

]. The effect of oxidation is illustrated in Fig. 5, which presents the real-part of the PS refractive index before and after thermal oxidation. The refractive indices were determined for samples anodized with a 88.6 mA/cm2 current density for 12 s [25

25. V. Torres-Costa, R. J. Martín-Palma, and J. M. Martínez-Duart, “Optical constants of porous silicon films and multilayers determined by genetic algorithms,” J. Appl. Phys. 96, 4197–4203 (2004). [CrossRef]

]. The PS refractive index curves also show Cauchy-like dispersion behavior. Considering PS optical absorption and dispersion, it is obvious that accurately designing interference filters that display reflective peaks below 500 nm is a challenging task.

Fig. 5 Real part of the refractive index for as-anodized and thermally oxidized porous silicon.

3.3. Gas sensing properties of dual-peak filters

The gas sensing properties of thermally oxidized PS dual-peak filters shown in Fig. 4 were examined by comparing their responsiveness to ethanol vapor. Responsiveness was evaluated by observing the reflective peak redshift during vapor exposure. In order to reduce error caused by measurement inaccuracy, the resonant peak position was determined as a geometrical average for a set of values that exceeded a predetermined threshold. Figure 6 shows the response of two different filters (samples S1 and S2) when exposed to 8012 ± 172 ppm of ethanol vapor. As we recall from section 3.2, the only difference between these two samples was the depth-wise positioning of the quasisinusoidal refractive index variation. For Fig. 6 (a) the sine waves are in superposition, whereas for Fig. 6 (b) as successive waves, i.e. stacked filter layers. Reflectance spectra for the samples were recorded before ethanol exposure, and once per minute after ethanol vapor was introduced to the measurement chamber. The initial response for both filters is fast (Fig. 6) and both spectra are already fully redshifted to their final positions after one minute exposure. The stacked structure (Fig. 6 (b)) is more sensitive and displays a larger redshift for both reflective peaks. This might be due to the slightly smaller pore sizes in comparison to the superimposed filter structure (Fig. 6 (a)), a difference resulting from the larger anodization current amplitude variation in the superimposed structure, although the differences in the pore size distributions are expected to be quite minimal [30

30. T. Jalkanen, J. Tuura, E. Mäkilä, and J. Salonen, “Electro-optical porous silicon gas sensor with enhanced selectivity,” Sens. Actuators B 147, 100–104 (2010). [CrossRef]

].

Fig. 6 Recorded redshifts induced by 8012 ± 172 ppm of ethanol vapor, measured for dual-peak rugate filters produced with an anodization current density profile composed of two sine waves with different amplitude and periodicity, (a) in superposition (sample S1), (b) as successive waves, i.e. stacked structure (sample S2). Peak 1 refers to the lower wavelength peaks around 500 nm, whereas peak 2 shows the redshift values obtained for the higher wavelength reflective peak.

After 12 min ethanol exposure, the gas flow to the sensing chamber was switched back to pure nitrogen flow, and reflectance spectra were recorded once per minute for the following 10 min. The superimposed dual-peak filter recovers clearly faster. Both peaks recover from the ethanol exposure almost identically (peak 2 being slightly slower), and after 5 min the peaks are less than 1 nm from their original position. After 9 min the peaks have returned to their initial positions. As for the stacked structure the recovery is much slower. In addition, peak 2, which originates from the lower filter layer, recovers more slowly. This was expected since gas desorption is decelerated by the upper rugate filter layer. Recovery of peak 1 is also slower in comparison to the superimposed dual-peak filter. This can be understood as a consequence of differences in sample thicknesses and ethanol desorption from the lower filter layer passing through the upper filter. Even after the 10 min recovery period, the peaks did not reach their original positions. The difference in the total anodization times for the superimposed sample S1 (175 s) and the stacked sample S2 (375 s) results in a clear difference in porous layer thicknesses, which should explain the observed differences in recovery times.

Reproducibility of the sensing results was examined by preparing two stacked-type dual-peak filters with identical anodization parameters. The parameters were the same as used for sample S3 in Table 1. Figure 7 compares the measured redshift values for the two filters when exposed to 8012 ± 172 ppm of ethanol vapor. The redshift for both filters occurs during the first minute of ethanol exposure. The redshift values for the samples differ slightly, with the average difference in redshift being 0.6 nm for peak 1 and 0.9 nm for peak 2. In general, the observed sensitivity, response, and recovery behaviour does not differ much from the stacked sample response presented in Fig. 6 (b).

Fig. 7 Response of two stacked dual-peak filters to 8012 ± 172 ppm of ethanol vapor. The filters were produced with identical anodization parameters (sample S3).

Although the anodization parameters for the two samples were identical, the reflectance peaks displayed by the filters were situated in slightly different wavelengths (approximately 15 nm difference for peak 1 and 20 nm for peak 2). This is attributed to small changes in electrolyte concentration and slight differences in backside electrical contact to the Si wafer during anodization. These differences in the obtained filters are presumably responsible for the slight differences in the observed gas sensing properties. The differences in gas sensing properties remained even when the redshift values were normalized with the respective reflective peak positions.

3.4. Refractive index matching and apodization

Figure 8 shows the effects of quintic matching layers for a stacked dual-peak and a superimposed triple-peak PS rugate filter. The total thickness of the quintic layer determines the width of the wavelength region for which the sidelobes are suppressed [22

22. W. H. Southwell and R. L. Hall, “Rugate filter sidelobe suppression using quintic and rugated quintic matching layers,” Appl. Opt. 28, 2949–2951 (1989). [CrossRef] [PubMed]

]. Here a 9 s quintic anodization period ranging from 126.6 mA/cm2 to 88.6 mA/cm2 was used for the air-PS interface, and an 18 s quintic cycle from 88.6 mA/cm2 to 0 mA/cm2 was applied for the PS-silicon interface. The stacked rugate filter was generated by successive anodization of two sine waves, with the first one oscillating between 101.3 and 75.9 mA/cm2 and the second one between 94.9 and 82.3 mA/cm2. The period lengths were 3 and 4.5 s, with the total anodization times being 120 and 180 s, respectively. Anodization current density profile for the triple-peak filter was constructed according to Equation 2. The parameters used for the anodization process are shown in Table 2.

Fig. 8 Effect of quintic refractive index matching layers to the reflectance spectra of multipeak PS rugate filters. (a) Reflectance spectra for stacked dual-peak rugate filters, where the upper spectrum is obtained for a sample without quintic matching layers. The sample with quintic matching layers incorporated in the design (below) displays significant side-lobe suppression. (b) Reflectance spectra for superimposed triple-peak rugate filters, with (lower spectrum) and without (upper spectrum) quintic matching layers. The insets display the anodization current density profiles J(t) for the samples including quintic refractive index matching layers.

Table 2. Anodization parameters for a superimposed triple-peak PS rugate filter. The offset current density was 88.6 mA/cm2 with the total anodization time being 240 s. The reflectance spectrum for a filter obtained with these parameters is shown in Fig. 8 (b).

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From Fig. 8 it is obvious that the addition of quintic matching layers greatly reduces the intensity of the sidelobes. For the stacked structure (Fig. 8 (a)) a noticeable difference is observed in the shape of the second stopband, originating from the lower filter layer. The suppressed fringe pattern is hardly visible, which simplifies the determination of the peak position and also alleviates the possible problems that might be encountered in gas sensing applications. For the triple-peak superimposed rugate structure (Fig. 8 (b)) a clear decrease in the sidelobe intensity is also observed. The stopband shapes in the superposition filter are not greatly affected by the refractive index matching layers, but due to sidelobe suppression the reflective peaks stand out from the background more clearly. Figure 9 shows a cross-sectional SEM micrograph of the stacked dual-peak structure with quintic refractive index layers.

Fig. 9 Cross-sectional SEM micrograph of a stacked dual-peak PS rugate filter with quintic refractive index matching layers. The arrow indicates the interface between the filter layers. The scale bar at the bottom equals 2 μm.

Second reason for the existence of sidelobes is the abrupt truncation of the sine wave at the filter interfaces. As a result the refractive index profile is not smoothly changing throughout the filter structure [23

23. W. H. Southwell, “Using apodization functions to reduce sidelobes in rugate filters,” Appl. Opt. 28, 5091–5094 (1989). [CrossRef] [PubMed]

]. Even with the addition of refractive index matching layers, transition points where the index profile is not mathematically differentiable remain. This issue can be dealt with by introducing apodization to the sinusoidal refractive index profile. This has been proven to suppress the sidelobes [23

23. W. H. Southwell, “Using apodization functions to reduce sidelobes in rugate filters,” Appl. Opt. 28, 5091–5094 (1989). [CrossRef] [PubMed]

], but it comes with the cost of decreased optical density of the reflective stopband. Gaussian apodization [23

23. W. H. Southwell, “Using apodization functions to reduce sidelobes in rugate filters,” Appl. Opt. 28, 5091–5094 (1989). [CrossRef] [PubMed]

] and half-apodization [24

24. H. A. Abu-Safia, A. I. Al-Sharif, and I. O. Abu Aljarayesh, “Rugate filter sidelobe suppression using half-apodization,” Appl. Opt. 32, 4831–4835 (1993). [CrossRef] [PubMed]

] are often used as window functions for rugate filters. The use of the Gaussian can be mathematically understood when the Fourier synthesis approach to dielectric thin film filter design is considered [17

17. B. G. Bovard, “Rugate filter theory: an overview,” Appl. Opt. 32, 5427–5442 (1993). [CrossRef] [PubMed]

, 34

34. E. Delano, “Fourier synthesis of multilayer films,” J. Opt. Soc. Am. 57, 1529–1533 (1967). [CrossRef]

36

36. B. G. Bovard, “Rugate filter design: the modified Fourier transform technique,” Appl. Opt. 29, 24–30 (1990). [CrossRef] [PubMed]

]. Gaussian is a Fourier eigenfunction, i.e. a shape-invariant signal under the Fourier transform operation. Mathematically the Gaussian extends to infinity, but in practice it can be used to make the transition points between sine waves and matching layers smoother.

Both Gaussian apodization [33

33. S. Ilias, T. Böcking, K. Kilian, P. J. Reece, J. Gooding, K. Gaus, and M. Gal, “Porous silicon based narrow line-width rugate filters,” Opt. Mater. 29, 619–622 (2007). [CrossRef]

] and half-apodization [20

20. E. Lorenzo, C. J. Oton, N. E. Capuj, M. Ghulinyan, D. Navarro-Urrios, Z. Gaburro, and L. Pavesi, “Porous silicon-based rugate filters,” Appl. Opt. 44, 5415–5421 (2005). [CrossRef] [PubMed]

, 21

21. N. Ishikura, M. Fujii, K. Nishida, S. Hayashi, and J. Diener, “Dichroic rugate filters based on birefringent porous silicon,” Opt. Express 16, 15531–15539 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-20-15531. [CrossRef] [PubMed]

], have been demonstrated for PS. However, all the filter designs have been for near infrared region, where light absorption and dispersion are negligibly small. In order to test the feasibility of Gaussian apodization for visible range applications, single-line rugate filters with the reflective peak around 500 nm were prepared. Sinusoidal wave with a 3 s period length was modulated between 101.3 and 75.9 mA/cm2 for 120 s. Figure 10 compares the differences in reflectance spectra between single-line rugate filters prepared with and without Gaussian apodization.

Fig. 10 Three single-line rugate filters with (a) normal sinusoidal profile, (b) sinusoidal profile with Gaussian apodization, and (c) sinusoidal profile with Gaussian apodization and quintic refractive index matching layers incorporated at the beginning and end of the anodization current profile.

Surprisingly the sidelobe intensity actually increases in comparison to the reflective peak intensity, with the addition of Gaussian apodization (Fig. 10 (a) and (b)). This might be partially due to light absorption and dispersion (Fig. 3 and 5), which are not accounted for in the Fourier transform approach. Another factor might be the reported decrease in the optical density of the reflective peak [23

23. W. H. Southwell, “Using apodization functions to reduce sidelobes in rugate filters,” Appl. Opt. 28, 5091–5094 (1989). [CrossRef] [PubMed]

]. When refractive index matching layers are incorporated to the apodized rugate interfaces, clear sidelobe suppression is obtained (Fig. 10 (c)). This would suggest that for the visible range best results in terms of sidelobe suppression are obtained by merely adding the quintic matching layers to the filter design.

3.5. Effects of quintic index matching in gas sensing

The effects of quintic matching layers to the gas sensing properties of multipeak PS rugate filters were evaluated by subjecting the filters shown in Fig. 8 to ethanol vapor. Figure 11 presents the recorded resonant peak redshifts for the stacked dual-peak structures with and without quintic refractive index matching layers. Analogous to the dual-peak filters in section 3.2, a smaller redshift is observed for peak 1 (situated around 500 nm), whereas peak 2 (around 700 nm) undergoes a larger redshift. The results are similar to the ones shown in Fig. 6 (b) and Fig. 7. Most important observation is obviously the fact that the incorporation of quintic matching layers does not interfere with the gas sensing properties of the filter structure. However, since the interference fringe pattern in peak 2 stopband is suppressed, exact determination of peak position is simplified.

Fig. 11 Response of stacked PS rugate filters to 8012 ± 172 ppm of ethanol vapor. The incorporation of quintic refractive index matching layers does not affect the response time and sensitivity of the porous structure.

The superimposed triple-peak filters demonstrated similar behaviour under ethanol vapor exposure, i.e. the quintic matching layers did not seem to have a noticeable effect to the gas sorption properties of the filter structure. However, since the superimposed structures do not display disturbing interference fringes over the stopband regions to begin with, the addition of quintic matching layers is not a necessity unless one specifically wants to achieve higher transmission for the non-stopband regions. Recovery time after ethanol exposure for the superimposed triple-peak filters was also considerably longer when compared to the superimposed dual-peak filter (sample S1). Increased recovery time is attributed to the increased anodization time when preparing the triple-peak filter, which resulted in increased filter thickness. This also confirms that the recorded differences in recovery time between the superimposed and stacked samples S1 and S2 (Fig. 6) result from differences in total porous layer thicknesses.

4. Conclusions

The structural differences in various types of PS multistopband rugate filters lead to differences in gas adsorption and desorption properties. Higher sensitivity can be obtained with stacked filters, whereas the superposition filter structure allows the preparation of thinner filter layers, which promotes faster recovery from vapor exposure. Interference fringes caused by the interfaces between filter layers can be problematic for stacked structures. However, this phenomenon can be minimized by the use of quintic refractive index matching layers. In addition, the index matching layers do not have an adverse effect on the sensing properties of the filters. Incorporation of Gaussian apodization to the filter design as a method for sidelobe suppression is not supported by the results. This may be a result of strong light absorption and dispersion that PS exhibits at the lower wavelength area of the visible range. Based on the results both the stacked and the superimposed filter structure show promise in gas sensing applications.

Acknowledgments

This work was partially supported by the Grant-in-Aid from the Japan Society of Promotion of Science for Scientific Research (B) under Grant No. 22350092. T. Jalkanen acknowledges financial support from MEXT, the Japanese Ministry of Education, Culture, Sports, Science & Technology. The authors would like to thank Dr. Y. Suzuki for technical assistance with the SEM measurements.

References and links

1.

L. T. Canham, “Silicon quantum wire array fabricated by electrochemical and chemical dissolution of wafers,” Appl. Phys. Lett. 57, 1046–1048 (1990). [CrossRef]

2.

A. Halimaoui, C. Oules, G. Bomchil, A. Bsiesy, F. Gaspard, R. Herino, M. Ligeon, and F. Muller, “Electroluminescence in the visible range during anodic oxidation of porous silicon films,” Appl. Phys. Lett. 59, 304–306 (1991). [CrossRef]

3.

N. Koshida and H. Koyama, “Visible electroluminescence from porous silicon,” Appl. Phys. Lett. 60, 347–349 (1992). [CrossRef]

4.

C. Pickering, M. I. J. Beale, D. J. Robbins, P. J. Pearson, and R. Greef, “Optical properties of porous silicon films,” Thin Solid Films 125, 157–163 (1985). [CrossRef]

5.

G. Vincent, “Optical properties of porous silicon superlattices,” Appl. Phys. Lett. 64, 2367–2369 (1994). [CrossRef]

6.

M. G. Berger, C. Dieker, M. Thönissen, L. Vescan, H. Lüth, H. Münder, W. Theiss, M. Wernke, and P. Grosse, “Porosity superlattices: a new class of Si heterostructures,” J. Phys. D. 27, 1333–1336 (1994). [CrossRef]

7.

M. G. Berger, R. Arens-Fischer, M. Thönissen, M. Krüger, S. Billat, H. Lüth, S. Hilbrich, W. Theiss, and P. Grosse, “Dielectric filters made of PS: advanced performance by oxidation and new layer structures,” Thin Solid Films 297, 237–240 (1997). [CrossRef]

8.

V. Torres-Costa and R. J. Martín-Palma, “Application of nanostructured porous silicon in the field of optics. A review,” J. Mater. Sci. 45, 2823–2838 (2010). [CrossRef]

9.

I. Schechter, M. Ben-Chorin, and A. Kux, “Gas sensing properties of porous silicon,” Anal. Chem. 67, 3727–3732 (1995). [CrossRef]

10.

R. B. Bjorklund, S. Zangooie, and H. Arwin, “Color changes in thin porous silicon films caused by vapor exposure,” Appl. Phys. Lett. 69, 3001–3003 (1996). [CrossRef]

11.

P. A. Snow, E. K. Squire, P. St. J. Russell, and L. T. Canham, “Vapor sensing using the optical properties of porous silicon Bragg mirrors,” J. Appl. Phys. 86, 1781–1784 (1999). [CrossRef]

12.

M. Arroyo-Hernández, R. J. Martín-Palma, V. Torres-Costa, and J. M. Martínez-Duart, “Porous silicon optical filters for biosensing applications,” J. Non-Cryst. Solids 352, 2457–2460 (2006). [CrossRef]

13.

B. H. King, A. M. Ruminski, J. L. Snyder, and M. J. Sailor, “Optical-fiber-mounted porous silicon photonic crystals for sensing organic vapor breakthrough in activated carbon,” Adv. Mater. 19, 4530–4534 (2007). [CrossRef]

14.

M. S. Salem, M. J. Sailor, K. Fukami, T. Sakka, and Y. H. Ogata, “Sensitivity of porous silicon rugate filters for chemical vapor detection,” J. Appl. Phys. 103, 083516 (2008). [CrossRef]

15.

T. Jalkanen, V. Torres-Costa, J. Salonen, M. Bjorkqvist, E. Mäkilä, J. M. Martínez-Duart, and V.-P. Lehto, “Optical gas sensing properties of thermally hydrocarbonized porous silicon Bragg reflectors,” Opt. Express 17, 5446–5456 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-7-5446. [CrossRef] [PubMed]

16.

A. M. Ruminski, M. M. Moore, and M. J. Sailor, “Humidity-compensating sensor for volatile organic compounds using stacked porous silicon photonic crystals,” Adv. Funct. Mater. 18, 3418–3426 (2008). [CrossRef]

17.

B. G. Bovard, “Rugate filter theory: an overview,” Appl. Opt. 32, 5427–5442 (1993). [CrossRef] [PubMed]

18.

F. Cunin, T. A. Schmedake, J. R. Link, Y. Y. Li, J. Koh, S. N. Bhatia, and M. J. Sailor, “Biomolecular screening with encoded porous-silicon photonic crystals,” Nat. Mater. 1, 39–41 (2002). [CrossRef]

19.

S. O. Meade, M. S. Yoon, K. H. Ahn, and M. J. Sailor, “Porous silicon photonic crystals as encoded microcarriers,” Adv. Mater. 16, 1811–1814 (2004). [CrossRef]

20.

E. Lorenzo, C. J. Oton, N. E. Capuj, M. Ghulinyan, D. Navarro-Urrios, Z. Gaburro, and L. Pavesi, “Porous silicon-based rugate filters,” Appl. Opt. 44, 5415–5421 (2005). [CrossRef] [PubMed]

21.

N. Ishikura, M. Fujii, K. Nishida, S. Hayashi, and J. Diener, “Dichroic rugate filters based on birefringent porous silicon,” Opt. Express 16, 15531–15539 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-20-15531. [CrossRef] [PubMed]

22.

W. H. Southwell and R. L. Hall, “Rugate filter sidelobe suppression using quintic and rugated quintic matching layers,” Appl. Opt. 28, 2949–2951 (1989). [CrossRef] [PubMed]

23.

W. H. Southwell, “Using apodization functions to reduce sidelobes in rugate filters,” Appl. Opt. 28, 5091–5094 (1989). [CrossRef] [PubMed]

24.

H. A. Abu-Safia, A. I. Al-Sharif, and I. O. Abu Aljarayesh, “Rugate filter sidelobe suppression using half-apodization,” Appl. Opt. 32, 4831–4835 (1993). [CrossRef] [PubMed]

25.

V. Torres-Costa, R. J. Martín-Palma, and J. M. Martínez-Duart, “Optical constants of porous silicon films and multilayers determined by genetic algorithms,” J. Appl. Phys. 96, 4197–4203 (2004). [CrossRef]

26.

M. S. Salem, M. J. Sailor, T. Sakka, and Y. H. Ogata, “Electrochemical preparation of a rugate filter in silicon and its deviation from the ideal structure,” J. Appl. Phys. 101, 063503 (2007). [CrossRef]

27.

H. A. MacLeod, Thin-film Optical Filters, 2nd. ed. (Adam Hilger Ltd., 1986). [CrossRef]

28.

M. Kildemo, O. Hunderi, and B. Drévillon, “Approximation of reflection coefficients for rapid real-time calculation of inhomogenous films,” J. Opt. Soc. Am. A 14, 931–939 (1997). [CrossRef]

29.

J. Salonen, K. Saarinen, J. Peura, J. Viinikanoja, I. Salomaa, E. Laine, and J. Kauppinen, “Dispersive Fourier transform spectroscopy of free-standing porous silicon films,” Mater. Res. Soc. Symp. Proc. 486, 323–327, (1998). [CrossRef]

30.

T. Jalkanen, J. Tuura, E. Mäkilä, and J. Salonen, “Electro-optical porous silicon gas sensor with enhanced selectivity,” Sens. Actuators B 147, 100–104 (2010). [CrossRef]

31.

J. Salonen, V.-P. Lehto, and E. Laine, “Thermal oxidation of free-standing porous silicon films,” Appl. Phys. Lett. 70, 637–639 (1997). [CrossRef]

32.

W. H. Southwell, “Graded-index antireflection coatings,” Opt. Lett. 8, 584–586 (1983). [CrossRef] [PubMed]

33.

S. Ilias, T. Böcking, K. Kilian, P. J. Reece, J. Gooding, K. Gaus, and M. Gal, “Porous silicon based narrow line-width rugate filters,” Opt. Mater. 29, 619–622 (2007). [CrossRef]

34.

E. Delano, “Fourier synthesis of multilayer films,” J. Opt. Soc. Am. 57, 1529–1533 (1967). [CrossRef]

35.

B. G. Bovard, “Derivation of a matrix describing a rugate dielectric thin film,” Appl. Opt. 27, 1998–2005 (1988). [CrossRef] [PubMed]

36.

B. G. Bovard, “Rugate filter design: the modified Fourier transform technique,” Appl. Opt. 29, 24–30 (1990). [CrossRef] [PubMed]

OCIS Codes
(040.6040) Detectors : Silicon
(280.4788) Remote sensing and sensors : Optical sensing and sensors
(230.5298) Optical devices : Photonic crystals
(310.6845) Thin films : Thin film devices and applications

ToC Category:
Sensors

History
Original Manuscript: May 12, 2011
Manuscript Accepted: June 5, 2011
Published: June 24, 2011

Virtual Issues
Vol. 6, Iss. 8 Virtual Journal for Biomedical Optics

Citation
Tero Jalkanen, Jarno Salonen, Vicente Torres-Costa, Kazuhiro Fukami, Tetsuo Sakka, and Yukio H. Ogata, "Structural considerations on multistopband mesoporous silicon rugate filters prepared for gas sensing purposes," Opt. Express 19, 13291-13305 (2011)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-19-14-13291


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References

  1. L. T. Canham, “Silicon quantum wire array fabricated by electrochemical and chemical dissolution of wafers,” Appl. Phys. Lett. 57, 1046–1048 (1990). [CrossRef]
  2. A. Halimaoui, C. Oules, G. Bomchil, A. Bsiesy, F. Gaspard, R. Herino, M. Ligeon, and F. Muller, “Electroluminescence in the visible range during anodic oxidation of porous silicon films,” Appl. Phys. Lett. 59, 304–306 (1991). [CrossRef]
  3. N. Koshida and H. Koyama, “Visible electroluminescence from porous silicon,” Appl. Phys. Lett. 60, 347–349 (1992). [CrossRef]
  4. C. Pickering, M. I. J. Beale, D. J. Robbins, P. J. Pearson, and R. Greef, “Optical properties of porous silicon films,” Thin Solid Films 125, 157–163 (1985). [CrossRef]
  5. G. Vincent, “Optical properties of porous silicon superlattices,” Appl. Phys. Lett. 64, 2367–2369 (1994). [CrossRef]
  6. M. G. Berger, C. Dieker, M. Thönissen, L. Vescan, H. Lüth, H. Münder, W. Theiss, M. Wernke, and P. Grosse, “Porosity superlattices: a new class of Si heterostructures,” J. Phys. D. 27, 1333–1336 (1994). [CrossRef]
  7. M. G. Berger, R. Arens-Fischer, M. Thönissen, M. Krüger, S. Billat, H. Lüth, S. Hilbrich, W. Theiss, and P. Grosse, “Dielectric filters made of PS: advanced performance by oxidation and new layer structures,” Thin Solid Films 297, 237–240 (1997). [CrossRef]
  8. V. Torres-Costa and R. J. Martín-Palma, “Application of nanostructured porous silicon in the field of optics. A review,” J. Mater. Sci. 45, 2823–2838 (2010). [CrossRef]
  9. I. Schechter, M. Ben-Chorin, and A. Kux, “Gas sensing properties of porous silicon,” Anal. Chem. 67, 3727–3732 (1995). [CrossRef]
  10. R. B. Bjorklund, S. Zangooie, and H. Arwin, “Color changes in thin porous silicon films caused by vapor exposure,” Appl. Phys. Lett. 69, 3001–3003 (1996). [CrossRef]
  11. P. A. Snow, E. K. Squire, P. St. J. Russell, and L. T. Canham, “Vapor sensing using the optical properties of porous silicon Bragg mirrors,” J. Appl. Phys. 86, 1781–1784 (1999). [CrossRef]
  12. M. Arroyo-Hernández, R. J. Martín-Palma, V. Torres-Costa, and J. M. Martínez-Duart, “Porous silicon optical filters for biosensing applications,” J. Non-Cryst. Solids 352, 2457–2460 (2006). [CrossRef]
  13. B. H. King, A. M. Ruminski, J. L. Snyder, and M. J. Sailor, “Optical-fiber-mounted porous silicon photonic crystals for sensing organic vapor breakthrough in activated carbon,” Adv. Mater. 19, 4530–4534 (2007). [CrossRef]
  14. M. S. Salem, M. J. Sailor, K. Fukami, T. Sakka, and Y. H. Ogata, “Sensitivity of porous silicon rugate filters for chemical vapor detection,” J. Appl. Phys. 103, 083516 (2008). [CrossRef]
  15. T. Jalkanen, V. Torres-Costa, J. Salonen, M. Bjorkqvist, E. Mäkilä, J. M. Martínez-Duart, and V.-P. Lehto, “Optical gas sensing properties of thermally hydrocarbonized porous silicon Bragg reflectors,” Opt. Express 17, 5446–5456 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-7-5446 . [CrossRef] [PubMed]
  16. A. M. Ruminski, M. M. Moore, and M. J. Sailor, “Humidity-compensating sensor for volatile organic compounds using stacked porous silicon photonic crystals,” Adv. Funct. Mater. 18, 3418–3426 (2008). [CrossRef]
  17. B. G. Bovard, “Rugate filter theory: an overview,” Appl. Opt. 32, 5427–5442 (1993). [CrossRef] [PubMed]
  18. F. Cunin, T. A. Schmedake, J. R. Link, Y. Y. Li, J. Koh, S. N. Bhatia, and M. J. Sailor, “Biomolecular screening with encoded porous-silicon photonic crystals,” Nat. Mater. 1, 39–41 (2002). [CrossRef]
  19. S. O. Meade, M. S. Yoon, K. H. Ahn, and M. J. Sailor, “Porous silicon photonic crystals as encoded microcarriers,” Adv. Mater. 16, 1811–1814 (2004). [CrossRef]
  20. E. Lorenzo, C. J. Oton, N. E. Capuj, M. Ghulinyan, D. Navarro-Urrios, Z. Gaburro, and L. Pavesi, “Porous silicon-based rugate filters,” Appl. Opt. 44, 5415–5421 (2005). [CrossRef] [PubMed]
  21. N. Ishikura, M. Fujii, K. Nishida, S. Hayashi, and J. Diener, “Dichroic rugate filters based on birefringent porous silicon,” Opt. Express 16, 15531–15539 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-20-15531 . [CrossRef] [PubMed]
  22. W. H. Southwell and R. L. Hall, “Rugate filter sidelobe suppression using quintic and rugated quintic matching layers,” Appl. Opt. 28, 2949–2951 (1989). [CrossRef] [PubMed]
  23. W. H. Southwell, “Using apodization functions to reduce sidelobes in rugate filters,” Appl. Opt. 28, 5091–5094 (1989). [CrossRef] [PubMed]
  24. H. A. Abu-Safia, A. I. Al-Sharif, and I. O. Abu Aljarayesh, “Rugate filter sidelobe suppression using half-apodization,” Appl. Opt. 32, 4831–4835 (1993). [CrossRef] [PubMed]
  25. V. Torres-Costa, R. J. Martín-Palma, and J. M. Martínez-Duart, “Optical constants of porous silicon films and multilayers determined by genetic algorithms,” J. Appl. Phys. 96, 4197–4203 (2004). [CrossRef]
  26. M. S. Salem, M. J. Sailor, T. Sakka, and Y. H. Ogata, “Electrochemical preparation of a rugate filter in silicon and its deviation from the ideal structure,” J. Appl. Phys. 101, 063503 (2007). [CrossRef]
  27. H. A. MacLeod, Thin-film Optical Filters , 2nd. ed. (Adam Hilger Ltd., 1986). [CrossRef]
  28. M. Kildemo, O. Hunderi, and B. Drévillon, “Approximation of reflection coefficients for rapid real-time calculation of inhomogenous films,” J. Opt. Soc. Am. A 14, 931–939 (1997). [CrossRef]
  29. J. Salonen, K. Saarinen, J. Peura, J. Viinikanoja, I. Salomaa, E. Laine, and J. Kauppinen, “Dispersive Fourier transform spectroscopy of free-standing porous silicon films,” Mater. Res. Soc. Symp. Proc. 486, 323–327, (1998). [CrossRef]
  30. T. Jalkanen, J. Tuura, E. Mäkilä, and J. Salonen, “Electro-optical porous silicon gas sensor with enhanced selectivity,” Sens. Actuators B 147, 100–104 (2010). [CrossRef]
  31. J. Salonen, V.-P. Lehto, and E. Laine, “Thermal oxidation of free-standing porous silicon films,” Appl. Phys. Lett. 70, 637–639 (1997). [CrossRef]
  32. W. H. Southwell, “Graded-index antireflection coatings,” Opt. Lett. 8, 584–586 (1983). [CrossRef] [PubMed]
  33. S. Ilias, T. Böcking, K. Kilian, P. J. Reece, J. Gooding, K. Gaus, and M. Gal, “Porous silicon based narrow line-width rugate filters,” Opt. Mater. 29, 619–622 (2007). [CrossRef]
  34. E. Delano, “Fourier synthesis of multilayer films,” J. Opt. Soc. Am. 57, 1529–1533 (1967). [CrossRef]
  35. B. G. Bovard, “Derivation of a matrix describing a rugate dielectric thin film,” Appl. Opt. 27, 1998–2005 (1988). [CrossRef] [PubMed]
  36. B. G. Bovard, “Rugate filter design: the modified Fourier transform technique,” Appl. Opt. 29, 24–30 (1990). [CrossRef] [PubMed]

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