- Email: [email protected]
Time-resolved sensing of chemical species in porous silicon optical microcavity
Sensors and Actuators B 100 (2004) 168–172
Time-resolved sensing of chemical species in porous silicon optical microcavity L. De Stefano a,∗ , L. Moretti b , I. Rendina a , A.M. Rossi c b
a National Council of Research—IMM, via P. Castellino III, 80131 Napoli, Italy DIMET—University “Mediterranea” of Reggio Calabria, Località Feo di Vito, 89060 Reggio Calabria, Italy c Istituto Elettrotecnico Nazionale “G. Ferraris”, Strada delle Cacce 91, Turin, Italy
Available online 18 February 2004
Abstract Time-resolved measurements of red-shifts in the reflectivity spectra of porous silicon multi-layer microcavities, due to exposure to vapor of chemical species, give deep insight about the spatial concentration of the liquid condensed into the pores. Results clearly indicate that capillary condensation starts immediately and proceeds homogeneously all over the stack, yielding a uniform concentration distribution. © 2003 Elsevier B.V. All rights reserved. Keywords: Porous silicon; Optical sensors; Microcavities; Low-dimensional silicon structure
1. Introduction Porous silicon (PS) is, by far, used in sensing applications due to its specific surface area which can be of the order of 500 m2 cm−3 : in this way, a very effective interaction with several chemical and biological matters can be assured. The adsorption of chemical substances into the pores modifies the physical properties of the PS structure, such as its dielectric function, thus optical sensors, based on this technology, can be feasible. In particular, the use of PS microcavities as optical chemical sensors, based on resonant peak shifts measurements in the reflectivity spectra due to capillary condensation of vapors in the silicon pores, have been demonstrated [1–7]. The optical PS microcavity (PSMC) is made of a Fabry–Pèrot cavity of /2-thickness between two distributed Bragg reflectors (DBRs). Several alternating pairs of PS layers, having different refractive indexes, obtained modulating the porosity, constitute the DBRs. Sensitivity and response time, both depending on pore filling dynamic, are key issues in practical use of these kinds of devices. For this reason, in this work, we have studied both numerically and experimentally, the dynamics of sensor response. With this aim, we have recorded time-resolved optical reflection spectra of PS microcavities on exposure to iso-propanol. Then we have compared the experimental results with two different models of pore filling dynamic: one model assumes that the filling of the porous matrix occurs homogeneously ∗ Corresponding author. E-mail address: [email protected] (L. De Stefano).
0925-4005/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.snb.2003.12.044
all over the PS multi-layer structure; on the other hand, the second model hypothesizes that the filling process proceeds non-homogeneously along the stack, starting from the exposed surface of the porous multi-layer structure.
2. Numerical simulations and experimental results The PS microsensor is modeled as a finite multi-layer stack of isotropic two-phase media, silicon and air, on an infinite half-space of bulk Si: the effective dielectric function can be calculated applying the Bruggeman effective medium approximation theory [8]. The reflectivity spectra are reproduced by an optical transfer matrix method, including variation of material properties with wavelength [9]. The physical structure of the device is characterized by alternate layers of different porosities: a concentration gradient of the liquid into the porous matrix might be expected [10]. As we already pointed out, two different models for the filling process have been considered: in the first one, we assume that the eventual partial filling of the porous multi-layer matrix measured during experiments is due to the homogeneous partial filling of each porous layer forming the stack; on the other hand, the second model hypothesizes that, in the case of partial filling of the whole stack, only some layers are completely filled by the condensed vapor. In both cases, the physical effect is an increase of the multi-layer average refractive index, which results in a shift towards longer wavelengths of the microcavity reflectivity spectrum.
L. De Stefano et al. / Sensors and Actuators B 100 (2004) 168–172
169
1.0
Reflectivity (a. u.)
0.9
0.8
0.7
0.6
0.5
Unperturbed cavity After exposure to Iso-propanol
0.4 1275
1300
1325
1350
1375
1400
1425
1450
1475
1500
W avelength (nm) Fig. 1. Reflectivity spectrum of the PSMC after the exposure to iso-propanol.
The experimental set up is very simple: a white source (tungsten lamp, 400 nm < λ < 1800 nm) illuminates, through an optical fiber and a collimator, the microcavity with an angle of incidence of 20◦ respect to the normal. The reflected light is collected by an objective and coupled into a multimode fiber. The signal is directed in an optical spectrum analyser (Ando, Mod. AQ-6315B) and measured with a 0.2 nm resolution. The porous silicon sensor is placed in a closed vial with a quartz window for optical access. Each measurement starts after that a small amount of volatile liquid added to the vial quickly saturates with its vapors the atmosphere surrounding the sensor. In Fig. 1, the experimental red shift measured for iso-propanol is reported. The data refers to a microcavity made of 29 layers, 14 layers for each DBR and one for the optical microcavity. The DBR structures are made alternating high and low porosities layers with 57 and 76% porosity, respectively. More details on the microsensor fabrication processes are reported in [3]. According to the first model, we have to assume that when the PSMC is exposed to chemical vapors, the air in the pores is substituted by the organic molecules due to capillary condensation, so that, at equilibrium, the chemicals vapors fill a certain volume in each layer. The filling process is really homogeneous all over the stack if the air volume is between 0 and the lower porosity value, otherwise, the process proceeds only in high porosity layers. Fig. 2 shows the calculated wavelength shifts () of the transmission peak as a function of liquid layer volume fraction (LLF), i.e. the pore volume filled by liquid, for exposure to iso-propanol. The change of slope for a layer liquid fraction volume of 0.57 corresponds to the complete filling of the low porosity layers. A comparison between the experimental peak shift (λ = 111 nm) and the theoret-
ical one gives a LLF value of 0.26 for iso-propanol (see Fig. 2). Another way to model the vapor penetration into the pores is assuming that the condensed vapor completely fills each layer, replacing all the air into its pores, and the process advances layer by layer from the top (exposed surface) to the bottom of the PSMC. In fact, the PS multilayer exchanges air and vapor with the outside only at the interface between the first layer surface and air. In our case, the stack is composed of 29 layers, so that the filling process can be described as a discrete sequence of 30 steps: (1) empty PSMC, (2) first layer completely filled and rest of PSMC empty, (3) first and second layer completely filled and the rest of PSMC empty, and so on; (30) all the PSMC layers are completely filled. In Fig. 3, the resonance peak shift calculated as a function of the number of layers filled with iso-propanol condensed vapor, is reported. The filling of the first and the second DBR contributes quite asymmetrically to total peak shift. After the first six layer filling we can only observe a small peak shift due to capillary condensation; a more pronounced peak shift happens when each period of the first DBR is completely filled. The Fabry–Pèrot cavity filling, step 15th to 16th, induces a increase of 65 nm. This result outlines the strong influence of the optical cavity (viz., a defect in a periodic structure) on the device sensitivity. In this case, comparing these numerical findings with the peak shift value registered, we can conclude, that only the first DBR has been filled in the experiment. By looking only at the final result of the vapor–PSMC interaction, i.e. the cavity peak shift, there is no way to establish which model is right or wrong between the two proposed. A real breakthrough in this question could come from the analysis of the reflectivity spectra time-evolution as the vapor penetration proceeds: this statement is well emphasized by numerical
170
L. De Stefano et al. / Sensors and Actuators B 100 (2004) 168–172
300
Peak shift (nm)
250 Experimental value for Iso-propanol
200
150
100
Full filling of low porosity layers
50
0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Porosity Fig. 2. Calculated wavelength shift of the PSMC peak as a function of the iso-propanol layer liquid fraction.
results reported in Fig. 4: here, the simulated PSMC reflectivity spectra, with respect to the evolution of iso-propanol vapor penetration, are compared for both models considered. The first unlabeled figure at the bottom is relative to the unperturbed microcavity; insets (a), (b) and (c) show the spectrum red-shift as a function of homogeneous filling for several LLF, while insets (d), (e) and (f) illustrate the discrete and inhomogeneous one. In case of homogeneous distribution along the stack (first model), a rigid translation, without any distortion of the spectrum, towards higher wavelengths is clearly pointed out; in the other, the asymmetrical
cavity filling reflects in marked changes of its shape during the process. In fact, when only the first DBR is filled, inset (d), the PSMC is almost completely detuned due to the mismatched DBR reflectivity, therefore the transmittance peak nearly disappeared, and the stop-band is larger. The optical cavity filling, inset (e), causes again the appearance of a sharp resonance peak, but in a rather distorted reflectivity spectrum. In both cases, when the capillary condensation process ends, insets (c) and (f), the reflectivity spectra have the same shape as the unperturbed condition except for the
300
200
Filling DBR #1 150
Filling DBR #2
100
50
{
Peak Shift (nm)
250
Filling cavity 0 0
5
10
15
20
25
Number of layer filled Fig. 3. Calculated peak shift as a function of totally filled layer number.
30
L. De Stefano et al. / Sensors and Actuators B 100 (2004) 168–172
171
Fig. 4. PSMC calculated reflectivity spectra at different filling level: (a), (b) and (c) insets are relative to PSMC homogeneously filled by vapors with LLF of 0.26, 0.52. 0.79, respectively; (d), (e), and (f) insets are relative to discrete and inhomogeneous filling in the following order: only DBR # 1 filled; DBR # 1 plus optical Fabry–P`erot cavity filled and PSMC totally filled. The unlabeled graphic represents the unperturbed cavity spectrum.
transmittance peak which has a greater FWHM, due to the decreased refractive index contrast between the wet high and low porosity layers compared to the dry nhigh /nlow value.
The numerical picture, in the case of a non-homogeneous filling process, does not agree with the experimental results reported in Fig. 5, where the responses of the PSMC under test, recorded at different time instants during the
3.0 1.5
t=561 s
0.0 3.0
Reflectivity (u.a.)
1.5
t=389 s
0.0 3.0 1.5
t=217 s
0.0 3.0 1.5
t=45 s
0.0 3.0 1.5
t=0 s
0.0
1050 1100 1150 1200 1250 1300 1350 1400 1450 1500 1550 1600
W avelength (nm) Fig. 5. Experimental reflectivity spectra registered as function of exposure time.
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L. De Stefano et al. / Sensors and Actuators B 100 (2004) 168–172
seconds and therefore much shorter than those obtainable in other standard gas sensors. Moreover, the sensing technique shows to be completely reversible, which makes the sensor re-usable.
3.5
Iso-propanol gas in
Reflectivity (a. u.)
3.0
References
τid=8.7 s
2.5
τrec=1.7 s
2.0
gas out 1.5 0
50
100
150
200
250
Time (s)
Fig. 6. Single wavelength, time-resolved measurement in the case of iso-propanol.
iso-propanol capillary condensation process, have been plotted. In fact, the measurements, obtained by exposing the PSMC to the vapors generated by 50 l of liquid iso-propanol in a closed vial, show a quite rigid shift of the reflectivity spectrum as a function of the exposure time. The absence of distortions in the spectra is, on the contrary, in fair qualitative agreement with the prediction of homogeneous filling model. In Fig. 6, time resolved reflectivity measurements at the iso-propanol resonance wavelength in the case of PSMC direct exposure to the gas under analysis are depicted: the identification and recovery times are of the order of few
[1] P.A. Snow, E.K. Squire, P.St.J. Russel, L.T. Canham, Vapor sensing using the optical properties of porous silicon Bragg mirrors, J. Appl. Phys. 86 (1999) 1781. [2] V. Mulloni, L. Pavesi, Porous silicon microcavities as optical chemical sensors, Appl. Phys. Lett. 76 (2000) 2523. [3] L. De Stefano, I. Rendina, L. Moretti, A.M. Rossi, Porous silicon microcavities for optical hydrocarbons detection, Sens. Actuat. A 104 (2) (2003) 179–182. [4] L. De Stefano, I. Rendina, L. Moretti, A.M. Rossi, Optical sensing of flammable substances using porous silicon microcavities, Mat. Sci. Eng. B 100 (3) (2003) 271–274. [5] A. Motohashi, M. Kawakami, H. Aoyagi, A. Kinoshita, A. Satou, Gas identification by a single gas sensor using porous silicon as the sensitive material, Jap. J. Appl. Phys. 34 (10) (1995) 5840–5843. [6] H.F. Arrand, A. Loni, R. Arens-Fischer, M.G. Kruger, M. Thoenissen, H. Lueth, S. Kershaw, N.N. Vorazov, Solvent detection using porous silicon optical waveguides, J. Lumin. 80 (1999) 119–123. [7] J. Gao, T. Gao, M.J. Sailor, A porous silicon vapor sensor based on laser interferometry, Appl. Phys. Lett. 77 (2000) 901–903. [8] J.E. Spanier, I.P. Herman, Use of hybrid phenomenological and statistical effective-medium theories of dielectric functions to model the infrared reflectance of porous SiC films, Phys. Rev. 61 (2000) 10437. [9] M.A. Muriel, A. Carballar, Internal field distributions in fiber Bragg gratings, IEEE P. Technol. Lett. 9 (1997) 955. [10] P. Allcock, P.A. Snow, Time-resolved sensing of organic vapors in low modulating porous silicon dielectric mirrors, J. Appl. Phys. 90 (10) (2001) 5052.
Time-resolved sensing of chemical species in porous silicon optical microcavity L. De Stefano a,∗ , L. Moretti b , I. Rendina a , A.M. Rossi c b
a National Council of Research—IMM, via P. Castellino III, 80131 Napoli, Italy DIMET—University “Mediterranea” of Reggio Calabria, Località Feo di Vito, 89060 Reggio Calabria, Italy c Istituto Elettrotecnico Nazionale “G. Ferraris”, Strada delle Cacce 91, Turin, Italy
Available online 18 February 2004
Abstract Time-resolved measurements of red-shifts in the reflectivity spectra of porous silicon multi-layer microcavities, due to exposure to vapor of chemical species, give deep insight about the spatial concentration of the liquid condensed into the pores. Results clearly indicate that capillary condensation starts immediately and proceeds homogeneously all over the stack, yielding a uniform concentration distribution. © 2003 Elsevier B.V. All rights reserved. Keywords: Porous silicon; Optical sensors; Microcavities; Low-dimensional silicon structure
1. Introduction Porous silicon (PS) is, by far, used in sensing applications due to its specific surface area which can be of the order of 500 m2 cm−3 : in this way, a very effective interaction with several chemical and biological matters can be assured. The adsorption of chemical substances into the pores modifies the physical properties of the PS structure, such as its dielectric function, thus optical sensors, based on this technology, can be feasible. In particular, the use of PS microcavities as optical chemical sensors, based on resonant peak shifts measurements in the reflectivity spectra due to capillary condensation of vapors in the silicon pores, have been demonstrated [1–7]. The optical PS microcavity (PSMC) is made of a Fabry–Pèrot cavity of /2-thickness between two distributed Bragg reflectors (DBRs). Several alternating pairs of PS layers, having different refractive indexes, obtained modulating the porosity, constitute the DBRs. Sensitivity and response time, both depending on pore filling dynamic, are key issues in practical use of these kinds of devices. For this reason, in this work, we have studied both numerically and experimentally, the dynamics of sensor response. With this aim, we have recorded time-resolved optical reflection spectra of PS microcavities on exposure to iso-propanol. Then we have compared the experimental results with two different models of pore filling dynamic: one model assumes that the filling of the porous matrix occurs homogeneously ∗ Corresponding author. E-mail address: [email protected] (L. De Stefano).
0925-4005/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.snb.2003.12.044
all over the PS multi-layer structure; on the other hand, the second model hypothesizes that the filling process proceeds non-homogeneously along the stack, starting from the exposed surface of the porous multi-layer structure.
2. Numerical simulations and experimental results The PS microsensor is modeled as a finite multi-layer stack of isotropic two-phase media, silicon and air, on an infinite half-space of bulk Si: the effective dielectric function can be calculated applying the Bruggeman effective medium approximation theory [8]. The reflectivity spectra are reproduced by an optical transfer matrix method, including variation of material properties with wavelength [9]. The physical structure of the device is characterized by alternate layers of different porosities: a concentration gradient of the liquid into the porous matrix might be expected [10]. As we already pointed out, two different models for the filling process have been considered: in the first one, we assume that the eventual partial filling of the porous multi-layer matrix measured during experiments is due to the homogeneous partial filling of each porous layer forming the stack; on the other hand, the second model hypothesizes that, in the case of partial filling of the whole stack, only some layers are completely filled by the condensed vapor. In both cases, the physical effect is an increase of the multi-layer average refractive index, which results in a shift towards longer wavelengths of the microcavity reflectivity spectrum.
L. De Stefano et al. / Sensors and Actuators B 100 (2004) 168–172
169
1.0
Reflectivity (a. u.)
0.9
0.8
0.7
0.6
0.5
Unperturbed cavity After exposure to Iso-propanol
0.4 1275
1300
1325
1350
1375
1400
1425
1450
1475
1500
W avelength (nm) Fig. 1. Reflectivity spectrum of the PSMC after the exposure to iso-propanol.
The experimental set up is very simple: a white source (tungsten lamp, 400 nm < λ < 1800 nm) illuminates, through an optical fiber and a collimator, the microcavity with an angle of incidence of 20◦ respect to the normal. The reflected light is collected by an objective and coupled into a multimode fiber. The signal is directed in an optical spectrum analyser (Ando, Mod. AQ-6315B) and measured with a 0.2 nm resolution. The porous silicon sensor is placed in a closed vial with a quartz window for optical access. Each measurement starts after that a small amount of volatile liquid added to the vial quickly saturates with its vapors the atmosphere surrounding the sensor. In Fig. 1, the experimental red shift measured for iso-propanol is reported. The data refers to a microcavity made of 29 layers, 14 layers for each DBR and one for the optical microcavity. The DBR structures are made alternating high and low porosities layers with 57 and 76% porosity, respectively. More details on the microsensor fabrication processes are reported in [3]. According to the first model, we have to assume that when the PSMC is exposed to chemical vapors, the air in the pores is substituted by the organic molecules due to capillary condensation, so that, at equilibrium, the chemicals vapors fill a certain volume in each layer. The filling process is really homogeneous all over the stack if the air volume is between 0 and the lower porosity value, otherwise, the process proceeds only in high porosity layers. Fig. 2 shows the calculated wavelength shifts () of the transmission peak as a function of liquid layer volume fraction (LLF), i.e. the pore volume filled by liquid, for exposure to iso-propanol. The change of slope for a layer liquid fraction volume of 0.57 corresponds to the complete filling of the low porosity layers. A comparison between the experimental peak shift (λ = 111 nm) and the theoret-
ical one gives a LLF value of 0.26 for iso-propanol (see Fig. 2). Another way to model the vapor penetration into the pores is assuming that the condensed vapor completely fills each layer, replacing all the air into its pores, and the process advances layer by layer from the top (exposed surface) to the bottom of the PSMC. In fact, the PS multilayer exchanges air and vapor with the outside only at the interface between the first layer surface and air. In our case, the stack is composed of 29 layers, so that the filling process can be described as a discrete sequence of 30 steps: (1) empty PSMC, (2) first layer completely filled and rest of PSMC empty, (3) first and second layer completely filled and the rest of PSMC empty, and so on; (30) all the PSMC layers are completely filled. In Fig. 3, the resonance peak shift calculated as a function of the number of layers filled with iso-propanol condensed vapor, is reported. The filling of the first and the second DBR contributes quite asymmetrically to total peak shift. After the first six layer filling we can only observe a small peak shift due to capillary condensation; a more pronounced peak shift happens when each period of the first DBR is completely filled. The Fabry–Pèrot cavity filling, step 15th to 16th, induces a increase of 65 nm. This result outlines the strong influence of the optical cavity (viz., a defect in a periodic structure) on the device sensitivity. In this case, comparing these numerical findings with the peak shift value registered, we can conclude, that only the first DBR has been filled in the experiment. By looking only at the final result of the vapor–PSMC interaction, i.e. the cavity peak shift, there is no way to establish which model is right or wrong between the two proposed. A real breakthrough in this question could come from the analysis of the reflectivity spectra time-evolution as the vapor penetration proceeds: this statement is well emphasized by numerical
170
L. De Stefano et al. / Sensors and Actuators B 100 (2004) 168–172
300
Peak shift (nm)
250 Experimental value for Iso-propanol
200
150
100
Full filling of low porosity layers
50
0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Porosity Fig. 2. Calculated wavelength shift of the PSMC peak as a function of the iso-propanol layer liquid fraction.
results reported in Fig. 4: here, the simulated PSMC reflectivity spectra, with respect to the evolution of iso-propanol vapor penetration, are compared for both models considered. The first unlabeled figure at the bottom is relative to the unperturbed microcavity; insets (a), (b) and (c) show the spectrum red-shift as a function of homogeneous filling for several LLF, while insets (d), (e) and (f) illustrate the discrete and inhomogeneous one. In case of homogeneous distribution along the stack (first model), a rigid translation, without any distortion of the spectrum, towards higher wavelengths is clearly pointed out; in the other, the asymmetrical
cavity filling reflects in marked changes of its shape during the process. In fact, when only the first DBR is filled, inset (d), the PSMC is almost completely detuned due to the mismatched DBR reflectivity, therefore the transmittance peak nearly disappeared, and the stop-band is larger. The optical cavity filling, inset (e), causes again the appearance of a sharp resonance peak, but in a rather distorted reflectivity spectrum. In both cases, when the capillary condensation process ends, insets (c) and (f), the reflectivity spectra have the same shape as the unperturbed condition except for the
300
200
Filling DBR #1 150
Filling DBR #2
100
50
{
Peak Shift (nm)
250
Filling cavity 0 0
5
10
15
20
25
Number of layer filled Fig. 3. Calculated peak shift as a function of totally filled layer number.
30
L. De Stefano et al. / Sensors and Actuators B 100 (2004) 168–172
171
Fig. 4. PSMC calculated reflectivity spectra at different filling level: (a), (b) and (c) insets are relative to PSMC homogeneously filled by vapors with LLF of 0.26, 0.52. 0.79, respectively; (d), (e), and (f) insets are relative to discrete and inhomogeneous filling in the following order: only DBR # 1 filled; DBR # 1 plus optical Fabry–P`erot cavity filled and PSMC totally filled. The unlabeled graphic represents the unperturbed cavity spectrum.
transmittance peak which has a greater FWHM, due to the decreased refractive index contrast between the wet high and low porosity layers compared to the dry nhigh /nlow value.
The numerical picture, in the case of a non-homogeneous filling process, does not agree with the experimental results reported in Fig. 5, where the responses of the PSMC under test, recorded at different time instants during the
3.0 1.5
t=561 s
0.0 3.0
Reflectivity (u.a.)
1.5
t=389 s
0.0 3.0 1.5
t=217 s
0.0 3.0 1.5
t=45 s
0.0 3.0 1.5
t=0 s
0.0
1050 1100 1150 1200 1250 1300 1350 1400 1450 1500 1550 1600
W avelength (nm) Fig. 5. Experimental reflectivity spectra registered as function of exposure time.
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L. De Stefano et al. / Sensors and Actuators B 100 (2004) 168–172
seconds and therefore much shorter than those obtainable in other standard gas sensors. Moreover, the sensing technique shows to be completely reversible, which makes the sensor re-usable.
3.5
Iso-propanol gas in
Reflectivity (a. u.)
3.0
References
τid=8.7 s
2.5
τrec=1.7 s
2.0
gas out 1.5 0
50
100
150
200
250
Time (s)
Fig. 6. Single wavelength, time-resolved measurement in the case of iso-propanol.
iso-propanol capillary condensation process, have been plotted. In fact, the measurements, obtained by exposing the PSMC to the vapors generated by 50 l of liquid iso-propanol in a closed vial, show a quite rigid shift of the reflectivity spectrum as a function of the exposure time. The absence of distortions in the spectra is, on the contrary, in fair qualitative agreement with the prediction of homogeneous filling model. In Fig. 6, time resolved reflectivity measurements at the iso-propanol resonance wavelength in the case of PSMC direct exposure to the gas under analysis are depicted: the identification and recovery times are of the order of few
[1] P.A. Snow, E.K. Squire, P.St.J. Russel, L.T. Canham, Vapor sensing using the optical properties of porous silicon Bragg mirrors, J. Appl. Phys. 86 (1999) 1781. [2] V. Mulloni, L. Pavesi, Porous silicon microcavities as optical chemical sensors, Appl. Phys. Lett. 76 (2000) 2523. [3] L. De Stefano, I. Rendina, L. Moretti, A.M. Rossi, Porous silicon microcavities for optical hydrocarbons detection, Sens. Actuat. A 104 (2) (2003) 179–182. [4] L. De Stefano, I. Rendina, L. Moretti, A.M. Rossi, Optical sensing of flammable substances using porous silicon microcavities, Mat. Sci. Eng. B 100 (3) (2003) 271–274. [5] A. Motohashi, M. Kawakami, H. Aoyagi, A. Kinoshita, A. Satou, Gas identification by a single gas sensor using porous silicon as the sensitive material, Jap. J. Appl. Phys. 34 (10) (1995) 5840–5843. [6] H.F. Arrand, A. Loni, R. Arens-Fischer, M.G. Kruger, M. Thoenissen, H. Lueth, S. Kershaw, N.N. Vorazov, Solvent detection using porous silicon optical waveguides, J. Lumin. 80 (1999) 119–123. [7] J. Gao, T. Gao, M.J. Sailor, A porous silicon vapor sensor based on laser interferometry, Appl. Phys. Lett. 77 (2000) 901–903. [8] J.E. Spanier, I.P. Herman, Use of hybrid phenomenological and statistical effective-medium theories of dielectric functions to model the infrared reflectance of porous SiC films, Phys. Rev. 61 (2000) 10437. [9] M.A. Muriel, A. Carballar, Internal field distributions in fiber Bragg gratings, IEEE P. Technol. Lett. 9 (1997) 955. [10] P. Allcock, P.A. Snow, Time-resolved sensing of organic vapors in low modulating porous silicon dielectric mirrors, J. Appl. Phys. 90 (10) (2001) 5052.