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Refractive index sensor based on the diamond like carbon diffraction grating
Thin Solid Films 519 (2011) 4082–4086
Contents lists available at ScienceDirect
Thin Solid Films j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / t s f
Refractive index sensor based on the diamond like carbon diffraction grating Tomas Tamulevičius ⁎, Rimas Šeperys, Mindaugas Andrulevičius, Vitoldas Kopustinskas, Šarūnas Meškinis, Sigitas Tamulevičius Institute of Materials Science of Kaunas University of Technology, Savanorių Ave. 271, LT-50131, Kaunas, Lithuania
a r t i c l e
i n f o
Available online 20 January 2011 Keywords: SiOx doped DLC Refractive index Sensor Sub-wavelength diffraction grating
a b s t r a c t In this work we present an optical refractive index (RI) sensor based on the spectral analysis of anomalies in the optical response from the diffraction grating employing polarized polychromatic light. The sensor consists of holographic diffraction grating (period 423.5 nm) coated with a thin (110 nm) SiOx doped diamond like carbon film (DLC) that defines sensitivity of the sensor as well as the range of the spectral analysis. The deposition of the DLC film (synthesized by the direct ion beam deposition from the hydrocarbon source) has influence on the shape but not on the position of the anomalies observed in the specular reflection spectrum. From the reflection spectra the RI dispersion curve of liquid analyte–water was obtained. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Diamond like carbon (DLC) films received considerable interest due to their outstanding mechanical, chemical, optical and electrical properties making them useful for a wide range of contemporary applications [1,2]. DLC films can be used as constructional material or protective coating providing necessary properties for the microdevices and extending the range of their possible applications. Optical bandgap [1,3], surface energy [1,3], dielectric [1,2], mechanical [1,4], and many other DLC properties can be easily controlled by changing deposition conditions. Several diamond and DLC applications for the optical devices based on the periodical structures, such as DLC/porous silicon antireflection coating for solar cells [5], phase shift diffraction gratings (DGs) [6], arrays of double-sided lenses [7] and long period optical fiber grating refractive index (RI) sensors [8] have been recently demonstrated. It was reported in [8] that the application of a DLC coating on a fiber with a long period grating which results in the increased sensitivity of the infrared wavelength range RI sensor by 15 times. The abrupt changes in the reflection spectrum from a DG were firstly described more than one hundred years ago by R. W. Wood but the theories explaining this phenomenon quantitatively were deduced just at the end of the last century by several authors [9]. The experimental attempts to use DGs for the determination of RI, absorbance and colloidal particle characterization has been reported [10,11]. Spectral response of the specular reflection from the grating illuminated with a polarized broad band source was analyzed
⁎ Corresponding author. Tel.: +370 37 313432; fax: +370 37 314423. E-mail addresses: [email protected] (T. Tamulevičius), [email protected] (R. Šeperys), [email protected] (M. Andrulevičius), [email protected] (V. Kopustinskas), [email protected] (Š. Meškinis), [email protected] (S. Tamulevičius). 0040-6090/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.tsf.2011.01.099
enabling the sensitivity of the RI changes of 2 · 10− 6 [10]. The RI determination method employing a prism with a grating and a monochromatic light source which provides the accuracy of 1 · 10− 4 is demonstrated in [11]. In our recent work we have reported that the gratings formed in photopolymer [12,13] can be employed for the RI determination and that the deposition of the nanoparticles increases the sensitivity of the method, while the use of the subwavelength grating enables one to determine the RI of the analyte for two different wavelengths by a single measurement. This work is devoted to the analysis of the holographic DG coated with a DLC film that provides sensitivity and inertness to the system [1,3] — it protects the grating formed in the photoresist from the effect of different solvents: such as prevents dissolving, swelling or shrinking of the resist. 2. Theoretical considerations Abrupt changes emerge in the reflectance or transmittance spectra from the DG when the particular condition of illumination creates thresholds at which a transmitted diffraction order is transformed from a propagating to an evanescent one [9,10]. Light diffraction from the periodical structures is described by the DG equation [9]: mλ = dðn1 sin α + n2 sin βm Þ:
ð1Þ
Fig. 1 shows light beam paths and used notations in the case of the transmission DG, consisting of the fused silica (FS)-substrate material and grating material (photoresist coated with DLC) that are in contact with the analyte. When light incident on the subwavelength DG at a critical angle αcr is polychromatic, several wavelengths λcr for different diffraction orders mcr (e.g. ±1) can obey the threshold situation where the light undergoes total internal reflection (TIR) condition — βm =±90° (see Fig. 1 dotted line).
T. Tamulevičius et al. / Thin Solid Films 519 (2011) 4082–4086
Fig. 1. Geometry of the holographic DG and used notations: H and E stand for the magnetic and electrical vectors of the electromagnetic wave, m = 0, ±1, ± 2… is the diffraction order, λ — diffracted wavelength, d — period of the DG, α and βm angles of incidence and diffraction respectively, and n1 and n2 — RI of the substrate medium and the cladding (analyte), respectively.
Using the threshold position (described by mcr, λcr, and αcr) obtained from the spectra it is possible to calculate RI of the analyte (n2) employing Eq. (2) that was derived from the Eq. (1) keeping in mind that sinβm =1: n2 =
mcr λcr −n1 sin αcr : d
ð2Þ
On the other hand, in the experiment it is useful to calculate the threshold angle (or wavelength), when other experimental details are known. Therefore Eq. (1) can be rewritten: αcr = sin
−1
1 mcr λcr −n2 sin βm : n1 d
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Transmittance and reflectance spectra of the DLC film deposited on FS substrates were evaluated employing UV/VIS/NIR Avantes AvaSpec-2048 spectrometer (spectral range (SR): 172–1100 nm, resolution 1.4 nm) and a light source AvaSpec-DHc (SR: 200–2500 nm). The thickness and RI of the DLC film (deposited on Si) were measured by a laser ellipsometer Gaertner L115 (λ = 632.8 nm). The reflected, transmitted and waveguided light from the grating (d = 423.5 nm) was analyzed in a simple optical setup consisting of a white light source (halogen lamp), collimating optics (three FS lenses) and a Glan–Taylor polarizing prism. A fluid cell together with the diffraction grating DG was attached to the goniometric stage (resolution 1′). The spectra were coupled to the optical fiber and the data was collected with the AvaSpec-2048 spectrometer (SR: 360– 860 nm, resolution 1.2 nm). A quartz lens detecting the reflection spectra (standard SMA connector) was fixed on a platform that can be rotated independently around the same axis as the grating. The optical setup can be found in [12,13]. The measured spectra were normalized to the lamp spectrum taking into account different polarizations and integration times. The spectra were collected at different angles of incidence considering the limitations of the optical setup (for the reflected α ≥ 10° and α ≥ 0° for transmitted and waveguided light). To enhance the signal, the first derivative of the reflection coefficient (dR(λ)/dλ) was calculated employing the Savitzky–Golay Smoothing (SGS) procedure, whereby the data was fitted by a second order polynomial expansion and the derivative was obtained by using a 51 point filter [15]. Measurements of the empty cell (air) and cell filled with distilled water were performed at room temperature (18 °C). There were 2 ml of the analyte (water) used for the measurements. The dispersion curves of air [16] and water [17] that were used in the theoretical calculations were taken from the literature.
ð3Þ
The detailed theories quantitatively describing the anomalous properties of the gratings are described elsewhere [9,10]. It should be noted that the number of anomalies emerging in the spectrum depends on the grating material and the RI of the top layer of the grating (in our experiment — DLC coating) is a limiting factor for the range of RI analysis of analyte. 3. Experimental details The sinusoidal profile DGs were formed in a positive tone maP1205 photoresist (Micro resist technology GmbH) spincoated (4000 rpm) on a FS substrate (S5-1) employing interference lithography. The optical setup and experimental details can be found in [14]. We have fabricated the gratings of d = 423.5 and 436.8 nm. The periods of the produced gratings were estimated by optical means measuring the angles of diffraction with a laser diode (λ = 405 nm) [13]. The SiOx doped DLC films were deposited at room temperature by 800 eV energy ion beam using a closed drift direct current ion source from a mixture of the hexamethyldisiloxane (C6H18Si2O — HMDSO) vapor with hydrogen as a feed gas. More experimental details can be found in [2]. The DLC films were deposited on photoresist DGs as well as in parallel on FS and crystalline silicon substrates for the optical characterization of the film. The surface of the DG (d = 436.8 nm, half of the sample was coated with DLC employing a shadow mask) was investigated with a FEI Quanta FEG200 scanning electron microscope (SEM) working in a low vacuum mode (chamber pressure 80 Pa, water vapor). The SEM images were taken for tilted samples (45°) seeking an enhanced spatial impression. Analysis of the SEM images was performed employing ImageJ software.
4. Results By measuring the DLC film deposited on the Si substrate with an ellipsometer we have determined the thickness (t = 110 nm) and RI (n = 1.8 (λ = 632.8 nm)) of the film. Optical transmittance and reflectance spectra of the DLC film deposited on the FS substrates were recorded (see Fig. 2 inset) and the absorption coefficient was calculated (Fig. 2). The results of the SEM analysis of the bulk and DLC coated grating are demonstrated in Fig. 3. The root mean square (rms) of the gray scale intensity profiles along the ridge and the groove of the DG micrographs were calculated.
Fig. 2. Absorption coefficient (abs) of the DLC film versus photon energy calculated employing equation abs = 1/t · ln((1 − R)/T) and measured transmittance (T) and reflectance (R) spectra presented in the inset.
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Fig. 3. SEM micrographs of the bulk DG sample (see inset) and after coating it with a DLC film. The calculated gray scale rms values of the DLC coated DG sample along the line are: on the ridge (r) 138 and on the groove (g) 106. The inset demonstrates bulk grating where rms was evaluated (r — 130 and g — 90) on the same sized magnification micrograph as in the case of the DLC coated DG. Scale bar 1 μm.
The anomalous properties of the spectral response from the grating formed in the photoresist and coated with DLC were investigated by measuring the reflected, transmitted and waveguided light (as shown in Fig. 1). The corresponding spectra for TM and TE polarizations are demonstrated in Fig. 4. The specular reflection from the photoresist grating on the FS substrate before and after deposition of the DLC film was investigated for the different angles of incidence (α = 10°–24°) employing TM and TE polarizations and analyte ambient air (the spectra for TM polarization are demonstrated in Fig. 4 a and for TE polarization — Fig. 4 b). To elucidate influence of the DLC coating on the threshold values (λcr) we have calculated the first derivatives of the spectra employing SGS. To obtain the RI of the analyte, the specular reflection spectra were taken from the grating coated with DLC that was in contact with the analytes: ambient air and water. The first derivative curves obtained for the different angles of incidence and for TM polarization are presented in Fig. 5. Experimentally obtained threshold positions (λcr where the dR(λ)/ dλ = 0 (or has maximum) depending on the shape of the R(λ) [10]) (Fig. 5) in the specular reflection spectra for the different analytes and geometry corresponding to the evanescent waves (m = ±1) were compared with the theoretical values obtained from the Eq. (3) (Fig. 6). An analysis of the anomalies that were originated by the presence of the analyte (air or water) was performed. One could also analyze the anomalies emerging from the effective RI of the grating material but this was not performed in this work. Employing the experimentally determined threshold positions we have obtained the RI dispersion curve of the liquid analyte–water. 5. Discussion According to [2] amorphous carbon films deposited by direct ion beam from HMDSO under the same conditions as described in the experimental part can be referred as DLC films with sp3 bonds that were determined by Raman scattering. It should be noted that deposition of SiOx doped DLC films employing hydrogen as a feed gas enables to control RI and provides a broad optical band gap (3.12– 3.58 eV) [3]. The absorption coefficient of such DLC film, deposited on the FS substrate possesses a broad transmission window starting from 400 nm (3 eV) (where the transmittance becomes constant in the
Fig. 4. Spectral composition of the reflected (R), transmitted (T) and waveguided (WG) (for m = − 1 and m = + 1 diffraction orders) light measured (for α = 10°–16°, increment 2°) for TM (a) and TE (b) polarizations from the grating coated with the DLC film. Truncated lines represent the measurements of the bulk grating and solid lines — grating coated with DLC.
measured spectral window and reaches 90%) (Fig. 2). One can conclude that DLC film used in our spectroscopic device provides accurate measurements in the 400–900 nm range. The interference fringes in the short wavelength region (200–400 nm) of the reflectance spectra show a common behavior of the thin film [6]. From the SEM micrographs of the tilted grating sample (see Fig. 3) we have observed only small changes of the shape and roughness of the sinusoidal profile grating after deposition of DLC. By measuring the height of the surface features present perpendicularly to the grating grooves one can roughly estimate that the grating coated with DLC had slightly shrunk (height of the ridge was reduced approximately by 13%) after the deposition of the coating. The roughening of the surface after the deposition of the coating (rms value of the gray scale intensity profile along the line on the groove increased by 18%, while along the top of the ridge was almost the same) could be addressed to the effect of ion bombardment as described in [18]. In addition, changes of the profile form (in plane and out of plane shrinkage) could be due to residual tensile stress in the DLC film, which has been reported to be in the range of 0.07–0.15 GPa [4]. According to the specular reflection from the grating (analyte ambient air) measured before and after the deposition of DLC (at the same place of the sample), it was found that at different angles of incidence, the positions of the anomalies in the reflection spectra do not change but the shape of the anomalies does change (see Fig. 4). Such behavior of the grating was expected, because the threshold
T. Tamulevičius et al. / Thin Solid Films 519 (2011) 4082–4086
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spectrum in the case of TM polarization at 700 nm of the grating coated with DLC is better expressed than in case for the bulk grating. The anomalous response of the grating can be investigated in all three (reflected, transmitted and waveguided light) modes in the wavelength range (400–900 nm) (Fig. 4). Moreover all three modes can be employed for the RI determination. Maximum sensitivity of the method was obtained employing TM polarization (like in [12,13]) and the reflection mode that was used in further investigations. The critical wavelength positions of the anomalies in the reflection spectrum which were determined from the experimental measurements when the grating was in contact with air (Fig. 5 a) and with water (Fig. 5 b) are in good correlation with the results obtained according to Eq. (3) (see Fig. 6). One can see that in case of the analyte water there exist two positions in the α(λ) dependence (Fig. 6) that are explained by the existence of two diffraction maxima (−1: empty triangles and + 1: empty squares) that undergo the TIR condition. Using the experimentally determined threshold values (from Fig. 6) we have calculated the dispersion curve of the analyte (water) employing Eq. (2) (see inset of Fig. 6) that is in good correspondence with the theoretical one [17]. Taking into account the spectrometer resolution, the goniometer readout and the uncertainty of the DG period we have estimated the uncertainty of the RI determination method that was equal to 4.1 · 10− 3. The experimentally obtained RI values were within the limits of the calculated uncertainties. Moreover the DLC coated grating provided stable results for the multiple measurements related to the multiple refilling of the cell with the analyte. No changes in the geometry and as a result in the reflection spectra were detected due to the exposure of the grating to the typical reagents used in the photolithography procedures. 6. Conclusions
Fig. 5. The first derivative of specular reflection spectra (calculated employing SGS) of the DLC coated grating in contact with air (a) and water (b) measured for different angles of incidence (10°–20°) employing TM polarization.
position (λcr) depends on the period of grating and the angle of incidence, while the influence of the profile shape and material does change the general character of the anomalies (R(λ) or dR(λ)/dλ) in the spectrum [9,10]. One can see (Fig. 4) that the anomaly in the specular reflection
We have shown that our system–sinusoidal profile sub wavelength DG formed in the photoresist on FS and coated with a thin SiOx doped DLC layer (110 nm, n = 1.8)–is suitable for sensing of the changes of the RI (analyte water). Deposition of the DLC film has influence on the shape of the reflection coefficient but not on the position of the anomalies observed in the spectrum of specular reflection. It is shown that the grating sensor can be employed for both TM and TE polarizations in three different modes where the anomalies in the reflected, transmitted and waveguided light can be detected. Measurements at many angles of incidence enable to define the RI dispersion curve of the analyte. The DLC coating ensures chemical inertness of the system preserving the spectral range necessary for the measurement. Acknowledgements This research was funded by a grant (No. MIP-80/2010) from the Research Council of Lithuania and COST Actions MP0604 and MP0803. T.T. acknowledges Lithuanian State Studies Foundation for the PhD student scholarship. References
Fig. 6. Experimentally determined threshold positions (dots, increment 2°) obtained for the TM polarization of different analytes (air and water) and theoretical functions αcr (λcr) (solid and truncated lines) calculated with Eq. (3). RI dispersion curve of water calculated employing Eq. (2) is given in the inset.
[1] J. Robertson, Mater. Sci. Eng. R 37 (2002) 129. [2] Š. Meškinis, K. Šlapikas, R. Gudaitis, S. Tamulevičius, V. Kopustinskas, A. Guobienė, G. Niaura, Vacuum 82 (2008) 617. [3] Š. Meškinis, V. Kopustinskas, K. Šlapikas, S. Tamulevičius, A. Guobienė, R. Gudaitis, V. Grigaliūnas, Thin Solid Films 515 (2006) 636. [4] Š. Meškinis, S. Tamulevičius, V. Kopustinskas, A. Gudonytė, V. Grigaliūnas, J. Jankauskas, R. Gudaitis, Mater. Sci. Medžiagotyra 15 (2009) 201. [5] K. Ait-hamouda, A. Ababou, N. Gabouze, Mater. Sci. Forum 609 (2009) 172. [6] G.A. Cirino, R.D. Mansano, P. Verdonck, R.G. Jasinevicius, L.G. Neto, Surf. Coat. Technol. 204 (2010) 2966. [7] C.L. Lee, M.D. Dawson, E. Gu, Opt. Mater. 32 (2010) 1123. [8] M. Smietana, J. Szmidt, M.L. Korwin-Pawlowski, W.J. Bock, J. Grabarczyk, Diamond Relat. Mater. 16 (2007) 1374. [9] E.G. Loewen, E. Popov, Diffraction Gratings and Applications, Marcel Dekker Inc., New York, 1997. [10] B.B. Anderson, A.M. Brodsky, L.W. Burgess, Anal. Chem. 68 (1996) 1081.
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[11] S. Sainov, Rev. Sci. Instrum. 62 (1991) 3106. [12] A. Šileikaitė, T. Tamulevičius, S. Tamulevičius, M. Andrulevičius, J. Puišo, A. Guobienė, I. Prosyčevas, M. Madsen, C. Maibohm, H.G. Rubahn, in: David L. Andrews, Nunzi Jean-Michel, Ostendorf Andreas (Eds.), Proceedings of SPIE, Nanophotonics II, 6988, 2008, p. 69881Q. [13] T. Tamulevičius, M. Andrulevičius, A. Šileikaitė, L. Puodžiukynas, V. Morkūnas, S. Tamulevičius, in: A. Grigonis (Ed.), Radiation Interaction with Material and its Use in Technologies 2008, Kaunas Univ Technology Press, Kaunas, 2008, p. 66.
[14] T. Tamulevičius, S. Tamulevičius, M. Andrulevičius, A. Guobienė, L. Puodžiukynas, G. Janušas, E. Griškonis, Mater. Sci. Medžiagotyra 13 (2007) 183. [15] A. Savitzky, M.J.E. Golay, Anal. Chem. 36 (1964) 1627. [16] B. Edlén, Metrologia 2 (1966) 71. [17] D.J. Segelstein, M. S. Thesis, University of Missouri-Kansas City, 1981. [18] D. Nest, T.-Y. Chung, D.B. Graves, S. Engelmann, R.L. Bruce, F. Weilnboeck, G.S. Oehrlein, D. Wang, C. Andes, E.A. Hudson, Plasma Processes Polym. 6 (2009) 649.
Contents lists available at ScienceDirect
Thin Solid Films j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / t s f
Refractive index sensor based on the diamond like carbon diffraction grating Tomas Tamulevičius ⁎, Rimas Šeperys, Mindaugas Andrulevičius, Vitoldas Kopustinskas, Šarūnas Meškinis, Sigitas Tamulevičius Institute of Materials Science of Kaunas University of Technology, Savanorių Ave. 271, LT-50131, Kaunas, Lithuania
a r t i c l e
i n f o
Available online 20 January 2011 Keywords: SiOx doped DLC Refractive index Sensor Sub-wavelength diffraction grating
a b s t r a c t In this work we present an optical refractive index (RI) sensor based on the spectral analysis of anomalies in the optical response from the diffraction grating employing polarized polychromatic light. The sensor consists of holographic diffraction grating (period 423.5 nm) coated with a thin (110 nm) SiOx doped diamond like carbon film (DLC) that defines sensitivity of the sensor as well as the range of the spectral analysis. The deposition of the DLC film (synthesized by the direct ion beam deposition from the hydrocarbon source) has influence on the shape but not on the position of the anomalies observed in the specular reflection spectrum. From the reflection spectra the RI dispersion curve of liquid analyte–water was obtained. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Diamond like carbon (DLC) films received considerable interest due to their outstanding mechanical, chemical, optical and electrical properties making them useful for a wide range of contemporary applications [1,2]. DLC films can be used as constructional material or protective coating providing necessary properties for the microdevices and extending the range of their possible applications. Optical bandgap [1,3], surface energy [1,3], dielectric [1,2], mechanical [1,4], and many other DLC properties can be easily controlled by changing deposition conditions. Several diamond and DLC applications for the optical devices based on the periodical structures, such as DLC/porous silicon antireflection coating for solar cells [5], phase shift diffraction gratings (DGs) [6], arrays of double-sided lenses [7] and long period optical fiber grating refractive index (RI) sensors [8] have been recently demonstrated. It was reported in [8] that the application of a DLC coating on a fiber with a long period grating which results in the increased sensitivity of the infrared wavelength range RI sensor by 15 times. The abrupt changes in the reflection spectrum from a DG were firstly described more than one hundred years ago by R. W. Wood but the theories explaining this phenomenon quantitatively were deduced just at the end of the last century by several authors [9]. The experimental attempts to use DGs for the determination of RI, absorbance and colloidal particle characterization has been reported [10,11]. Spectral response of the specular reflection from the grating illuminated with a polarized broad band source was analyzed
⁎ Corresponding author. Tel.: +370 37 313432; fax: +370 37 314423. E-mail addresses: [email protected] (T. Tamulevičius), [email protected] (R. Šeperys), [email protected] (M. Andrulevičius), [email protected] (V. Kopustinskas), [email protected] (Š. Meškinis), [email protected] (S. Tamulevičius). 0040-6090/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.tsf.2011.01.099
enabling the sensitivity of the RI changes of 2 · 10− 6 [10]. The RI determination method employing a prism with a grating and a monochromatic light source which provides the accuracy of 1 · 10− 4 is demonstrated in [11]. In our recent work we have reported that the gratings formed in photopolymer [12,13] can be employed for the RI determination and that the deposition of the nanoparticles increases the sensitivity of the method, while the use of the subwavelength grating enables one to determine the RI of the analyte for two different wavelengths by a single measurement. This work is devoted to the analysis of the holographic DG coated with a DLC film that provides sensitivity and inertness to the system [1,3] — it protects the grating formed in the photoresist from the effect of different solvents: such as prevents dissolving, swelling or shrinking of the resist. 2. Theoretical considerations Abrupt changes emerge in the reflectance or transmittance spectra from the DG when the particular condition of illumination creates thresholds at which a transmitted diffraction order is transformed from a propagating to an evanescent one [9,10]. Light diffraction from the periodical structures is described by the DG equation [9]: mλ = dðn1 sin α + n2 sin βm Þ:
ð1Þ
Fig. 1 shows light beam paths and used notations in the case of the transmission DG, consisting of the fused silica (FS)-substrate material and grating material (photoresist coated with DLC) that are in contact with the analyte. When light incident on the subwavelength DG at a critical angle αcr is polychromatic, several wavelengths λcr for different diffraction orders mcr (e.g. ±1) can obey the threshold situation where the light undergoes total internal reflection (TIR) condition — βm =±90° (see Fig. 1 dotted line).
T. Tamulevičius et al. / Thin Solid Films 519 (2011) 4082–4086
Fig. 1. Geometry of the holographic DG and used notations: H and E stand for the magnetic and electrical vectors of the electromagnetic wave, m = 0, ±1, ± 2… is the diffraction order, λ — diffracted wavelength, d — period of the DG, α and βm angles of incidence and diffraction respectively, and n1 and n2 — RI of the substrate medium and the cladding (analyte), respectively.
Using the threshold position (described by mcr, λcr, and αcr) obtained from the spectra it is possible to calculate RI of the analyte (n2) employing Eq. (2) that was derived from the Eq. (1) keeping in mind that sinβm =1: n2 =
mcr λcr −n1 sin αcr : d
ð2Þ
On the other hand, in the experiment it is useful to calculate the threshold angle (or wavelength), when other experimental details are known. Therefore Eq. (1) can be rewritten: αcr = sin
−1
1 mcr λcr −n2 sin βm : n1 d
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Transmittance and reflectance spectra of the DLC film deposited on FS substrates were evaluated employing UV/VIS/NIR Avantes AvaSpec-2048 spectrometer (spectral range (SR): 172–1100 nm, resolution 1.4 nm) and a light source AvaSpec-DHc (SR: 200–2500 nm). The thickness and RI of the DLC film (deposited on Si) were measured by a laser ellipsometer Gaertner L115 (λ = 632.8 nm). The reflected, transmitted and waveguided light from the grating (d = 423.5 nm) was analyzed in a simple optical setup consisting of a white light source (halogen lamp), collimating optics (three FS lenses) and a Glan–Taylor polarizing prism. A fluid cell together with the diffraction grating DG was attached to the goniometric stage (resolution 1′). The spectra were coupled to the optical fiber and the data was collected with the AvaSpec-2048 spectrometer (SR: 360– 860 nm, resolution 1.2 nm). A quartz lens detecting the reflection spectra (standard SMA connector) was fixed on a platform that can be rotated independently around the same axis as the grating. The optical setup can be found in [12,13]. The measured spectra were normalized to the lamp spectrum taking into account different polarizations and integration times. The spectra were collected at different angles of incidence considering the limitations of the optical setup (for the reflected α ≥ 10° and α ≥ 0° for transmitted and waveguided light). To enhance the signal, the first derivative of the reflection coefficient (dR(λ)/dλ) was calculated employing the Savitzky–Golay Smoothing (SGS) procedure, whereby the data was fitted by a second order polynomial expansion and the derivative was obtained by using a 51 point filter [15]. Measurements of the empty cell (air) and cell filled with distilled water were performed at room temperature (18 °C). There were 2 ml of the analyte (water) used for the measurements. The dispersion curves of air [16] and water [17] that were used in the theoretical calculations were taken from the literature.
ð3Þ
The detailed theories quantitatively describing the anomalous properties of the gratings are described elsewhere [9,10]. It should be noted that the number of anomalies emerging in the spectrum depends on the grating material and the RI of the top layer of the grating (in our experiment — DLC coating) is a limiting factor for the range of RI analysis of analyte. 3. Experimental details The sinusoidal profile DGs were formed in a positive tone maP1205 photoresist (Micro resist technology GmbH) spincoated (4000 rpm) on a FS substrate (S5-1) employing interference lithography. The optical setup and experimental details can be found in [14]. We have fabricated the gratings of d = 423.5 and 436.8 nm. The periods of the produced gratings were estimated by optical means measuring the angles of diffraction with a laser diode (λ = 405 nm) [13]. The SiOx doped DLC films were deposited at room temperature by 800 eV energy ion beam using a closed drift direct current ion source from a mixture of the hexamethyldisiloxane (C6H18Si2O — HMDSO) vapor with hydrogen as a feed gas. More experimental details can be found in [2]. The DLC films were deposited on photoresist DGs as well as in parallel on FS and crystalline silicon substrates for the optical characterization of the film. The surface of the DG (d = 436.8 nm, half of the sample was coated with DLC employing a shadow mask) was investigated with a FEI Quanta FEG200 scanning electron microscope (SEM) working in a low vacuum mode (chamber pressure 80 Pa, water vapor). The SEM images were taken for tilted samples (45°) seeking an enhanced spatial impression. Analysis of the SEM images was performed employing ImageJ software.
4. Results By measuring the DLC film deposited on the Si substrate with an ellipsometer we have determined the thickness (t = 110 nm) and RI (n = 1.8 (λ = 632.8 nm)) of the film. Optical transmittance and reflectance spectra of the DLC film deposited on the FS substrates were recorded (see Fig. 2 inset) and the absorption coefficient was calculated (Fig. 2). The results of the SEM analysis of the bulk and DLC coated grating are demonstrated in Fig. 3. The root mean square (rms) of the gray scale intensity profiles along the ridge and the groove of the DG micrographs were calculated.
Fig. 2. Absorption coefficient (abs) of the DLC film versus photon energy calculated employing equation abs = 1/t · ln((1 − R)/T) and measured transmittance (T) and reflectance (R) spectra presented in the inset.
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Fig. 3. SEM micrographs of the bulk DG sample (see inset) and after coating it with a DLC film. The calculated gray scale rms values of the DLC coated DG sample along the line are: on the ridge (r) 138 and on the groove (g) 106. The inset demonstrates bulk grating where rms was evaluated (r — 130 and g — 90) on the same sized magnification micrograph as in the case of the DLC coated DG. Scale bar 1 μm.
The anomalous properties of the spectral response from the grating formed in the photoresist and coated with DLC were investigated by measuring the reflected, transmitted and waveguided light (as shown in Fig. 1). The corresponding spectra for TM and TE polarizations are demonstrated in Fig. 4. The specular reflection from the photoresist grating on the FS substrate before and after deposition of the DLC film was investigated for the different angles of incidence (α = 10°–24°) employing TM and TE polarizations and analyte ambient air (the spectra for TM polarization are demonstrated in Fig. 4 a and for TE polarization — Fig. 4 b). To elucidate influence of the DLC coating on the threshold values (λcr) we have calculated the first derivatives of the spectra employing SGS. To obtain the RI of the analyte, the specular reflection spectra were taken from the grating coated with DLC that was in contact with the analytes: ambient air and water. The first derivative curves obtained for the different angles of incidence and for TM polarization are presented in Fig. 5. Experimentally obtained threshold positions (λcr where the dR(λ)/ dλ = 0 (or has maximum) depending on the shape of the R(λ) [10]) (Fig. 5) in the specular reflection spectra for the different analytes and geometry corresponding to the evanescent waves (m = ±1) were compared with the theoretical values obtained from the Eq. (3) (Fig. 6). An analysis of the anomalies that were originated by the presence of the analyte (air or water) was performed. One could also analyze the anomalies emerging from the effective RI of the grating material but this was not performed in this work. Employing the experimentally determined threshold positions we have obtained the RI dispersion curve of the liquid analyte–water. 5. Discussion According to [2] amorphous carbon films deposited by direct ion beam from HMDSO under the same conditions as described in the experimental part can be referred as DLC films with sp3 bonds that were determined by Raman scattering. It should be noted that deposition of SiOx doped DLC films employing hydrogen as a feed gas enables to control RI and provides a broad optical band gap (3.12– 3.58 eV) [3]. The absorption coefficient of such DLC film, deposited on the FS substrate possesses a broad transmission window starting from 400 nm (3 eV) (where the transmittance becomes constant in the
Fig. 4. Spectral composition of the reflected (R), transmitted (T) and waveguided (WG) (for m = − 1 and m = + 1 diffraction orders) light measured (for α = 10°–16°, increment 2°) for TM (a) and TE (b) polarizations from the grating coated with the DLC film. Truncated lines represent the measurements of the bulk grating and solid lines — grating coated with DLC.
measured spectral window and reaches 90%) (Fig. 2). One can conclude that DLC film used in our spectroscopic device provides accurate measurements in the 400–900 nm range. The interference fringes in the short wavelength region (200–400 nm) of the reflectance spectra show a common behavior of the thin film [6]. From the SEM micrographs of the tilted grating sample (see Fig. 3) we have observed only small changes of the shape and roughness of the sinusoidal profile grating after deposition of DLC. By measuring the height of the surface features present perpendicularly to the grating grooves one can roughly estimate that the grating coated with DLC had slightly shrunk (height of the ridge was reduced approximately by 13%) after the deposition of the coating. The roughening of the surface after the deposition of the coating (rms value of the gray scale intensity profile along the line on the groove increased by 18%, while along the top of the ridge was almost the same) could be addressed to the effect of ion bombardment as described in [18]. In addition, changes of the profile form (in plane and out of plane shrinkage) could be due to residual tensile stress in the DLC film, which has been reported to be in the range of 0.07–0.15 GPa [4]. According to the specular reflection from the grating (analyte ambient air) measured before and after the deposition of DLC (at the same place of the sample), it was found that at different angles of incidence, the positions of the anomalies in the reflection spectra do not change but the shape of the anomalies does change (see Fig. 4). Such behavior of the grating was expected, because the threshold
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spectrum in the case of TM polarization at 700 nm of the grating coated with DLC is better expressed than in case for the bulk grating. The anomalous response of the grating can be investigated in all three (reflected, transmitted and waveguided light) modes in the wavelength range (400–900 nm) (Fig. 4). Moreover all three modes can be employed for the RI determination. Maximum sensitivity of the method was obtained employing TM polarization (like in [12,13]) and the reflection mode that was used in further investigations. The critical wavelength positions of the anomalies in the reflection spectrum which were determined from the experimental measurements when the grating was in contact with air (Fig. 5 a) and with water (Fig. 5 b) are in good correlation with the results obtained according to Eq. (3) (see Fig. 6). One can see that in case of the analyte water there exist two positions in the α(λ) dependence (Fig. 6) that are explained by the existence of two diffraction maxima (−1: empty triangles and + 1: empty squares) that undergo the TIR condition. Using the experimentally determined threshold values (from Fig. 6) we have calculated the dispersion curve of the analyte (water) employing Eq. (2) (see inset of Fig. 6) that is in good correspondence with the theoretical one [17]. Taking into account the spectrometer resolution, the goniometer readout and the uncertainty of the DG period we have estimated the uncertainty of the RI determination method that was equal to 4.1 · 10− 3. The experimentally obtained RI values were within the limits of the calculated uncertainties. Moreover the DLC coated grating provided stable results for the multiple measurements related to the multiple refilling of the cell with the analyte. No changes in the geometry and as a result in the reflection spectra were detected due to the exposure of the grating to the typical reagents used in the photolithography procedures. 6. Conclusions
Fig. 5. The first derivative of specular reflection spectra (calculated employing SGS) of the DLC coated grating in contact with air (a) and water (b) measured for different angles of incidence (10°–20°) employing TM polarization.
position (λcr) depends on the period of grating and the angle of incidence, while the influence of the profile shape and material does change the general character of the anomalies (R(λ) or dR(λ)/dλ) in the spectrum [9,10]. One can see (Fig. 4) that the anomaly in the specular reflection
We have shown that our system–sinusoidal profile sub wavelength DG formed in the photoresist on FS and coated with a thin SiOx doped DLC layer (110 nm, n = 1.8)–is suitable for sensing of the changes of the RI (analyte water). Deposition of the DLC film has influence on the shape of the reflection coefficient but not on the position of the anomalies observed in the spectrum of specular reflection. It is shown that the grating sensor can be employed for both TM and TE polarizations in three different modes where the anomalies in the reflected, transmitted and waveguided light can be detected. Measurements at many angles of incidence enable to define the RI dispersion curve of the analyte. The DLC coating ensures chemical inertness of the system preserving the spectral range necessary for the measurement. Acknowledgements This research was funded by a grant (No. MIP-80/2010) from the Research Council of Lithuania and COST Actions MP0604 and MP0803. T.T. acknowledges Lithuanian State Studies Foundation for the PhD student scholarship. References
Fig. 6. Experimentally determined threshold positions (dots, increment 2°) obtained for the TM polarization of different analytes (air and water) and theoretical functions αcr (λcr) (solid and truncated lines) calculated with Eq. (3). RI dispersion curve of water calculated employing Eq. (2) is given in the inset.
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