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Determination of optical parameters of organic and inorganic thin films using both surface plasmon resonance and Abelès-Brewster methods
Optik 142 (2017) 426–435
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Optik journal homepage: www.elsevier.de/ijleo
Original research article
Determination of optical parameters of organic and inorganic thin films using both surface plasmon resonance and Abelès-Brewster methods Y.M. Espinosa-Sánchez a,∗ , D. Luna-Moreno a , M. Rodríguez-Delgado b , A. Sánchez-Álvarez c a
Centro de Investigaciones en Óptica A. C., A. P. 1-948, León, Gto, 37150, Mexico Laboratorio de Nanotecnología Ambiental, Centro del Agua para América Latina y el Caribe, Tecnológico de Monterrey, Monterrey, Nuevo León 64849, Mexico c Universidad Tecnológica de León, Blvd. Universidad Tecnológica #225, Col. San Carlos, León, Gto, 37670, Mexico b
a r t i c l e
i n f o
Article history: Received 15 December 2016 Received in revised form 6 April 2017 Accepted 28 May 2017 Keywords: Plasmons Optical constants Optical properties of surfaces
a b s t r a c t We present two methods to characterize organic and inorganic thin films. The thin films characterization was performed employing an opto-mechanical system, which uses light with p polarization from a He-Ne laser operating at 632.8 nm. This system is based on the methods of Abelès-Brewster and surface plasmon resonance in the prism-based Kretschmann configuration. The metallic thin films characterization is made using surface plasmon resonance method while dielectric thin films (organic and inorganic) are characterized using both methods The optical parameters were obtained through a LabVIEW program based on the Fresnel equations by matrix method. The proposed system was proved through the optical characterization of gold, zinc sulfide and bovine serum albumin thin films with a fast, simple and accurate response and the optical parameters were obtained for each tested film. The refractive index and extinction coefficient values obtained for the gold thin film were 0.1758 and 3.3895, respectively, with a thickness of 53 nm; a refractive index of 2.3501 was measured for the zinc sulfide thin film showing a thicknesses of 28.42 nm; meanwhile bovine serum albumin presented a refractive index of 1.5595 with a thickness of 143.75 nm. © 2017 Elsevier GmbH. All rights reserved.
1. Introduction Nowadays there are many ways to measure the optical properties of a thin film, but before choosing a method firstly should be considered that usually, the optical properties of a thin film are quite different from those of the bulk material [1,2]. The study of the optical properties of thin films has been widely reported using different methods. However, the difference in the reported results between works, even using the same techniques, has revealed the complexity of this kind of study
∗ Corresponding author. E-mail addresses: [email protected], [email protected] (Y.M. Espinosa-Sánchez), [email protected] (D. Luna-Moreno), [email protected] (M. Rodríguez-Delgado), [email protected] (A. Sánchez-Álvarez). http://dx.doi.org/10.1016/j.ijleo.2017.05.090 0030-4026/© 2017 Elsevier GmbH. All rights reserved.
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[3]. e.g., the refractive index of thin films strongly depends on the deposition technique [4–7]; yielding a different surface morphology response depending on the method employed [8]. Since the refractive index of a thin film is an indirect measurement, the use of fitting models that matches the measured data in order to estimate the optical constants is common [9–13]. Almost as important as the model is the accuracy of the actual measurements. The calibration verification is an indispensable step in the measurement of the performance that will be used for the optical constant extraction [14]. The most commonly used methods to measure the optical properties of thin films are reflectance and transmittance [13–15], ellipsometry [16], and surface plasmon resonance (SPR) methods, for metallic [17,18] and dielectric [19] flat thin film or for a cylindrical thin film over a fiber optic [10]. Each one of these techniques has their own advantages and can complement each other. It is known that the main application of thin films is in the fields of sensing and biosensing [20], in this sense, the thin films characterization plays a determinant role because the optical parameters control guarantees a better performance of the thin films. Also, these parameters are responsible for the refractive indexes range that the sensor will be capable of detecting, as well as the resolution in which the refractive index changes can be detected. In this work is used a –2 opto-mechanical system with two motorized rotation stages of 0.01◦ of angular resolution to scan the reflected light from the sample, using light with p polarization of a He-Ne laser centered at 632.8 nm. The system is based on the Abelès-Brewster (A-B) and SPR methods, which stand out for their simplicity and rather high sensitivity. Through them is possible to obtain the optical parameters (refractive index and thickness) of dielectric (organic and inorganic) and metallic thin films that produce surface plasmon wave. The system, in the SPR method, uses the prism coupling in the Kretschmann configuration, in which a prism with is interconnected with a waveguide metal-dielectric, which is composed of a metallic thin film and a dielectric [21]. The potential of SPR for characterization of thin films and monitoring processes at metal interfaces was recognized in the late seventies [20]. The unique combination of an extremely high sensitivity to optical properties of surface layers and the ease of their real time continuous monitoring are the main advantage of the SPR over other optical techniques [22]. The A-B technique is one of the most popular for the determination of the optical thin film refractive index. The method consists of illuminating regions of a substrate with and without thin film coating with laser light with p polarization. The incidence angle is scanned to find the angle of common reflectance for the substrate and the coating, so the angle of convergence will be the Brewster angle for the thin film coating. The refractive index of the thin film is estimated by applying the tangent of the Brewster angle (n = tan B ) [23]. The achievement of this work is that the fact of using the methods separately and combining them makes possible to obtain reliable, accurate and fast results. Furthermore, a wide range of refractive indexes and/or very thin thicknesses of films can be measured even without a previous knowledge of the thin film or sample to be measured. This wide range of tuning is reached using prisms or substrates of different refractive indexes. e.g., glasses of BK7, SK16 and SF6 with refractive indexes of 1.51509, 1.62041 and 1.7988 [24] respectively. To obtain the refractive index (real and complex part) and thickness of a metallic thin film the SPR method is used followed by a fitting process. To get the optical parameters for a dielectric (organic and inorganic) thin film, both methods are used, A-B method for the refractive index and SPR method for the thickness. By measuring in this way more accurate results can be obtained. This because the presence of many variables makes the fitting process more complicated, so having found the refractive index (using the A-B method), the only parameter to be found with the fitting process will be the thickness, which ensures faster and more accurate measurements. Two inorganic thin films, metallic (gold, Au) and dielectric (zinc sulfide, ZnS); and an organic film (bovine serum albumin, BSA) were chosen as models to determine the efficiency of the system proposed. 2. Theoretical SPR curve The optical reflection of multilayer thin film was estimated by the matrix method, which transfers the electric and magnetic fields parallel to each interface (tangential components) from the rear to the front of the assembly of the SPR phenomena in the Kretschmann configuration. The electric and magnetic fields are expressed as column vectors, and each film as a transfer matrix, thus the calculus involves successive multiplications of the column vectors by the transfer matrix. The final amplitudes are associated with the transmitted wave since there is no returning wave in the emergent medium [14]. The characteristic matrix of the thin film system is expressed as shown in Eq. (1)
B
C
=
k j=1
⎡ ⎣
cos ıj i sin ıj
i sin ıj j cos ıj
⎤
⎦ 1 ,
(1)
s
where optical admittance of the jth layer film is j = nj / cos j for TM polarization and j = nj cos j for TE polarization
and s is the optical admittance of the substrate or sample medium (s = ns / cos s for TM polarization and S = ns cos s for TE polarization). B and C represent the amplitude of the normalized electric and magnetic fields, respectively, ıj is the
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Fig. 1. Experimental setup for SPR measurement in the Kretschmann configuration.
phase thickness (given for, ıj = 2nj dj cos j /), d is the physical thickness, n is the refractive index of the thin film, ns is the refractive index of the substrate or sample medium, is the wavelength, and is the angle for the incident medium. Y is the admittance of the assembly system (Y = C/B). The reflectance amplitude is given by Eq. (2), r=
0 − Y , 0 + Y
(2)
and the Reflectance is expressed by Eq. (3), R = |r|2 = |
0 − Y 2 | , 0 + Y
(3)
where n0 is the refractive index of the incident medium, which in this case corresponds to a prism. The problem is then reduced to finding the reflectance of the simple ideal interface between an incident medium n0 and a medium of admittance Y. The refractive index and thickness calculus of the thin films were found by fitting the theoretical and experimental curves. Let R (, d, n, ) be the reflectance function. Where is the incidence angle, d is the thickness, n is the refractive index and is the wavelength. Initially, we have M experimental data organized as ( k , R k )for1 ≤ k ≤ M
(4)
where Rk depends on dk and nk (thickness and refractive index of the layers, respectively). But, some of them are unknown values and must be calculated. This is accomplished by finding the parameters which make the curve fit the experimental data. In order to find the curve that best fits the experimental data, the function F was constructed. F=
M
R k , ds , ns , − Rk
2
(5)
k=1
Clearly, the optimal dk and nk values to minimize F must satisfy Eq. (6)
∂F ∂F = =0 ∂ds ∂ns
(6)
To determine the reflectance parameters of the experimental curve obtained with the system, the curve was approximated by least squares fitting the unconstrained nonlinear parameter optimization. The Nelder-Mead algorithm simplex direct search using derivative-free method was used [25,26]. 3. Experimental section 3.1. Instrumental configuration The arrangement used for SPR measurements was the Kretschmann configuration, as shown in Fig. 1. Under this scheme, a prism was mounted on a rotation stage (). The photodetector was set in a different rotation stage (2), to capture the
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Fig. 2. Schematic diagram for the Abelès-Brewster method.
reflected signal through the prism. A polarized He-Ne laser (Uniphase mod. 1101P), centered at 632.8 nm of 1.5 mw of minimum output power, and minimum polarization ratio of 500:1 was launched into a hemicylindrical shaped prism with its flat face looking downward to validate normal incidence. The advantage of using a hemicylindrical prism is that the refraction problem is avoided. Other types of prisms, which show this problem, have the drawback of giving a limited dynamic range that could be unsuitable for high refractive index measurement. The experimental setup was also adapted to use the Abelès-Brewster method, illustrated in Fig. 2. 3.2. Measurement of experimental SPR curves The theoretical SPR curve for a gold thin film over a BK7 prism was calculated using a LabVIEW program, which is based on the matrix method. A thin film of 50 nm of gold was deposited by means of thermal evaporation in a vacuum chamber onto two BK7 hemicylindrical prisms. Au pellets with a purity of 99.99% were used to be evaporated at a rate of 5–10 Å/s in an atmosphere of 8 × 10−6 mbars. The thickness was estimated using a quartz-crystal microbalance thickness monitor (Leybold Inficon XTC/2 Depositions Controllers). To ensure homogeneous thicknesses in the prisms, these are located perpendicularly at the longest distance (about 36 cm) from the source of evaporation in the vacuum chamber and at the nearest position to the thickness monitor. To obtain the SPR curve, a gold-coated prism was set over the rotation stage of the experimental setup. The surface plasmon resonance was detected using LabVIEW program to drive and acquire data. The He-Ne laser was launched into the prism and the angular interrogation was made from 30 to 90◦ . Accuracy is usually strongly dependent on the calibration procedure. In this sense, an alignment and calibration procedure of various steps was employed: a) flat surface of the prism is aligned with a rotation center, a position that assures that the reflected signal is always at the center of the photodetector; b) once the laser light hit the spherical surface of the prism, two back reflections (spherical and flat prism surface) will be observed, both reflections have to be aligned and to coincide with the direction of the incident light (an iris diaphragm is employed to minimize the width of the reflection beams); c) the scan of the reflected light through the prism within a range of 30–90 ◦ is performed in order to assure that the reflected beam stays in the center of the photodetector (4 mm); and d) the theoretical critical and SPR angles of the prism and the experimental angles obtained from the measurement are compared, if there is a shift in the critical angle, this error is taken into account as a correction value for the experimental measurement. The inorganic dielectric thin film chosen to be deposited over the gold thin film in the prism was zinc sulfide. The behavior of the SPR curve for two layers was obtained theoretically (in the same way that was made for the gold layer), this in order to know the most favorable thicknesses for the inorganic dielectric thin film and how many degrees the SPR angle would be shifted. A ZnS thin film was deposited onto two BK7 prisms with Au thin film (for SPR measurement). At the same time, it was deposited over two BK7 substrates (for A-B measurements). ZnS with a purity of 99.99% was used to be evaporated at a rate of 5 Å/s in an atmosphere of 8 × 10−6 mbars. In the same evaporation were obtained two different thicknesses for the ZnS film, this was made putting one prism and one substrate near of the source of evaporation in the vacuum chamber (greater thickness) and one prism and one substrate far of the source of evaporation (lower thickness). This was done with the aim of obtaining significant differences between the thicknesses of the films and compare them. Subsequently, the SPR curves were obtained and in the same way as before, the angular interrogation was made from 30 to 90◦ . In Fig. 3 the SPR curves are shown.
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Fig. 3. Experimental SPR curves of BK7 hemicylindrical prisms coated with Au and ZnS thin films, and with Au and BSA thin films, where the solid curve corresponds to the ZnS thin film with lower thickness (resonance angle of 54.87◦ ), the dashed one to the ZnS thin film with greater thickness (resonance angle of 74.47◦ ) and the dotted one to the Au and BSA thin films.
To obtain the organic dielectric thin film, a BSA solution was deposited by drop casting method onto two gold-coated prisms (BK7 and SF6) and over an LAFN2 glass substrate. Bovine serum albumin (reagent grade) and the organic solvents for surface cleaning (acetone and ethanol) were obtained from Sigma (USA). BSA solution was prepared by complete dissolution of 1 mg of corresponding protein in 1 mL PBS buffer. Before the formation of the BSA thin film, a cleaning step was performed onto the gold/glass-coated prisms. The surfaces were consecutively rinsed in acetone, ethanol, and water. Then the gold/glass layers were dried with air. To prepare the BSA monolayers, a total of 300 L of the solution (1 mg/mL) was carefully spread over the surface of the gold-coated prisms and glass substrate. After spreading the solution, the liquid layer was allowed to evaporate and dried overnight at room temperature. Once the solvent was evaporated, the SPR curves of both prisms were measured. In Fig. 3 the SPR curve for BK7 prism is displayed. As can be seen, the SPR phenomenon is not manifested, this is attributed to the prism refractive index is lower than the BSA refractive index, whereby the surface plasmons in the interface between the metal and the dielectric (BSA) could not be excited, therefore, no decrease in the reflected energy was observed [27]. 3.3. Procedure for obtaining the Abelès- Brewster curves Two BK7 substrates were coated with different thicknesses of ZnS thin films for the A-B measurement. Only half of the substrates were coated, thereby having a step of the thin film on each substrate. The He-Ne laser was directed toward a surface (substrate) partially coated with ZnS thin film. The substrate was positioned on the rotation stage of the experimental setup to scan the incident angle of the laser beam, and it was placed over a mechanical mount (built specially for its use in Brewster and A-B measurements). The mechanical mount has two sliding plates to locate the rotational center at the edge of the substrate and three adjustment screws to align it. The angle of incidence is calibrated by moving the mechanical mount with the substrate so that the beam is reflected back on the incident beam and assigning = 00 . In the measurement of the refractive index through the A-B method [28], the film-coated and the uncoated substrate part were illuminated, scanning the incident angle from, scanning the incident angle from 30 to 90◦ . The interception angle of the curves corresponds to the film Brewster angle. This is because no light was reflected from the ambient-film interface at the film Brewster angle; then, the reflectivity of the film-covered substrate is the same as the uncoated substrate at the Brewster angle ( B ). Thus, the refractive index of the film was calculated using the expression n = tan B . Since the Brewster angle (minimum reflection angle of the curve) of the BK7 substrate was very close to the minimum reflection angle of the BSA film (uncoated and coated reflection curves overlapped and there was not a unique interception angle), a high refractive index glass, i.e. LAFN2, was tested. A thin film of BSA was deposited onto an LAFN2 substrate. After, the measurement of the refractive index of the organic film was made by the A-B method. 3.4. Extracting optical parameters of the dielectric thin films through the surface plasmon resonance technique The refractive index and thickness estimation of the Au and the thickness BSA and ZnS were found through the fitting of the theoretical and experimental curves. As the refractive index of the inorganic and organic dielectric thin films was found
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Fig. 4. SPR curve fitting for an interface of Au/air, where the complex refractive index found was n = 0.1758 and k = 3.3895 with a thickness of 53 nm.
using the Abelès-Brewster method, these values were used in the fitting process. Thus, the curves fitting process are reduced to the use of only the thickness parameter, avoiding ambiguities in the final results, as is common in a curve fitting process to obtain several parameters [29]. The theoretical and fitting process of the curves were calculated from standard optical constants for the materials making up the four media (BK7/SF6, Au, ZnS/BSA, air), or two layers, optical structure using a LabVIEW program which was done based on the calculation of the Fresnel reflection coefficients for the structure using the matrix formalism [14]. 4. Results In the measurement of refractive index using a rotation system -2, the complex refractive index and thickness of a gold thin film onto a BK7 hemicylindrical prism was measured through SPR method, while the refractive indexes of an inorganic and organic dielectric thin films (ZnS and BSA, respectively) were measured through the A-B method. All the parameters obtained with both methods were used to determine the thicknesses in the SPR curves fitting of the ZnS and BSA thin films deposited onto BK7 and SF6 gold-coated prisms, produced in the same evaporation process of the ZnS/substrate and in the same BSA/substrate deposition process. 4.1. Refractive index measurement of a metallic thin film using the SPR method The refractive index and thickness of the gold thin film were found through the fitting of the theoretical and experimental SPR curves. The fitting of the theoretical and experimental SPR curves using LabVIEW program for an Au/air interface (system of three media and one layer) is shown in Fig. 4. The parameters of the input and output media were fixed to n0 = 1.51509 for BK7 [24], n3 = 1 for air [30]; the parameters corresponding to media 2, or layer 1, were given in the fitting process. The optical parameters obtained for layer 1 (Au thin film) were n = 0.1758, k = 3.3895, and d = 53 nm from the fitting process with air. Different refractive indexes are found in the literature for the same thin film, e.g. for a gold thin film it can be found several values: n1 = 0.06656–4.0452i [31], n2 = 0.19–3.305i [29], n3 = 0.18344–3.43321i [32], and n4 = 0.1758–3.3895i,which is a value obtained in this work and also in other tests under different measurement conditions. Fig. 5 shows the theoretical SPR curves for the aforementioned values, considering a thickness of 50 nm and air (n = 1) and water (n = 1.33) as the dielectric adjacent mediums to the metallic thin film. The difference in the gold refractive index values shows the importance of the optical characterization by means a reliable method which allows repeatability in the thin film fabrication and consequently in its usage. The sensitivity of the SPR sensor is given by the ratio of change in the sensor output to change in the quantity to be measured (e.g. refractive index), S = /n, where n is the measured refractive index of the probe medium and is the variation of the resonance angle. A wavelength of 632.8 nm for a He-Ne laser was used for the stability and polarized intensity output characteristics, with sensitivity being about 7.44 × 10−3 RIU/0 [33]. 4.2. Refractive index measurement of dielectric and organic thin film using the Abelès- Brewster method The A-B measurement for a ZnS step thin film is shown in Fig. 6. For the film B = 66.95◦ , and therefore, n = 2.3501. A substrate of a standard refractive index was used to determine the error factor in the measurements. If there was a difference
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Fig. 5. Theoretical SPR curves for different refractive index described in the literature.
Fig. 6. Reflectance curves of a BK7 substrate with step coating of ZnS thin. The interception angle of the curves, the Brewster angle of the thin film, was B = 66.950 , with n = 2.3501.
in the measured Brewster angle, this error was considered as a correction factor. Considering that the minimum value for the angle measurement is = 0.010 , this value affects the refractive index in n (n = tg(B + ) − n). This = 0.010 is considered as the absolute error. The absolute error for a refractive index of 2.3501 (Brewster angle n/n = 4.68x10−4 of 66.950 ) and 0.01 ◦ of resolution is n = 0.0011, and the relative errors of Fig. 7 displays the measurement for a BSA step thin film, with B = 57.33◦ and n = 1.5595. For LAFN2 substrate with BSA step the values obtained were B = 60.18◦ and n = 1.7447. 4.3. Thicknesses measurement of a ZnS and BSA thin films using the A-B and SPR methods For the fitting of the theoretical and experimental SPR curves from the prism/Au/ZnS/Air or BSA/air interface only thickness parameters were adjusted (Fig. 8) since the refractive index of ZnS and BSA films were already determined through the A-B method, and the Au refractive index and its thickness were obtained through the SPR curves fitting of the BK7 and SF6 gold-coated prisms. The thicknesses obtained for the ZnS thin films were 20.27 nm (with a resonance angle sp1 = 54.87◦ ) and 28.42 nm (with a resonance angle sp2 = 74.47◦ ), for the prism farthest and nearest to thickness monitor and the evaporation source, respectively. The shift degrees between sp1 and sp2 were 19.6◦ ( sp ) with a thickness change of sp /dZnS = 2.4◦ /nm 8.15 nm (dZnS ), so the sensitivity Based on this experimental data was found that with the maximum angular resolution of the SPR system (0.01◦ ) changes of 0.004 nm can be determined for materials of refractive indexes similar or close to the ZnS refractive index (2.3501). The thickness obtained for the BSA thin film was 143.75 nm.
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Fig. 7. Reflectance curves of an LAFN2 substrate with step coating of BSA thin film, where the Brewster angle for the LAFN2 was B = 60.180 with n = 1.7446. The interception angle of the curves, the Brewster angle of the BSA thin film was B = 57.33 0 with n = 1.5595.
Fig. 8. SPR curves fitting. a) BK7/Au prism coated with a ZnS thin film with a thickness of 20.27 nm, b) BK7/Au prism coated with a ZnS thin film with a thickness of 28.42 nm, and c) SF6/Au prism coated with a BSA thin film with a thickness of 143.75 nm.
With the experimental combination of BK7 prism (n = 1.51509)/Au (n = 0.1758, k = 3.3895, d = 53 nm)/ZnS (n = 2.3501) layers with very thin thickness can be measured. While with an experimental combination of SF6 prism (n = 1.7988)/Au (n = 0.1758, k = 3.3895, d = 53 nm)/BSA (n = 1.5595) layers with thicker thickness (about 140 nm) can be measured. The refractive indexes published in the ref. [34] for Au, n = 0.17832 and k = 3.3660, and the refractive index in ref. [35] for ZnS, n = 2.3505, are very close to the values obtained in this work, while for the LAFN2 substrate the refractive index n = 1.7405 [30] is near the value obtained with the A-B method.
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5. Conclusions The determination of the optical parameters, complex refractive index and thickness, of metallic thin film (gold onto a BK7 hemicylindrical prism) using light with p polarization from a He-Ne laser operating at 632.8 nm in a rotation system -2, through the SPR method, as well as the determination of the optical parameters (refractive index and thickness) of dielectric organic and inorganic (BSA and ZnS, respectively) thin films using both A-B and SPR methods, shows that using these methods, the optical parameters can be determined easily, simply, quickly, accurately and unambiguously. To have a good measurement of the Brewster angle using A-B method, the refractive indexes of the material and the substrate should be quite different. This ensures that a crossing of the reflectivity curves will be obtained away from the angle of minimum reflection of the substrate and in this way, the determination of the thin film refractive index will be easier. 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Wright, Convergence properties of the Nelder-Mead simplex method in low dimensions, SIAM J. Optim. 9 (1988) 112–147. [26] D. Luna-Moreno, Y.M. Espinosa Sánchez, Y.R. Ponce de León, E. Noé Arias, G. Garnica Campos, Virtual instrumentation in LabVIEW for multiple optical characterizations on the same opto-mechanical system, Optik 126 (2015) 1923–1929. [27] S.A. Maier, Plasmonics: Fundamentals and Applications, Springer, New York, 2007, pp. 42. [28] H.E. Bennet, J.M. Bennet, Precision measurements in thin films optics, in: Georg Hass, Rudolf E. Thun (Eds.), Physics of Thin Films, vol. 4, Academic Press New York and London, 1967 (Chap. 1). [29] Y.W. Fen, W.M. Mat Yunus, M.M. Monksin, Z.A. Talib, N.A. Yusof, Optical Properties of Crosslinked Chitosan Thin Film with Glutaraldehyde Using Surface Plasmon Resonance Technique, Am. J. Eng. Appl. Sci. 4 (1) (2011) 61–65. [30] Handbook of Chemistry and Physics, in: R.C. Weast (Ed.), CRC Press, Boca Raton, Florida, 1988, p. E-382.
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Optik journal homepage: www.elsevier.de/ijleo
Original research article
Determination of optical parameters of organic and inorganic thin films using both surface plasmon resonance and Abelès-Brewster methods Y.M. Espinosa-Sánchez a,∗ , D. Luna-Moreno a , M. Rodríguez-Delgado b , A. Sánchez-Álvarez c a
Centro de Investigaciones en Óptica A. C., A. P. 1-948, León, Gto, 37150, Mexico Laboratorio de Nanotecnología Ambiental, Centro del Agua para América Latina y el Caribe, Tecnológico de Monterrey, Monterrey, Nuevo León 64849, Mexico c Universidad Tecnológica de León, Blvd. Universidad Tecnológica #225, Col. San Carlos, León, Gto, 37670, Mexico b
a r t i c l e
i n f o
Article history: Received 15 December 2016 Received in revised form 6 April 2017 Accepted 28 May 2017 Keywords: Plasmons Optical constants Optical properties of surfaces
a b s t r a c t We present two methods to characterize organic and inorganic thin films. The thin films characterization was performed employing an opto-mechanical system, which uses light with p polarization from a He-Ne laser operating at 632.8 nm. This system is based on the methods of Abelès-Brewster and surface plasmon resonance in the prism-based Kretschmann configuration. The metallic thin films characterization is made using surface plasmon resonance method while dielectric thin films (organic and inorganic) are characterized using both methods The optical parameters were obtained through a LabVIEW program based on the Fresnel equations by matrix method. The proposed system was proved through the optical characterization of gold, zinc sulfide and bovine serum albumin thin films with a fast, simple and accurate response and the optical parameters were obtained for each tested film. The refractive index and extinction coefficient values obtained for the gold thin film were 0.1758 and 3.3895, respectively, with a thickness of 53 nm; a refractive index of 2.3501 was measured for the zinc sulfide thin film showing a thicknesses of 28.42 nm; meanwhile bovine serum albumin presented a refractive index of 1.5595 with a thickness of 143.75 nm. © 2017 Elsevier GmbH. All rights reserved.
1. Introduction Nowadays there are many ways to measure the optical properties of a thin film, but before choosing a method firstly should be considered that usually, the optical properties of a thin film are quite different from those of the bulk material [1,2]. The study of the optical properties of thin films has been widely reported using different methods. However, the difference in the reported results between works, even using the same techniques, has revealed the complexity of this kind of study
∗ Corresponding author. E-mail addresses: [email protected], [email protected] (Y.M. Espinosa-Sánchez), [email protected] (D. Luna-Moreno), [email protected] (M. Rodríguez-Delgado), [email protected] (A. Sánchez-Álvarez). http://dx.doi.org/10.1016/j.ijleo.2017.05.090 0030-4026/© 2017 Elsevier GmbH. All rights reserved.
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[3]. e.g., the refractive index of thin films strongly depends on the deposition technique [4–7]; yielding a different surface morphology response depending on the method employed [8]. Since the refractive index of a thin film is an indirect measurement, the use of fitting models that matches the measured data in order to estimate the optical constants is common [9–13]. Almost as important as the model is the accuracy of the actual measurements. The calibration verification is an indispensable step in the measurement of the performance that will be used for the optical constant extraction [14]. The most commonly used methods to measure the optical properties of thin films are reflectance and transmittance [13–15], ellipsometry [16], and surface plasmon resonance (SPR) methods, for metallic [17,18] and dielectric [19] flat thin film or for a cylindrical thin film over a fiber optic [10]. Each one of these techniques has their own advantages and can complement each other. It is known that the main application of thin films is in the fields of sensing and biosensing [20], in this sense, the thin films characterization plays a determinant role because the optical parameters control guarantees a better performance of the thin films. Also, these parameters are responsible for the refractive indexes range that the sensor will be capable of detecting, as well as the resolution in which the refractive index changes can be detected. In this work is used a –2 opto-mechanical system with two motorized rotation stages of 0.01◦ of angular resolution to scan the reflected light from the sample, using light with p polarization of a He-Ne laser centered at 632.8 nm. The system is based on the Abelès-Brewster (A-B) and SPR methods, which stand out for their simplicity and rather high sensitivity. Through them is possible to obtain the optical parameters (refractive index and thickness) of dielectric (organic and inorganic) and metallic thin films that produce surface plasmon wave. The system, in the SPR method, uses the prism coupling in the Kretschmann configuration, in which a prism with is interconnected with a waveguide metal-dielectric, which is composed of a metallic thin film and a dielectric [21]. The potential of SPR for characterization of thin films and monitoring processes at metal interfaces was recognized in the late seventies [20]. The unique combination of an extremely high sensitivity to optical properties of surface layers and the ease of their real time continuous monitoring are the main advantage of the SPR over other optical techniques [22]. The A-B technique is one of the most popular for the determination of the optical thin film refractive index. The method consists of illuminating regions of a substrate with and without thin film coating with laser light with p polarization. The incidence angle is scanned to find the angle of common reflectance for the substrate and the coating, so the angle of convergence will be the Brewster angle for the thin film coating. The refractive index of the thin film is estimated by applying the tangent of the Brewster angle (n = tan B ) [23]. The achievement of this work is that the fact of using the methods separately and combining them makes possible to obtain reliable, accurate and fast results. Furthermore, a wide range of refractive indexes and/or very thin thicknesses of films can be measured even without a previous knowledge of the thin film or sample to be measured. This wide range of tuning is reached using prisms or substrates of different refractive indexes. e.g., glasses of BK7, SK16 and SF6 with refractive indexes of 1.51509, 1.62041 and 1.7988 [24] respectively. To obtain the refractive index (real and complex part) and thickness of a metallic thin film the SPR method is used followed by a fitting process. To get the optical parameters for a dielectric (organic and inorganic) thin film, both methods are used, A-B method for the refractive index and SPR method for the thickness. By measuring in this way more accurate results can be obtained. This because the presence of many variables makes the fitting process more complicated, so having found the refractive index (using the A-B method), the only parameter to be found with the fitting process will be the thickness, which ensures faster and more accurate measurements. Two inorganic thin films, metallic (gold, Au) and dielectric (zinc sulfide, ZnS); and an organic film (bovine serum albumin, BSA) were chosen as models to determine the efficiency of the system proposed. 2. Theoretical SPR curve The optical reflection of multilayer thin film was estimated by the matrix method, which transfers the electric and magnetic fields parallel to each interface (tangential components) from the rear to the front of the assembly of the SPR phenomena in the Kretschmann configuration. The electric and magnetic fields are expressed as column vectors, and each film as a transfer matrix, thus the calculus involves successive multiplications of the column vectors by the transfer matrix. The final amplitudes are associated with the transmitted wave since there is no returning wave in the emergent medium [14]. The characteristic matrix of the thin film system is expressed as shown in Eq. (1)
B
C
=
k j=1
⎡ ⎣
cos ıj i sin ıj
i sin ıj j cos ıj
⎤
⎦ 1 ,
(1)
s
where optical admittance of the jth layer film is j = nj / cos j for TM polarization and j = nj cos j for TE polarization
and s is the optical admittance of the substrate or sample medium (s = ns / cos s for TM polarization and S = ns cos s for TE polarization). B and C represent the amplitude of the normalized electric and magnetic fields, respectively, ıj is the
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Fig. 1. Experimental setup for SPR measurement in the Kretschmann configuration.
phase thickness (given for, ıj = 2nj dj cos j /), d is the physical thickness, n is the refractive index of the thin film, ns is the refractive index of the substrate or sample medium, is the wavelength, and is the angle for the incident medium. Y is the admittance of the assembly system (Y = C/B). The reflectance amplitude is given by Eq. (2), r=
0 − Y , 0 + Y
(2)
and the Reflectance is expressed by Eq. (3), R = |r|2 = |
0 − Y 2 | , 0 + Y
(3)
where n0 is the refractive index of the incident medium, which in this case corresponds to a prism. The problem is then reduced to finding the reflectance of the simple ideal interface between an incident medium n0 and a medium of admittance Y. The refractive index and thickness calculus of the thin films were found by fitting the theoretical and experimental curves. Let R (, d, n, ) be the reflectance function. Where is the incidence angle, d is the thickness, n is the refractive index and is the wavelength. Initially, we have M experimental data organized as ( k , R k )for1 ≤ k ≤ M
(4)
where Rk depends on dk and nk (thickness and refractive index of the layers, respectively). But, some of them are unknown values and must be calculated. This is accomplished by finding the parameters which make the curve fit the experimental data. In order to find the curve that best fits the experimental data, the function F was constructed. F=
M
R k , ds , ns , − Rk
2
(5)
k=1
Clearly, the optimal dk and nk values to minimize F must satisfy Eq. (6)
∂F ∂F = =0 ∂ds ∂ns
(6)
To determine the reflectance parameters of the experimental curve obtained with the system, the curve was approximated by least squares fitting the unconstrained nonlinear parameter optimization. The Nelder-Mead algorithm simplex direct search using derivative-free method was used [25,26]. 3. Experimental section 3.1. Instrumental configuration The arrangement used for SPR measurements was the Kretschmann configuration, as shown in Fig. 1. Under this scheme, a prism was mounted on a rotation stage (). The photodetector was set in a different rotation stage (2), to capture the
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Fig. 2. Schematic diagram for the Abelès-Brewster method.
reflected signal through the prism. A polarized He-Ne laser (Uniphase mod. 1101P), centered at 632.8 nm of 1.5 mw of minimum output power, and minimum polarization ratio of 500:1 was launched into a hemicylindrical shaped prism with its flat face looking downward to validate normal incidence. The advantage of using a hemicylindrical prism is that the refraction problem is avoided. Other types of prisms, which show this problem, have the drawback of giving a limited dynamic range that could be unsuitable for high refractive index measurement. The experimental setup was also adapted to use the Abelès-Brewster method, illustrated in Fig. 2. 3.2. Measurement of experimental SPR curves The theoretical SPR curve for a gold thin film over a BK7 prism was calculated using a LabVIEW program, which is based on the matrix method. A thin film of 50 nm of gold was deposited by means of thermal evaporation in a vacuum chamber onto two BK7 hemicylindrical prisms. Au pellets with a purity of 99.99% were used to be evaporated at a rate of 5–10 Å/s in an atmosphere of 8 × 10−6 mbars. The thickness was estimated using a quartz-crystal microbalance thickness monitor (Leybold Inficon XTC/2 Depositions Controllers). To ensure homogeneous thicknesses in the prisms, these are located perpendicularly at the longest distance (about 36 cm) from the source of evaporation in the vacuum chamber and at the nearest position to the thickness monitor. To obtain the SPR curve, a gold-coated prism was set over the rotation stage of the experimental setup. The surface plasmon resonance was detected using LabVIEW program to drive and acquire data. The He-Ne laser was launched into the prism and the angular interrogation was made from 30 to 90◦ . Accuracy is usually strongly dependent on the calibration procedure. In this sense, an alignment and calibration procedure of various steps was employed: a) flat surface of the prism is aligned with a rotation center, a position that assures that the reflected signal is always at the center of the photodetector; b) once the laser light hit the spherical surface of the prism, two back reflections (spherical and flat prism surface) will be observed, both reflections have to be aligned and to coincide with the direction of the incident light (an iris diaphragm is employed to minimize the width of the reflection beams); c) the scan of the reflected light through the prism within a range of 30–90 ◦ is performed in order to assure that the reflected beam stays in the center of the photodetector (4 mm); and d) the theoretical critical and SPR angles of the prism and the experimental angles obtained from the measurement are compared, if there is a shift in the critical angle, this error is taken into account as a correction value for the experimental measurement. The inorganic dielectric thin film chosen to be deposited over the gold thin film in the prism was zinc sulfide. The behavior of the SPR curve for two layers was obtained theoretically (in the same way that was made for the gold layer), this in order to know the most favorable thicknesses for the inorganic dielectric thin film and how many degrees the SPR angle would be shifted. A ZnS thin film was deposited onto two BK7 prisms with Au thin film (for SPR measurement). At the same time, it was deposited over two BK7 substrates (for A-B measurements). ZnS with a purity of 99.99% was used to be evaporated at a rate of 5 Å/s in an atmosphere of 8 × 10−6 mbars. In the same evaporation were obtained two different thicknesses for the ZnS film, this was made putting one prism and one substrate near of the source of evaporation in the vacuum chamber (greater thickness) and one prism and one substrate far of the source of evaporation (lower thickness). This was done with the aim of obtaining significant differences between the thicknesses of the films and compare them. Subsequently, the SPR curves were obtained and in the same way as before, the angular interrogation was made from 30 to 90◦ . In Fig. 3 the SPR curves are shown.
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Fig. 3. Experimental SPR curves of BK7 hemicylindrical prisms coated with Au and ZnS thin films, and with Au and BSA thin films, where the solid curve corresponds to the ZnS thin film with lower thickness (resonance angle of 54.87◦ ), the dashed one to the ZnS thin film with greater thickness (resonance angle of 74.47◦ ) and the dotted one to the Au and BSA thin films.
To obtain the organic dielectric thin film, a BSA solution was deposited by drop casting method onto two gold-coated prisms (BK7 and SF6) and over an LAFN2 glass substrate. Bovine serum albumin (reagent grade) and the organic solvents for surface cleaning (acetone and ethanol) were obtained from Sigma (USA). BSA solution was prepared by complete dissolution of 1 mg of corresponding protein in 1 mL PBS buffer. Before the formation of the BSA thin film, a cleaning step was performed onto the gold/glass-coated prisms. The surfaces were consecutively rinsed in acetone, ethanol, and water. Then the gold/glass layers were dried with air. To prepare the BSA monolayers, a total of 300 L of the solution (1 mg/mL) was carefully spread over the surface of the gold-coated prisms and glass substrate. After spreading the solution, the liquid layer was allowed to evaporate and dried overnight at room temperature. Once the solvent was evaporated, the SPR curves of both prisms were measured. In Fig. 3 the SPR curve for BK7 prism is displayed. As can be seen, the SPR phenomenon is not manifested, this is attributed to the prism refractive index is lower than the BSA refractive index, whereby the surface plasmons in the interface between the metal and the dielectric (BSA) could not be excited, therefore, no decrease in the reflected energy was observed [27]. 3.3. Procedure for obtaining the Abelès- Brewster curves Two BK7 substrates were coated with different thicknesses of ZnS thin films for the A-B measurement. Only half of the substrates were coated, thereby having a step of the thin film on each substrate. The He-Ne laser was directed toward a surface (substrate) partially coated with ZnS thin film. The substrate was positioned on the rotation stage of the experimental setup to scan the incident angle of the laser beam, and it was placed over a mechanical mount (built specially for its use in Brewster and A-B measurements). The mechanical mount has two sliding plates to locate the rotational center at the edge of the substrate and three adjustment screws to align it. The angle of incidence is calibrated by moving the mechanical mount with the substrate so that the beam is reflected back on the incident beam and assigning = 00 . In the measurement of the refractive index through the A-B method [28], the film-coated and the uncoated substrate part were illuminated, scanning the incident angle from, scanning the incident angle from 30 to 90◦ . The interception angle of the curves corresponds to the film Brewster angle. This is because no light was reflected from the ambient-film interface at the film Brewster angle; then, the reflectivity of the film-covered substrate is the same as the uncoated substrate at the Brewster angle ( B ). Thus, the refractive index of the film was calculated using the expression n = tan B . Since the Brewster angle (minimum reflection angle of the curve) of the BK7 substrate was very close to the minimum reflection angle of the BSA film (uncoated and coated reflection curves overlapped and there was not a unique interception angle), a high refractive index glass, i.e. LAFN2, was tested. A thin film of BSA was deposited onto an LAFN2 substrate. After, the measurement of the refractive index of the organic film was made by the A-B method. 3.4. Extracting optical parameters of the dielectric thin films through the surface plasmon resonance technique The refractive index and thickness estimation of the Au and the thickness BSA and ZnS were found through the fitting of the theoretical and experimental curves. As the refractive index of the inorganic and organic dielectric thin films was found
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Fig. 4. SPR curve fitting for an interface of Au/air, where the complex refractive index found was n = 0.1758 and k = 3.3895 with a thickness of 53 nm.
using the Abelès-Brewster method, these values were used in the fitting process. Thus, the curves fitting process are reduced to the use of only the thickness parameter, avoiding ambiguities in the final results, as is common in a curve fitting process to obtain several parameters [29]. The theoretical and fitting process of the curves were calculated from standard optical constants for the materials making up the four media (BK7/SF6, Au, ZnS/BSA, air), or two layers, optical structure using a LabVIEW program which was done based on the calculation of the Fresnel reflection coefficients for the structure using the matrix formalism [14]. 4. Results In the measurement of refractive index using a rotation system -2, the complex refractive index and thickness of a gold thin film onto a BK7 hemicylindrical prism was measured through SPR method, while the refractive indexes of an inorganic and organic dielectric thin films (ZnS and BSA, respectively) were measured through the A-B method. All the parameters obtained with both methods were used to determine the thicknesses in the SPR curves fitting of the ZnS and BSA thin films deposited onto BK7 and SF6 gold-coated prisms, produced in the same evaporation process of the ZnS/substrate and in the same BSA/substrate deposition process. 4.1. Refractive index measurement of a metallic thin film using the SPR method The refractive index and thickness of the gold thin film were found through the fitting of the theoretical and experimental SPR curves. The fitting of the theoretical and experimental SPR curves using LabVIEW program for an Au/air interface (system of three media and one layer) is shown in Fig. 4. The parameters of the input and output media were fixed to n0 = 1.51509 for BK7 [24], n3 = 1 for air [30]; the parameters corresponding to media 2, or layer 1, were given in the fitting process. The optical parameters obtained for layer 1 (Au thin film) were n = 0.1758, k = 3.3895, and d = 53 nm from the fitting process with air. Different refractive indexes are found in the literature for the same thin film, e.g. for a gold thin film it can be found several values: n1 = 0.06656–4.0452i [31], n2 = 0.19–3.305i [29], n3 = 0.18344–3.43321i [32], and n4 = 0.1758–3.3895i,which is a value obtained in this work and also in other tests under different measurement conditions. Fig. 5 shows the theoretical SPR curves for the aforementioned values, considering a thickness of 50 nm and air (n = 1) and water (n = 1.33) as the dielectric adjacent mediums to the metallic thin film. The difference in the gold refractive index values shows the importance of the optical characterization by means a reliable method which allows repeatability in the thin film fabrication and consequently in its usage. The sensitivity of the SPR sensor is given by the ratio of change in the sensor output to change in the quantity to be measured (e.g. refractive index), S = /n, where n is the measured refractive index of the probe medium and is the variation of the resonance angle. A wavelength of 632.8 nm for a He-Ne laser was used for the stability and polarized intensity output characteristics, with sensitivity being about 7.44 × 10−3 RIU/0 [33]. 4.2. Refractive index measurement of dielectric and organic thin film using the Abelès- Brewster method The A-B measurement for a ZnS step thin film is shown in Fig. 6. For the film B = 66.95◦ , and therefore, n = 2.3501. A substrate of a standard refractive index was used to determine the error factor in the measurements. If there was a difference
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Fig. 5. Theoretical SPR curves for different refractive index described in the literature.
Fig. 6. Reflectance curves of a BK7 substrate with step coating of ZnS thin. The interception angle of the curves, the Brewster angle of the thin film, was B = 66.950 , with n = 2.3501.
in the measured Brewster angle, this error was considered as a correction factor. Considering that the minimum value for the angle measurement is = 0.010 , this value affects the refractive index in n (n = tg(B + ) − n). This = 0.010 is considered as the absolute error. The absolute error for a refractive index of 2.3501 (Brewster angle n/n = 4.68x10−4 of 66.950 ) and 0.01 ◦ of resolution is n = 0.0011, and the relative errors of Fig. 7 displays the measurement for a BSA step thin film, with B = 57.33◦ and n = 1.5595. For LAFN2 substrate with BSA step the values obtained were B = 60.18◦ and n = 1.7447. 4.3. Thicknesses measurement of a ZnS and BSA thin films using the A-B and SPR methods For the fitting of the theoretical and experimental SPR curves from the prism/Au/ZnS/Air or BSA/air interface only thickness parameters were adjusted (Fig. 8) since the refractive index of ZnS and BSA films were already determined through the A-B method, and the Au refractive index and its thickness were obtained through the SPR curves fitting of the BK7 and SF6 gold-coated prisms. The thicknesses obtained for the ZnS thin films were 20.27 nm (with a resonance angle sp1 = 54.87◦ ) and 28.42 nm (with a resonance angle sp2 = 74.47◦ ), for the prism farthest and nearest to thickness monitor and the evaporation source, respectively. The shift degrees between sp1 and sp2 were 19.6◦ ( sp ) with a thickness change of sp /dZnS = 2.4◦ /nm 8.15 nm (dZnS ), so the sensitivity Based on this experimental data was found that with the maximum angular resolution of the SPR system (0.01◦ ) changes of 0.004 nm can be determined for materials of refractive indexes similar or close to the ZnS refractive index (2.3501). The thickness obtained for the BSA thin film was 143.75 nm.
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Fig. 7. Reflectance curves of an LAFN2 substrate with step coating of BSA thin film, where the Brewster angle for the LAFN2 was B = 60.180 with n = 1.7446. The interception angle of the curves, the Brewster angle of the BSA thin film was B = 57.33 0 with n = 1.5595.
Fig. 8. SPR curves fitting. a) BK7/Au prism coated with a ZnS thin film with a thickness of 20.27 nm, b) BK7/Au prism coated with a ZnS thin film with a thickness of 28.42 nm, and c) SF6/Au prism coated with a BSA thin film with a thickness of 143.75 nm.
With the experimental combination of BK7 prism (n = 1.51509)/Au (n = 0.1758, k = 3.3895, d = 53 nm)/ZnS (n = 2.3501) layers with very thin thickness can be measured. While with an experimental combination of SF6 prism (n = 1.7988)/Au (n = 0.1758, k = 3.3895, d = 53 nm)/BSA (n = 1.5595) layers with thicker thickness (about 140 nm) can be measured. The refractive indexes published in the ref. [34] for Au, n = 0.17832 and k = 3.3660, and the refractive index in ref. [35] for ZnS, n = 2.3505, are very close to the values obtained in this work, while for the LAFN2 substrate the refractive index n = 1.7405 [30] is near the value obtained with the A-B method.
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5. Conclusions The determination of the optical parameters, complex refractive index and thickness, of metallic thin film (gold onto a BK7 hemicylindrical prism) using light with p polarization from a He-Ne laser operating at 632.8 nm in a rotation system -2, through the SPR method, as well as the determination of the optical parameters (refractive index and thickness) of dielectric organic and inorganic (BSA and ZnS, respectively) thin films using both A-B and SPR methods, shows that using these methods, the optical parameters can be determined easily, simply, quickly, accurately and unambiguously. To have a good measurement of the Brewster angle using A-B method, the refractive indexes of the material and the substrate should be quite different. This ensures that a crossing of the reflectivity curves will be obtained away from the angle of minimum reflection of the substrate and in this way, the determination of the thin film refractive index will be easier. For practical purposes, replaceable SPR sensor chips could be used. These chips can be made by coating glass substrates (the substrate refractive index has to be of the same value to the prism refractive index that will be used) with gold by means of thermal evaporation in a vacuum chamber. Through refractive index matching liquid, the optical contact between the SPR chip and the prism can be established. Acknowledgments The authors would like to thank Carlos Juárez and Octavio Pompa for their assistance in the thin film evaporations. We would also like to extend our thanks to Mario Ruiz Berganza for his contribution in revising the paper and for his pertinent annotations. References [1] Handbook of Optical Constants of Solids, in: E. Palik (Ed.), Academic Press, 1985 (pp. 350.). [2] Handbook of Optical Constants of Solids II, in: E. Palik (Ed.), Academic Press, 1991 (pp. 602, 899.). [3] D.P. Arndt, R.M.A. Azzam, J.M. Bennett, J.P. Borgogno, C.K. Carniglia, W.E. Case, J.A. 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