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In this paper, a novel method to determine the thickness of thin metal film is put forward which uses Surface Plasmon Resonance (SPR) phase detection method. The relations between the metal film thickness and the phases of the transverse magnetic (TM) and transverse electric (TE) polarization of the reflected light are shown in the simulation results. By recording the interference patterns which contain the information of the phase differences in the experiments, the values of thickness are calculated. Both of the theoretical analysis and experimental results indicate that the approach presented is feasible and reliable. Thus, it is possible to use the method of phase detection to determine the thickness of thin metal films within 100nm in SPR prism couplers directly with nanometer resolution.
© 2014 Optical Society of America
1. Introduction
During the past two decades, surface plasmon resonance (SPR) technology has been widely used in electro-optical, chemical and biological sensors because of its extraordinary sensitivity to different refractive indexes and surface conditions [1–6]. Most conventional SPR sensors are based on measuring the intensity changes of output beam or the shift of SPR dips in the attenuated total reflection (ATR) spectrum [7,8]. In order to improve the resolution of SPR sensors, phase-sensitive schemes have been proposed in several recent researches [9–18] based on the phenomenon that the phase of transverse magnetic (TM) polarized component has a drastic variation but there is little change in relevant parameter of the transverse electric (TE) polarized one.
SPR sensors take advantage of the phenomenon of the surface plasmons (SPs) which are the special modes of electromagnetic waves at the metal-dielectric interface [19]. The common approaches to excitation of the SPs are by means of prism couplers, grating couplers and waveguide couplers. Ultra-thin metal films of thickness less than 100 nm have been widely used in these couplers, because part of incident light wave can penetrate through the metal films and then excite the SPs and greatly affect the sensitivity of sensors [20,21]. Obviously, the thickness of metal films plays a decisive role in the SPR sensors, and if the thickness value is measured precisely, the performance of sensors can be greatly optimized. In the present studies, the main methods for determination of the thickness of thin metal films in SPR schemes are by means of the reflection change and SPR curve dips in an ATR spectrum [22,23].
In this paper, an improved and optimized experiment system using phase detection method, put forward by our group, to determine the thickness of thin metal films in SPR prism couplers is presented. The relations between the phase and the thickness of thin metal films are studied and the possibility of utilizing the interference pattern to calculate the values of thickness is discussed. Our group has been committing to implement and improve this idea [24,25], and we haven't yet found papers which adopted similar idea to our researches.
2. Basic theory and approach
As shown in Fig. 1, one of the conventional configurations of the ATR method adopting Kretschmann-Raether geometry [7,19] is used to excite the SPs. A prism, refractive index np, consisting of a thin metal film with permittivity εm and thickness d, and a semi-infinite dielectric (here refers to air) with a refractive index na, forms a metal–air waveguide. When light wave incidents on the prism-metal interface, part of the light is reflected, and others which are called evanescent wave, propagates into the metal film and decays exponentially in the direction perpendicular to the interface. If the metal film is thin enough (less than 100 nm), the evanescent wave can penetrate through the metal film and couple with the SPs at the metal-air interface [21]. When the wave vector of the evanescent wave equals to that of the SPs, the SPR effect will occur. Therefore, the resonance condition and angle θSPR can be expressed as
where β is the propagation constant of the SPs, kx the wave vector of the evanescent wave, λ the wavelength of the incident light.According to the Fresnel’s equations, the reflection coefficient rpma and phase ϕ of the configuration can be described as [26]
where , for the TM polarized component, for the TE polarized component, where subscripts i, j refer to p, m, a respectively. Figure 2 indicates the dependencies of the phase and the metal film thickness for TM and TE polarization. As a result, the phase difference of the two polarizations as a function of the metal film thickness is shown in Fig. 3. From Fig. 3, a relative better linearity can be found to calculate the thickness of thin metal film and the value of thickness d can be calculated with measuring the phase difference Δϕ.
Fig. 2 Phase as a function of the metal film thickness for TM and TE polarization Configuration: BK7 glass (np = 1.51), gold film (εm = – 10.6 + i0.81 [27]), air (na = 1), λ = 632.8 nm, θSPR = 43.9°.
3. Experiments
The schematic diagram is shown in Fig. 4. A 5mW He-Ne laser operating at wavelength of 632.8 nm is used as a light source and a laser beam expander serves to collimate and broaden the light beam. A polarizer is used to obtain a linear polarization whose direction is at 45° from both TM and TE polarization. The light beam is then incident in the SPR prism coupler which is three-dimensionally illustrated in the dashed boxes of Fig. 4. The prism is made of BK7 glass and its bottom surface is covered partially by a layer of gold film with about several tens nm thick by magnetron sputtering. Moreover, the coupler is placed on a rotation stage which is fixed to an XYZ axis stage. The angle of incidence has to be around the value of resonance angle θSPR, so it is approximately 43.9° in the experiment. The light beam can scan the whole glass-gold and -air interface by the three-dimensional stage, in order to get the information of the gold film and the reference substrate region respectively. The reference substrate is the portion of the base of the prism that is not coated with the gold film.
The reflected light beam is separated into TM and TE components by a polarizing beam splitter. After the reflection from the two mirrors, both beams converge into a light again in another beam splitter with orthogonal polarizations. The beam is then directed through a polarizer to make the TM and TE components to keep a consistent polarization direction. Actually, the beam splitters, mirrors and polarizers together form a Mach-Zehnder configuration to gain interference fringes. Finally, the interference pattern is recorded by a CCD camera and processed by a computer.
The intensity of interference pattern can be expressed as the following equation based on the interference principle [26]
where I1 and I2 represent the intensity of the two coherent beams respectively. ΔS is the difference between the optical paths for the two waves which remains unchanged for the measuring process of gold film and reference substrate, while Δϕ has great variation respect to thickness variable. Therefore, the relation between the movement of the interference pattern and the phase difference can be described as the following equation.where x1 and x3 are the centerline position coordinates of two adjacent bright fringes with reference substrate, x2 is the centerline position coordinate of the bright fringe with gold film, and Δϕ(0) stands for the phase difference with reference substrate. The schematic diagram of the interference pattern is shown as Fig. 5.Based on Eq. (4), (5) and (7), the relation between the movement of the interference fringes and the thickness of the gold film has been established, and Fig. 3 illustrates how the phase difference varies as the thickness of the gold film, so the value of thickness can be determined by calculating the movement of the interference fringes.
4. Results and discussion
The typical images of the interference pattern in the reference substrate and gold film region are shown in Fig. 6(a) and 6(b) respectively. Figure 6(c) particularly illustrates the bending fringes of the transition region, which reflects the shift of the interference fringes more intuitively. The top part of the pattern is produced when the light beam is directed on the substrate region and the lower part is produced on the gold film region. The reflectivity of the gold film region is smaller than that of the substrate region under SPR, so the lower part appears darker. The benefit of using the interference pattern of the transition region to calculate the results is that it can eliminate the disturbance caused by light path. Thus, according to the method, we can get the thickness d = (31.2 ± 0.4) nm (mean ± SEM, n = 5, SEM is the standard error of the mean) by selecting a point of the transition region with five repeated measurements.
Fig. 6 Typical images of interference pattern in reference substrate (a), gold film (b) and transition (c) region.
Moreover, in order to verify the reliability of our result, the gold film is also deposited on a silicon chip while on the bottom surface of the prism. So the step height of the gold film on the chip, which is measured with an atomic force microscope (AFM, Nanoscope IIIa, operating in tapping mode, which is carefully calibrated by grating standard of NIST), can be regarded as the reference value of the gold film thickness of the prism coupler. The step height is approximately 30.3 nm as shown in Fig. 7 which derives from the AFM bundled software. Therefore, by comparing the measurement values of the thickness and the reference ones of the two experiments, the presented approach is feasible and reliable.
In addition, the experiments with deposited thickness of 20.0 nm and 50.0 nm have been studied, and the measurement results are d = (22.1 ± 0.6) nm and d = (50.6 ± 0.6) nm (mean ± SEM, n = 5) respectively. The error bar of the three experiments is shown in Fig. 8 and the results are expressed as mean ± SEM which illustrate the reasonably good repeatability of the approach. Furthermore, the thin gold films are taken as examples in this study to demonstrate feasibility of the method, because they are most commonly used in SPR prism couplers. This approach, of course, is also practical to other metals such as silver, copper, titanium, etc.
5. Conclusion
This paper proposes a novel method to determine the thickness of thin metal films in SPR prism couplers by the means of phase detection. The method takes advantage of the phase difference under SPR to calculate the value of thickness, and enables to record the interference patterns which contain the information of the phase difference. The approach can restrain the common mode noise caused by light path effectively, because of utilizing the image of the interference pattern in the transition region, so that more accurate and reliable results can be obtained. Compared to other methods, in addition to the new method, it is possible to use our method to determine the thickness of thin metal films within 100nm in SPR prism couplers directly. Moreover, the measuring system structure is simple, thus it is easier to implement, and its resolution can achieve sub nanometer level. So it would be convenient to use this method in other experiments with SPR prism couplers to determine the thickness of the thin metal films.
Acknowledgments
This work was supported by the Specialized Research Fund for the Doctoral Program of Higher Education, State Education Ministry of China (SRFDP No. 20120032110059).
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