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Abstract
A new surface plasmon resonance (SPR) configuration is proposed, which consists of a prism, a dielectric layer, a metal coating, and a matching liquid. The optical constants of each layer in the proposed prism-dielectric-metal-liquid (PDML) configuration have been optimized to match the SPR conditions and reach the strongest intensity. Combining the PDML configuration with spectroscopic ellipsometry, SPR spectroscopic ellipsometry (SPRSE) with a PDML configuration was developed. The SPR wavelength can be adjusted to the desired wavelength by varying the thickness of the dielectric layer. The amplitude and phase change, magnified by the SPR in the visible and near-infrared wavelengths, were obtained to determine the optical constants and thickness of ultrathin metal coatings. The extracted optical constants were found to be in good agreement with the results obtained using transmission electron microscopy (TEM) and X-ray reflectivity (XRR) techniques. These SPRSE measurements show great potential for characterizing the interface between a metal coating and a dielectric layer, and the surface uniformity of ultrathin metal coatings.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Ultrathin metal films and dielectric films are widely used in many applications, e.g., magnetic tunnel junctions (MTJ) and X-ray multilayers [1,2]. The thicknesses and optical constants of the ultrathin metal films in X-ray multilayers and MTJ devices directly determine the device performance. The increasing demand for high-performance nano-scaled devices [3] requires a more precise characterization of these ultrathin films. It is well known, in fact, that the optical properties of ultrathin films are quite different from those of bulk materials, owing to their special structure and deposition process [4,5].
In previous studies, surface plasmon resonance (SPR), which is widely used in biomolecules [6], was introduced in ellipsometry, using Kretschmann or Otto configurations to improve the measurement precision of the optical constants of the ultrathin coatings [7–10]. The SPR is an electric excitation that decays exponentially from the metal–dielectric interface into both media, while it propagates along the surface of the metal with a wave vector kx. According to Maxwell’s equations, kx is given by [11]
where k0 is the free-space wave vector, and εm and εd are the dielectric constants of a metal and a dielectric, respectively. SPR is induced when the parallel component of the wave vector of the light incident to the interface becomes equal to kx.In the Kretschmann configuration, where a thin metal film is sandwiched between a prism and air, the SPR wavelength is difficult to adjust to the visible wavelength, if the thickness of the metal film is ≤ 20 nm. In contrast, the Otto configuration, where an air gap exists between a prism and a metal film, allows the resonance position to be easily adjusted to visible wavelengths by varying the air-gap thickness. Unlike the Kretschmann configuration, the Otto configuration can be used for ultrathin films. However, the need for accurate and precise control of the separation between the prism and the metal surfaces makes the mechanical adjustment quite challenging.
In 2006, Bliokh et al. proposed a method for controlling the air-gap thickness with hundreds of nanometers using a convex-plane lens attached to a prism, in which the thickness of the air gap was automatically and gradually increased away from the contact point [12]. Since then, the Otto–Bliokh configuration has been used in many studies. In 2007, Iwata et al. theoretically proved that introducing an ellipsometric measurement technique to an absorption-based Otto configuration would further improve the measurement precision [13].
Recently, we experimentally introduced the Otto–Bliokh configuration to imaging ellipsometry and spectroscopic ellipsometry (SE) [14,15]. In these methods, the amplitude ratio Ψ and the phase difference Δ between the p-component and s-component of light are magnified, owing to the SPR absorption; thus, the magnified information enables slight variations to be distinguished with high sensitivity in the optical constants of ultrathin metal coatings. However, in the Otto–Bliokh configuration, the air gap is difficult to determine because it varies gradually; moreover, the beam spot must be limited during the measurement to minimize the variation of the air-gap thickness at the measured point. The fluctuation of the light source may also produce certain errors. In addition, the uncertainty in the air-gap thickness may result in multiple solutions in the extraction of the optical constants.
In this paper, a prism-dielectric-metal-liquid (PDML) configuration is proposed. A dielectric coating, with a several-hundred-nanometer thickness and a relatively small refractive index, is inserted between a prism and a metal coating. When measured, the metal is dipped in a liquid to match the SPR conditions and reach the strongest intensity. The accuracy of the dielectric layer reaches nanometers, which can be easily measured and accurately controlled. The resonance wavelength of the SPR excited in the PDML configuration can be set to the desired wavelength by carefully adjusting the thickness of the dielectric layer.
SPR spectroscopic ellipsometry (SPRSE) was developed by applying the PDML configuration to SE. This technique enables the characterization of the surface uniformity of the measured films. Simulated and experimental results show that SPRSE with the PDML configuration proposed in this paper provides high potential to precisely measure the optical constants of ultrathin metal coatings. Furthermore, the presented measurement method is very sensitive when determining the optical constants of ultrathin metal layers. This method enables the study of the interface between the plasmonic metal and dielectric coating.
2. Experimental setup
The optical setup of the proposed technique is depicted in Fig. 1. It consists of two main parts: the PDML configuration and the SE. The PDML configuration includes four layers, which are used to excite surface plasma waves. The first layer is a right-angle optical prism with a relatively high refractive index. The second layer is a dielectric layer with a relatively small refractive index. The several-hundred-nanometer thickness of the dielectric layer can be precisely and easily controlled using an advanced dielectric-deposition process and measured by a profiler or an atomic force microscope. The third layer is the metal coating to be measured and the fourth layer is a matching liquid with an optimized refractive index.
Fig. 1 Schematic diagram of an SPR spectroscopic ellipsometry setup, where the PDML configuration is inside the black dashed line.
Phase-modulated SE (HORIBA Jobin Yvon, UVISEL 2) was applied in this study. Light emitted by a xenon lamp covering the visible range and parts of both the ultraviolet and the near infrared range was converted to linearly polarized light by transmitting it through a polarizer; it then impacted the assembly at angle θ. The polarization state of the light reflected from the assembly was converted to an elliptically polarized state. The reflected light passed through a photoelastic modulator and analyzer. A monochromator was applied to select different wavelength. The intensity of the reflected light was measured by a detector to determine the ellipsometric parameters (Ψ, Δ) by analyzing the changes in the polarization.
Total internal reflection (TIR) occurs when light travels from the prism to the dielectric layer at an angle equal to or greater than the critical angle at the prism–dielectric interface. Light is supposed to be completely reflected into the incident medium, while the evanescent wave passes through the interface into the second medium. When the wave vector of the evanescent waves matched that of the surface plasma waves, the SPR condition was satisfied at the dielectric–metal interface. In addition, the energy reflectance of the p-polarized light decreased significantly before being reflected to the detector.
Ellipsometric parameters Ψ and Δ are introduced and defined by a complex ratio (ρ) of the p- and s-polarized Fresnel reflection coefficients rp and rs, respectively, which is given by
The optical constants of the ultrathin coatings were obtained by modeling the spectral and angular dependences of Ψ and Δ, and minimizing the mean square error (MSE) between the theoretical and experimental values; the MSE was defined as in the literature [14].The SPR can be excited optically at a specific angle and incidence wavelength by the evanescent wave present in the total internal reflection (TIR) [8]. To generate the TIR at the prism–dielectric interface, the refractive index of the dielectric layer should be lower than that of the prism. To improve the measurement accuracy and reduce the experimental difficulty, the TIR angle should not be too large, which requires a larger refractive-index difference between the dielectric layer and the prism [16].
The materials of the first and second layers in the PDML configuration were chosen as dense flint (ZF1) glass and magnesium fluoride (MgF2), respectively. Because ZF1 glass and MgF2 are transparent and have negligible absorption in the investigated range, the Sellmeier model was used, which gives the following [17]:
where n is the refractive index, λ is the light wavelength, Bn is proportional to the density of the effective electron states, and Cn represents a wavelength parameter corresponding to the effective electron energy level. The Bn and Cn values were taken from data reported in the literature [18,19].Because an SPR is very sensitive to refractive-index variations near the surface of the metal, which is very thin in the present experiment, the refractive index of the fourth layer in the PDML configuration has a great influence on the resonance behavior and should be carefully considered. When the resonance requirement is satisfied, the penetration depth of the evanescent wave is given as follows [20]:
where n1 is the refractive index of the prism, n4 is the refractive index of the substrate under the metal film, θ is the incident angle, and λ is the light wavelength. As the equation shows, the refractive index of the fourth layer strongly influences the light-penetration depth. Hence, the thickness of the dielectric layer and the refractive index of the substrate should be considered and optimized comprehensively, to confine the surface plasmon field to the vicinity of the metal-film surface.According to simulations, the refractive index of the fourth layer should be larger than that of the second layer. However, a commonly used solid substrate cannot fully adhere to the metal film, while a liquid could better satisfy such a condition. Based on these considerations, n-butanol was selected as the matching layer in this study, and the n-butanol Sellmeier coefficients in the dispersion formula were adopted from the literature [21]. A Drude model was applied for the ultrathin metal layer (third layer), and it gave [15]
where ωp is the metal plasma frequency, Γ is the collision frequency, and ε∞ is the constant offset for inter-band transitions. Three parameters, ωp, Γ, and the metal-film thickness d, were set as free parameters to minimize the MSE. To reduce the number of iterations and improve the computation efficiency of the multi-parameter-fitting procedure, it is important to select a reasonable initial set of values for the free parameters in the fitting. The initial values of ωp and Γ were adopted from data reported in the literature [15]; d was estimated from the material deposition rate.The optical constants of the ZF1 glass, MgF2 layer, and n-butanol were determined by SE, and simulated by the dispersion formula analyzed above; the initial values of the optical constants were taken from data reported in the literature [18,19,21], as shown in Fig. 2.
3. Calculation results
To compare the precision and sensitivity of the proposed SPRSE technique with those of SE without SPR excitation, the ellipsometric parameters of the two techniques were simulated using the above-described analysis. Under the simulated conditions, the first, second, third, and fourth layers in the PDML configuration were ZF1 glass, a 360-nm-thick MgF2 film, a 10-nm-thick silver (Ag) film, and n-butanol liquid, respectively. The spectral and angular dependences of Ψ and Δ were calculated as shown in Fig. 3.
Fig. 3 Simulated ellipsometric parameters (a) Ψ and (b) Δ as functions of the wavelength and incident angle of ellipsometry without SPR excitation. (c) Ψ and (d) Δ as functions of the wavelength and incident angle in SPRSE.
Figure 3 shows ellipsometric parameters Ψ and Δ for a 10-nm-thick Ag film, simulated for different angles and wavelengths of incident light, using ellipsometry without SPR excitation (Figs. 3(a) and 3(b)) and using the PDML configuration (Figs. 3(c) and 3(d)). Compared with the ellipsometry without SPR excitation, the ellipsometric parameters in the proposed SPRSE measurement experienced a significant variation at specific angles and wavelengths, indicating that this technique is highly sensitive to the incident angle and the light wavelength.
The sensitivity of SPRSE in the PDML configuration was compared with that of SE without SPR and SPRSE using an Otto–Bliokh configuration. The ellipsometric parameters in all cases were simulated in the spectral range from 500 to 2000 nm at a 64° angle of incidence. The ellipsometric parameters of Ag films with 9- and 10-nm thicknesses were taken as examples to compare these three methods.
The calculation results show that the difference in ellipsometric parameters between the 9-nm and 10-nm coatings is quite large for SPRSE using a PDML configuration and that using an Otto–Bliokh configuration. The resonance intensity and trends of the ellipsometric parameter curves in SPRSE using a PDML configuration are similar to that in SPRSE using an Otto–Bliokh configuration, as shown in Fig. 4.
Fig. 4 Simulated ellipsometric parameters (a) Ψ and (b) Δ for two different Ag-film thicknesses by means of SE without SPR, SPRSE using the PDML configuration, and SPRSE using the Otto–Bliokh configuration (OBC). The incident angle is 64° for the first two cases and 42° in the last case. The wavelengths range from 500 to 2000 nm in all cases.
The proposed technique has a higher sensitivity to film-thickness variations than SE without SPR, and is easier to implement than SPRSE with an Otto–Bliokh configuration, in which the air gap is difficult to control [22]. Therefore, even though the resonance in the two SPRSE techniques is very similar, the proposed technique has more advantages. For example, it overcomes the following drawbacks of SPRSE with an Otto–Bliokh configuration: i) the convex-plane lens is difficult to completely balance on the sample, ii) a slight tilt may induce a great error in the measurement, and iii) the vertex of the convex-plane lens is difficult to determine.
4. Experimental results
The magnesium fluoride (MgF2) films were deposited onto the inclined plane of the right-angle prism (ZF1 glass) using the electron-beam evaporation method. The base pressure was below 3.0 × 10−4 Pa, and the working pressure was 5.0 × 10−4 Pa. The designed thickness of the metal layer was controlled by adjusting the deposition time. The estimated deposition rate was 0.3 nm/s. Ultrathin Ag films with various thicknesses were deposited onto the MgF2 layer using the magnetron sputtering method. The base pressure was below 2.0 × 10−4 Pa, the working pressure was 0.5 Pa, and the sputtering power was 100 W. In this case, the metal-film thickness was controlled by adjusting the deposition time. The estimated deposition rate was 0.3 nm/s.
As shown in Fig. 5, Ag films with thicknesses of ~10 nm and ~15 nm were measured using the proposed SPRSE technique at an incidence angle of 64°. The fitted results are in good agreement with the experimental measurements, and the ellipsometric curves of these two films are significantly different, which provides good potential for distinguishing different film thicknesses and, furthermore, allows us to characterize ultrathin metal films with higher precision.
Fig. 5 Experimental results (dots) and fitted results (lines) of the ellipsometric parameters (a) Ψ and (b) Δ of a ~10-nm-thick Ag film and a ~15-nm-thick Ag film. In each case, the incident angle is 64°, and the wavelengths range from 500 nm to 2000 nm.
The thicknesses of these Ag films, determined by the SPRSE technique proposed in this paper, were compared with that determined by X-ray reflectivity (XRR) measurement, which was performed on a reflectometer with Cu-Kα (0.15406 nm) radiation over an angular range from 0 to 3°. The experimental data for Ag films with thicknesses of ~5, ~8, ~10, and ~15 nm are shown in Fig. 6. A comparison of the results from both methods shows that the SPRSE measurement results are in good agreement with the XRR measurement results.
Fig. 6 Thicknesses of the Ag films measured by SPRSE using the PDML configuration and X-ray reflectivity (XRR).
In addition, a transmission electron microscopy (TEM) measurement was performed to measure the cross section of the above sample. As shown in Fig. 7, the cross section of sample #3 reveals that the thickness of the Ag film is about 10.9 nm at the measured point, but it varies at different locations. The reason for this phenomenon may be the non-uniformity of the coating process, which is worth further study. The complex refractive index of this coating, measured by SPRSE with a PDML configuration, is shown in Fig. 8, and is consistent with the results measured by SPRSE with an Otto–Bliokh configuration. All of these results demonstrated the accuracy of this measurement.
Fig. 7 Transmission electron microscopy (TEM) image of the cross-sectional structure of an ultrathin Ag film deposited on a layer of MgF2 film.
Fig. 8 (a) Refractive index and (b) Extinction coefficient of a 10.9-nm-thick silver layer measured by SPRSE using the PDML configuration, and SPRSE using the Otto–Bliokh configuration (OBC).
The technique proposed in this paper enables measurements at different positions on the film surface because the sandwiched dielectric layer is fixed. Therefore, this method provides a method for characterizing the uniformity of the film thickness. As shown in Fig. 9(a), the SPRSE measurement was carried out on a sample (10.9-nm-thick Ag film on 362.3-nm-thick MgF2) at different positions along the YY’ axis with a 1-mm interval. The measured thicknesses at different locations are shown in Fig. 9(b), which indicates that the film thickness varies slightly from position to position.
Fig. 9 (a) Measurement points and YY’ axis on the surface of the Ag film with the PDML configuration and (b) film thickness of a 10.9-nm-thick Ag film measured at different positions along the YY’ axis, where the angle of incidence is 64°.
5. Conclusion
In this work, by combining a PDML configuration with spectroscopic ellipsometry, SPR spectroscopic ellipsometry was developed to measure the thickness and optical constants of ultrathin metal films. Through numerical calculations and corresponding experiments, we showed that the proposed experimental setup and measurement method has high potential for precisely measuring the optical constants of ultrathin metal films.
Experimental results confirmed that the measured ellipsometric parameters were in good agreement with those of the numerical calculations. This method was sensitive to variations in the optical constants of the measured metal films and offered numerous advantageous. The thickness of the dielectric layer sandwiched between the prism and the metal film was much easier to control than that of the air gap in the Otto configuration. This method shows great potential for characterizing the dielectric–metal interface. It also enables the characterization of the surface uniformity and provides repeatable and high-resolution measurements.
Funding
National Key Research and Development Project of China (2016YFE0104300), the Italian–Chinese Project of Great Relevance (PGR00799), and the National Natural Science Foundation of China (61405219, 11705259).
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