High-precision measurement of optical constants of ultra-thin coating using surface plasmon resonance spectroscopic ellipsometry in Otto-Bliokh configuration

Guohang Hu; Hongbo He; Anna Sytchkova; Jiaoling Zhao; Jianda Shao; Marialuisa Grilli; Angela Piegari

doi:10.1364/OE.25.013425

1. Introduction

Ultra-thin layers are widely used in optical and electrical systems, yet the determination of their complex refractive index (N = n + ik) and thickness d remains a difficult task. X-ray reflectivity (XRR) and transmittance electron microscopy (TEM) techniques are good tools to measure nanometer-level thicknesses, but they cannot measure the optical constants of materials. Ellipsometry is a sensitive technique to measure the refractive index and thickness at the same time. It allows characterization of angstrom-thin layers, but interconnectedness of the film optical constants and its geometrical thickness, intrinsic for all methods measuring optical thickness of coatings, poses at times difficult problem of data elaboration, especially for ultra-thin films. Surface plasmon resonance (SPR) was exploited for the study of the optical constants of ultra-thin layers in attenuated total reflectance (ATR) setups [1–3]. This technique uses the exceptional sensitivity of surface plasmons, which are collective oscillation of electrons at the interface between a conductor and a dielectric. The SP electric field decays exponentially from the metal-dielectric interface into both media, and its decay depth of dozens of nanometers ‘probes’ the materials adjacent to the metal-dielectric interface.

When Maxwell's equations are solved for the interface between a metal and a dielectric, SPR existence condition can be found. SP has component k_x of the wave vector parallel to the surface given by

k_{x} = k_{0} \sqrt{\frac{ε_{m} ε_{d}}{ε_{m} + ε_{d}}}

where k₀ is the free-space wave vector, ε_m and ε_d are the dielectric constants of the metal and dielectric, respectively. The following conditions are hence required for supporting the SPR: ε_m < -ε_d and Re{k_x}>k₀. The plasmonic wave can be excited either by coupling to the light traveling in an optically dense medium (a high-index prism in either Kretschmann [4] or Otto [5] configuration) or using a grating coupler, when the grating period provides the necessary addition to k₀.

Otto configuration (uncoated prism-air-sample) developed in 1968 for ATR measurement enables coupling of light wave with plasmonic wave on the sample’s metal surface [5]. Compared to more widely used Kretschmann configuration [4], where the prism is coated with a plasmonic metal of a certain optimal thickness and the SP is excited in the prism metal layer to probe dielectrics, Otto configuration allows more flexibility in probing of samples of any composition. The drawback of Otto configuration is the difficulty to control accurately the nanoscale thickness of air gap between the prism and the sample, both in terms of the distance measurement and the gap geometry. In 2006, Bliokh et al. [2] modified this configuration for the ATR measurement setup, adding a convex surface between the prism and the sample. In this geometry, the thickness of the air gap varies spatially and it is easily controlled through the prism surface curvature. The SPR reflectance dip forms a two-dimensional elliptical pattern on the sample surface. Recently, T. Iwata and G. Komoda demonstrated that Bliokh's configuration had high potential for obtaining the optical constants of metal or dielectric layer at single wavelength or at several wavelengths [3,6].

Traditionally hence, SPR-based setups for determining of optical constant were limited to a single wavelength, or at several wavelengths, from the reflectance intensity Rp versus variation of the incident angle. Few works studied the measurement of thin films by the phase change while the occurrence of SPR, although theoretical analysis have proved the advantage of phase change in determination of optical constant [7,8].

Nowadays, surface plasmon resonance (SPR)-based ellipsometry, or Total-internal reflection enhanced (TIRE) ellipsometry proposed in the beginning of years 2000 [7], is a well-established tool for various biological, medical, and chemical applications [9,10]. Such instruments normally combine ellipsometry with Kretschmann’s configuration of prism-sample coupling. Ellipsometry in Otto configuration was proposed recently [11].

In this paper, a SPR ellipsometry, based on Otto-Bliokh configuration, is proposed to combine sensitivity of surface plasmon with accessibility of optical constants and the advantages of ellipsometry. The resonance center can be adjusted by changing the thickness of air gap in the Otto-Bliokh configuration. A micron-size beam spot is used to achieve the nanoscale thickness of air gap. The amplitude and phase change induced by SPR in the visible and near-infrared spectral range have been obtained to determine the dispersion of optical constants and the thickness of the ultra-thin layer. Theoretical and experimental results have proved the high precision of this technique.

2. Experimental setup

2.1 SPR-based ellipsometry

The schematic diagram of the proposed setup is shown in Fig. 1. This facility can be separated into two main parts: an ellipsometry and an Otto configuration. The Otto configuration consists of optical prism, air gap, ultra-thin metal layer and substrate, which is used to excite surface plasmon wave. A phase modulated spectroscopic ellipsometry is applied in this study [12]. Light emitted by a Xenon lamp is linearly polarized before impacting the prism/sample assembly. The light beam is shaped to a micron-size spot achieving 63μm × 70μm at the sample surface for the incident angle of 41°. The reflected beam passes then through a photoelastic modulator, a second polarizer traditionally called analyzer and a monochromator. The reflected light intensity is measured by a detector.

Fig. 1 Schematic diagram of the SPR-based spectroscopic ellipsometry.

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We simplified the convex prism manufacturing by employment of a planoconvex singlet lens optically contacted to the bottom of a standard prism. The plane of a planoconvex singlet lens is optically matched with a rectangular prism using an index matching oil. The radius of the convex lens R is 3000mm. The convex surface in the prism-lens configuration contacts the sample surface at one point (contact point). The thickness of the air gap d_air between the plane surface of the sample and the curved surface of the planoconvex varies with distance r from the contact point along the sample surface. The d_air is calculated by the following equation

d_a i r = R - \sqrt{R^{2} - r^{2}}

To minimize the impact of the air gap thickness variation, a micron-scale beam spot is used. The length L of the beam spot is 63μm along X-axis. The variation of the air gap thickness in the beam spot can be calculated as follows

d_a i r_u n c e r = \sqrt{R^{2} - {(r - L / 2)}^{2}} - \sqrt{R^{2} - {(r + L / 2)}^{2}}

where d_air_uncer is the uncertainty of the air gap thickness. While R and r are 3000 mm and 1.2 mm, the thickness of the air gap, varying along the dimension of the light spot, is in the range from 228nm to 253nm. The average thickness of air gap is 240nm with the variation of 25nm, i.e. about ± 5% of the mean value. So the thickness of air gap is assumed as a constant value along the measurement spot. The apparatus allows also angular-resolved scans, ensuring that the incident angle on the sample was greater than the critical angle. Variation of the light beam spot position along the sample surface provides values of ellipsometric angles Ψ and Δ corresponding to various values of the air gap thickness.

2.2 Numerical Simulation of the sample-prism assembly

The prism/planoconvex lens /sample assembly can be considered as a multilayer stack on a plane substrate. In the simplest case of the Otto-Bliokh prism approached to a metal film covering a glass substrate, such multilayer consists of two layers: air layer and thin metal layer. The incident material is the glass of the prism, and output material is that of the substrate. The conventional characteristic matrix calculation can be then employed, and summarized as follows. The characteristic matrix of every layer (air gap, layers of the sample coating) in case of TE wave (s polarization) is [13]

M_{i} = [\begin{matrix} \cos (k_{0} n z \cos θ) & - \frac{i}{p} \sin (k_{0} n z \cos θ) \\ - i p \sin (k_{0} n z \cos θ) & \cos (k_{0} n z \cos θ) \end{matrix}],

where

p = \sqrt{ε / μ} \cos θ

. k₀, n, z, ε, μ are wave number, refractive index, thickness, permittivity and permeability of the layer, respectively. θ is the angle of incidence to the layer.

For TM wave (p polarization), the same equations hold, with p replaced by $q = \sqrt{μ / ε} \cos θ$ .

The characteristic matrix of this multilayer stack can be calculated in a standard way:

M = M_{1} M_{2} M_{3} ... M_{j} = [\begin{matrix} m_{11} & m_{12} \\ m {}_{21} & m {}_{22} \end{matrix}]

The subscript 1, 2, 3 … j indicates the layer sequence.

Then the reflectance of TE wave can be expressed as

r_{s} = \frac{(m_{11} + m_{12} p_{l}) p_{1} - (m_{21} + m_{22} p_{l})}{(m_{11} + m_{12} p_{l}) p_{1} + (m_{21} + m_{22} p_{l})}

where

p_{1} = \sqrt{ε_{1} / μ_{1}} \cos θ_{1}

and

p_{l} = \sqrt{ε_{l} / μ_{l}} \cos θ_{l}

ε₁ and ε_l are the dielectric permittivity of input and output materials, and μ₁ and μ_l their magnetic permeability.

For TM mode, the Eq. (6) holds, with p₁ and p_l replaced by $q_{1} = \sqrt{μ_{1} / ε_{1}} \cos θ_{1}$ and $q_{l} = \sqrt{μ_{l} / ε_{l}} \cos θ_{l}$

r_{p} = \frac{(m_{11} + m_{12} q_{l}) q_{1} - (m_{21} + m_{22} q_{l})}{(m_{11} + m_{12} q_{l}) q_{1} + (m_{21} + m_{22} q_{l})}

Then the complex reflectance ratio ρ = r_p/r_s = tan(Ψ)e^iΔ can be calculated and the amplitude ratio (ellipsometric angle Ψ) and the phase shift (ellipsometric angle Δ) can be obtained.

The optical constants of ultra-thin metal layer and coatings consisting of an ultrathin dielectric covering a thin metal layer on glass surface were obtained modelling the spectral dependence of the ellipsometric angles and minimizing the mean square error (MSE) between the experimental value and theoretical value. The MSE was defined as below.

M S E^{2} = \frac{1}{N} \sum_{i = 1}^{N} [{(\frac{Ψ_{i}^{m o d} - Ψ_{i}^{e x p}}{Ψ_{i}^{e x p}})}^{2} + {(\frac{Δ_{i}^{m o d} - Δ_{i}^{e x p}}{Δ_{i}^{e x p}})}^{2}]

where mod and exp represent the data calculated from the theoretical model and the experimental data, respectively. N is the number of measured Ψ and Δ pairs being included in the fitting. The refractive index of the prism and substrate in the wavelength range of interest (700-1200nm) is acquired from the dispersion of BK7 glass [14], while that of an ultra-thin metal layer can be expressed using the Drude model:

ε (ω) = ε_{\infty} - \frac{ω_{p}^{2}}{ω^{2} + i Γ ω}

with ω_p being the metal plasma frequency, Γ the collision frequency, ε_∞ the constant offset encountering for interband transitions. In the case of a single metal layer over the glass substrate, five parameters were set as free parameters to minimize the MSE, that were, ω_p, Γ, ε_∞, z, d_air, with z being the thickness of the metal ultra-thin layer.

To reduce the number of iterations and improve the computation efficiency in the multi-parameter fitting procedure, it is important to give a reasonable initial set of values for the free parameters in the fitting. The initial values of ω_p and Γ were adopted from [15], that of z was estimated from the material deposition rate, and that of d_air was assumed basing on the calculation using the Eq. (2).

3. Results and discussion

A careful alignment procedure has been elaborated to ensure accuracy of the measurement. A white light beam with the diameter of ~10mm is incident on the sample surface. This white light beam follows the same path like the micron-size beam for the SPR-based ellipsometry measurement, as shown in Fig. 1. The cm-size white light beam is used for the illumination of the prism-sample contact zone, and a microscope is applied for its observation. Figure 2 is an image of the sample surface, and at this position, a typical absorption spot due to the occurrence of SPR is observed. The absorption spot shape is different from the elliptical fringe described in [3], because in our experiment the wavelength range was different and varied from the visible to the near-infrared. Theoretical analysis suggests that the resonance spectral position shifts to shorter wavelengths and more light is absorbed while the distance r is decreased, so a black spot is formed.

Fig. 2 A SPR absorption spot observed for a thin gold film illuminated by a white light.

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Six samples of ultra-thin gold films with different thicknesses were deposited by magnetron DC-sputtering technique. The base pressure was below 5 × 10⁻⁴Pa, and the working pressure was 0.5Pa. The film thickness was controlled by the deposition time. Estimated deposition rate was 0.4nm/s.

Figure 3 shows the experimental values (circles) of both ellipsometric angles Ψ and Δ measured for the thinnest of the films, at different thicknesses of the air gap, and their model curves for their spectral dependence. The angle of incidence on the interface between convex surface and air gap was 42.36°. The thickness of this coating was determined to be 7.9nm. In Fig. 4, a cross-section of this ultra-thin gold coating observed by TEM image is shown. The black line is the cross section of the film which TEM-measured thickness was found to be in a good agreement with the thickness inferred from our ellipsometric measurement. Additionally, XRR technique [16] was applied to measure the thickness of the gold coatings, and the results are in good agreement with the two other techniques, as shown in Fig. 5. The complex refractive index of this coating, measured by SPR-based ellipsometry, is shown in Fig. 6, and is consistent with the bulk material reported in [17]. All of these results proved the accuracy of this measurement.

Fig. 3 The ellipsometric angles (a)Ψ and (b)Δ varied with light wavelength, obtained by SPR-based ellipsometry and numerical fitting, of a ultra-thin gold film at different thicknesses of the air gap.

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Fig. 4 The cross-section of an ultra-thin coating observed by TEM.

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Fig. 5 The thickness of ultra-thin gold coatings measured by XRR and SPR-based ellipsometry.

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Fig. 6 (a) Real part and (b) imaginary part of the refractive index of a 7.9nm thick gold layer compared to the values of bulk gold [17].

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Figure 7 reports the measured and modelled Ψ and Δ curves of ultra-thin gold film with thickness 7.9 nm, 10.3 nm and 15.3 nm, while the angle of incident on the interface between convex surface and air gap is 42.36°. As seen it easily distinguishes the difference between the thickness of 7.9 nm and 10.3 nm.

Fig. 7 The ellipsometric angles (a) Ψ and (b) Δ varied with light wavelength, obtained by SPR-based ellipsometry and numerical fitting, of gold films with different thickness. d_film is the thickness of the ultrathin gold film.

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The precision of our setup for ellipsometry in Otto-Bliokh configuration was estimated, and compared with that of ellipsometry without SPR excitation. The stratified medium theory is applied, as discussed in Section 2, examining the case of a single gold film with thickness 8nm on glass. The angle of incident on the interface between convex surface and air gap is chosen to be 42° and air gap thickness to be 300 nm. The simulated spectral and angular dependences of Ψ and Δ are shown in Fig. 8.

Fig. 8 (a)Ψ and (b) Δ varied with light wavelength and incident angle in ellipsometry without SPR. (c) Ψ and (d) Δ varied with light wavelength and incident angle in SPR-based ellipsometry.

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When the layer thickness increases from 8.0 nm to 8.1 nm, the resonance spectral position shifts from 948 nm to 942 nm, as shown in Fig. 9 (c) and (d), for both Ψ and Δ. When the refractive index increases by 0.05, Δ shifts by 18.5° at the wavelength of 940 nm, as seen in Fig. 10 (d). As seen, our SPR-based ellipsometry setup has a very high measurement sensitivity.

Fig. 9 (a) Ψ and (b) Δ varied with light wavelength in ellipsometry without SPR. (c) Ψ and (d) Δ varied with light wavelength in SPR-based ellipsometry. d_film is the thickness of the ultrathin gold film.

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Fig. 10 (a) Ψ and (b) Δ varied with light wavelength in ellipsometry without SPR. (c) Ψ and (d) Δ varied with light wavelength in SPR-based ellipsometry. n_film is the refractive index of the ultra-thin gold film with the thickness of 8nm [15].

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Therefore, it’s believed that the SPR-based ellipsometry has a good potential of measuring optical constants with high precision. Moreover, this kind of technique could also be used to measure the optical constants of ultra-thin dielectric coatings deposited on metal or semiconductor (layer or bulk) material supporting SPR, similarly to the approach described in [11] and [18].

4. Conclusion

A SPR spectroscopic ellipsometry, based on Otto-Bliokh configuration, is developed to combine sensitivity of surface plasmon with advantages of spectroscopic ellipsometry. The amplitude and phase change induced by SPR in the visible and near-infrared spectral range were measured to determine the dispersion of optical constants and the thickness of the ultra-thin layers. A set of ultrathin gold films were analyzed and the retrieved film thicknesses were found to be in excellent agreement with TEM and XRR measurement results. Experimental and theoretical analysis proved that this SPR-based ellipsometry has a high potential for extraction of optical constants of ultra-thin layers of plasmonic materials (metals and semiconductors) and non plasmonic layers over plasmonic materials.

Funding

National Key Research and Development Project of China (2016YFE0104300); International Science & Technology Cooperation Program of China (2012DFG51590); The Italian-Chinese Project of Great Relevance (PGR00799).

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High-precision measurement of optical constants of ultra-thin coating using surface plasmon resonance spectroscopic ellipsometry in Otto-Bliokh configuration

Abstract

1. Introduction

2. Experimental setup

2.1 SPR-based ellipsometry

2.2 Numerical Simulation of the sample-prism assembly

3. Results and discussion

4. Conclusion

Funding

References and links

Cited By

Figures (10)

Equations (8)

Optics Express