1. Introduction

Noninvasive characterization of polymeric thin films with a low dielectric constant draws much attention from many areas including industrial fields like packaging processes in semiconductor, integrated chip, multi-layered printed circuit board (PCB), and mobile device fabrication [1]. In particular, with narrowing the pattern size to sub-100 nm line dimension in advanced lithographic techniques, more accurate characterization method for polymeric resist material with a thickness of hundreds of nanometers has to be developed at multiple stage of pattern formation [2-6]. Furthermore, it should be noted that optical, chemical, thermal, and mechanical properties of the thin film, which have been known to have rather strong thickness dependence, must be proven to be compatible to be integrated into real devices [7, 8].

Many different types of optical methods are already available for thickness measurement of polymeric thin films based on different types of optical processes such as reflective interference, transmission, absorption, and emission. The available methods depend on the optical properties like refractive indices and absorbance, and emission quantum efficiency of either the polymeric film itself or a dopant [9-14]. If two different polymer films have very close refractive indices, then in such a case it is not easy to determine thickness of two chemically different polymeric thin films. Confocal reflectance microscopy has been also employed to characterize polymer films with a lateral resolution of hundreds of nanometers, but the method is only applicable to measure surface topography [15]. Infrared absorption microscopy is currently seeking to visualize the chemical composition of polymers at the expense of rather low spatial resolution due to its long wavelength [16]. Furthermore, confocal Raman and infrared near field scanning optical microscopy (IR NSOM) has further been investigated as another promising optical method for the characterization of polymer films [17]. The afore-mentioned methods can provide high resolution at the expense of rather long acquisition times due to the intrinsic low signal-to-noise ratio. Scanning transmission x-ray microscopy (STXM) based on synchrotron radiation soft x-ray beams has been shown to be a powerful imaging technique with high spatial resolution (~ 35 nm) as well as chemical selectivity [18].

Coherent anti-Stokes Raman scattering (CARS), one of a four-wave mixing process involving three laser fields interacting with the sample, was first implemented into microscopy using noncollinear excitation of pump and Stokes visible dye laser beams by Duncan et al. [21]. Zumbush et al reported that forward CARS microscopy under the collinearly propagating pump and Stokes laser beams has a high spatial resolution and three dimensional sectioning capabilities [22]. Later, many different types of microscopic techniques including backward-, epi-, polarized- and multiplex-CARS were utilized for many applications including in-vitro and in-vivo bio-medical imaging [23-25]. CARS microscopy has also been successfully applied for visualizing line pattern in polymeric photoresisters with chemical selectivity as well as with a high lateral resolution of about 270 nm [24]. Multiplex-CARS microscopy was also employed to identify and image the blended polymer films of high contrast [25-27]. However, there are no previous systematic investigations on thickness-dependence CARS signals for polymeric thin films with a thickness of hundreds of nanometers.

In CARS field, anti-Stokes light (ω _as) results from a coherent coupling between pump beam (ω _p) and stokes laser (ω _s). When the frequency difference (ω _p−ω _s) coincides with the frequency of Raman-active vibrational mode (ω _R) of the material, the CARS signal is considerably enhanced at the frequency ω _as (ω _as=2ω _p−ω _s). In general, CARS experiment could be considered as a degenerate four-wave mixing process. In the plane-wave approximation for a non-absorbing material, the CARS signal intensity, I₃, depends nonlinearly on the incident pump laser intensity, I₁ [20]:

in which n_i (i=1, 2, 3) is the refractive indices at the frequency of the pump, Stokes beam, and anti-Stokes beam, respectively. ε ₀ is permittivity, χ_CARS is the third-order nonlinear susceptibility, l is the thickness of sample, Δk the phase mismatch (Δk=k ₃−2k ₁+k ₂) and k_i (i=1, 2, 3) are the wavevectors for each one of the interacting lights. Generation of the CARS signal needs to fulfill the phase-matching condition, Δk·l≪π, which reflects the coherent nature of the CARS process.

It is important to notice that for a very thin film the phase-matching condition is usually satisfied both in forward and backward directions relative to the propagation direction of the excitation beams. Equation (1) further indicates that, for exact phase matching (Δk=0), the CARS signal should depend on the square of the film thickness, l ² when the term of $\mathrm{sinc}\left(\frac{\mathrm{\Delta }kl}{2}\right)$ is unity while keeping I₁ and I₂ constant. This allows us to propose that the thickness of polymer films could be measured by utilizing proper optical scheme without rigorous depth profile accompanied by rather long acquisition times. We have applied multiplex-CARS microscopy to measure the thickness of PMMA thin films. Even if polymeric film is much thinner than the axial resolution of CARS microscopy, we can quantitatively measure the polymer thickness by analyzing the observed CARS signal in terms of a coherent coupling of a resonant CARS field from polymeric thin films with a rather strong nonresonant field from glass substrate.

2. Experiments

2.1 Optical setup

Figure 1 exhibits the experimental set-up of multiplex-CARS microscopy based on a femtosecond laser oscillator [26, 27]. The fundamental output of a femtosecond laser (Coherent, MIRA 900) with a pulse duration of about 130 fs at 780 nm is divided into two beams by 3:7 beam splitters in power. The laser beam with a lower power is focused into a photonic crystal fiber (Crystal fiber, NL, PM, 750) with a length of 320 mm by an objective lens (20X, N.A.=0.4) to obtain a supercontinuum for Stokes light in CARS process. Another beam is spectrally filtered by an optical filter with a spectral bandwidth of about 30 cm^-1, and used for pump light after spatial filtering with a pinhole of 0.1 mm in diameter. The pump and stokes beams are combined both spatially and temporally with a reflective notch filter (FWHM=20 nm at 780 nm) and an optical delay, respectively, and focused collinearly into polymer films through an objective lens (Nikon, 100X, N.A.=0.9). The sample is mounted on an XYZ-translator (Thorlabs, MAX343). CARS signal in forward direction is collected by another objective lens and dispersed with a spectrograph (ARC, Spectra Pro-300i) and detected with an intensified charge coupled device (ICCD). The signal is fed into a personal computer for further analysis. The axial position of the focus of laser beams is maintained such that optimal coupling between samples and laser beams resulted in maximum CARS signal intensity.

 

Fig.1. Experimental setup of multiplex CARS microscopy for characterization of polymeric thin films.

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Fig.2. PMMA film thickness as a function of repeated number of coatings. The inset shows cross sectional profile of the ablated surface of PMMA thin film with 1500 nm in thickness. The thickness was determined by measuring the height difference between the intact surface of PMMA and the bare glass substrate.

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Laser powers for the pump and stokes light were kept to be 7.2 mW (0.095 nJ/pulse) and 2.2 mW (0.029 nJ/pulse) at a repetition rate of 76 MHz. To confirm the absence of any possible photo-induced damage of polymeric thin films, we have measured the time to cause any changes in multiplex-CARS spectra. But for all the polymeric films used in the present work no such observable changes are observed in either CARS signal intensity or spectral features upon photoexcitation of the samples for more than 5 minutes [28].

Spontaneous Raman scattering signals is collected with backscattering geometry at an excitation wavelength of 488 nm and dispersed by a double monochromator (Jobin-Yvon U-1000). The excitation laser light is efficiently removed by inserting a holographic optical filter (Kaiser, USA). The laser power and spectral line width are maintained at values less than 4 mW and 2 cm^-1, respectively [29].

2.2. Preparation of PMMA thin films coated on slide glass and their characterization

Polymeric thin films are prepared by spin casting of polymethylmethacrylate (PMMA, Mw=120,000, T_g=114 °C, Aldrich) solution in toluene on a glass substrate. A glass substrate (76 mm×26 mm, 1 mm thickness, Knittel Glaser, Germany) is cut into three equal parts, cleaned with acetone and methanol, sonicated in distilled water, and then dried at 80 °C in oven. PMMA solutions (5 % in weight) are coated on glass substrate by using a spin coater at a spinning speed of 2000 rpm for 15 s. The films are baked at 80 °C for 2 h. Successive coating and baking procedure resulted in thicker film. In order to determine the thickness of the films, we first precisely ablate the polymer films by utilizing ultrafast laser micro-processing. Due to the difference in ablation threshold value between the glass substrate and PMMA films, we could selectively remove only the PMMA films without any damage to the substrate [30]. Later, we obtained topographic images of the films around the processed area by atomic force microscopy (AFM, PSIA, Korea). Finally, we analyzed the surface morphology and determined the height of film surfaces on glass substrate. Figure 2 shows thin film thickness as a function of number of coating procedures. We have prepared PMMA films with thickness between 180 nm and 4300 nm. All the samples are characterized within 2 days after film preparation.

3. Results and Discussions

Figure 3(a) exhibits CARS spectral features of PMMA films coated on glass substrate with varying film thickness from 180 to 4300 nm. As shown in Fig. 3(b), spontaneous Raman spectral feature of bulk PMMA upon photoexcitation at 488 nm depicts several Raman modes at 2842 cm^-1, 2952 cm^-1 and 3050 cm^-1, which can be attributed to C-H vibration of two different CH₂ and CH₃ groups of PMMA, respectively [31]. Raman shifts of C-H vibration mode of the CH₂ group in CARS signal of PMMA thin films is in agreement with previously reported values of PMMA.

 

Fig. 3. Multiplex CARS (a) and cw-Raman spectral features (b) of PMMA thin films coated on a slide glass substrate. Raman peaks at 2842 cm^-1, 2932 cm^-1, 2952 cm^-1, 3000 cm^-1, and 3058 cm^-1 are in good agreement with reported values [15]. (c-g) are the selected CARS spectral features of PMMA films with a thickness of 180 nm, 715 nm, 1310 nm, 2070 nm, and 4300 nm, respectively. The experimental observation was denoted with black circle. The red solid lines are the best spectra resulted from the fitting procedure of the observed spectra with Eq (3-6) (see text).

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The intensity of the CARS signal gradually decreases with decrease in the thickness of the PMMA films. With decrease in the thickness of the films, the CARS signal of PMMA films shows apparent shifts in the peak position as well as a dip at the high frequency region. This observation from the thin films is quite consistence with the well-known optical interference between the resonant and nonresonant contribution of the third-order-CARS susceptibility observed in micron sized beads. The CARS signal intensity is plotted against the film thickness as shown in Fig. 4. The logarithmic plot is quite linear in the range of a thickness between 400 nm and 2250 nm. The slope of the plot is about 1.6, which is slightly lower than that of the theoretical prediction from Eq. (1) under exact phase matching conditions s (Δk=0).

 

Fig. 4. CARS intensity as a function of the thickness of the PMMA film. The experimental observation was denoted with black circle. Blue circles are the resonant CARS signal from PMMA film resulted from the fitting procedure of the observed spectra with Eq (3-6) (see text). Red solid line represents the dependence of resonant CARS signal resulted from theoretical consideration of CARS field scattered from PMMA disk. For comparison, the line with a slope of two was also displayed by green dotted line.

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Fig. 5. Radiation pattern of far-field CARS from PMMA disk (n=1.5). CARS scatters was centered at the tight focus with high numerical aperture (NA=0.9) with various thickness.

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The CARS signal intensity can also be explained in terms of intrinsic material properties of the third-order nonlinear susceptibility, χ ⁽³⁾ _CARS, which consists of a resonant (χ ⁽³⁾ _r) and a nonresonant term (χ ⁽³⁾ _nr) in the following form:

in which, ω_as denotes the frequency of the CARS signal. In our samples, χ ⁽³⁾ _nr is the sum of nonresonant third-order susceptibility for the glass substrate (χ ⁽³⁾ _Glass,nr) and PMMA (χ ⁽³⁾ _PMMA,nr). And also, since χ ⁽³⁾ _r is the sum of the third-order nonlinear susceptibility for all the Raman mode, which contributed to the CARS signal at ω_as, the Eq. (2) could be described as follows:

in which i denotes i-th Raman active vibration mode of PMMA. The resonant and nonresonant susceptibility of PMMA and glass substrate could also be expressed as follows: [31]

in which A_i is the amplitude of resonant susceptibility of i-th Raman mode with a band width of 2Γ at a peak frequency of Ω. B is the amplitude of the nonresonant susceptibility of PMMA and ω_c and Δ_c are the peak position and spectral full widths at half-maximum for nonresonant CARS signals. The nonresonant susceptibility of glass could also be described with same parameters of ω_c and Δ_c since the nonresonant CARS spectrum should be resemble to the spectral features of stokes beam, which is temporally synchronized with pump beam [16]. If this is the case, we could experimentally determine both the peak position and band width of the nonresonant CARS susceptibility as 2998 cm^-1 and 530 cm^-1, respectively, by fitting the CARS spectral features of intact glass substrate. (Figure 3) Since the axial resolution of current optical setup should be less than 2 µm, the contribution of glass substrate effect to the total CARS intensity should be negligible in thicker films. We have further determined the relative ratio of A_i to B by fitting the CARS spectral features of 4300 nm thick PMMA film. In the fitting procedure, we have used two different Raman resonance lines at 2842 cm^-1 and 2952 cm^-1 with a band width of 60 cm^-1 and 37 cm^-1, respectively. The ratio of the peak intensities of the two Raman resonance lines is fixed as 85:1. The relative ratio of the amplitude for resonant third-order susceptibility of the Raman mode at 2952 cm^-1 to that of nonresonant one was found to be 170: 1. This ratio was consistent with the observation that CARS signal from the thick PMMA films mainly comes from the resonant CARS field of PMMA. For very thin films with a thickness of hundreds of nanometers, the nonresonant CARS field of PMMA should be a minor contribution to the total CARS signal when compared to that of glass substrate. It is reasonable to assume that the changes in CARS signal of the thin films are mainly due to optical interference between the resonant third-order susceptibility of PMMA and the nonresonant term of glass substrate.

Figure 3(c-g) represent the selected CARS spectral features of PMMA films with thickness of 180 nm, 715 nm, 1310 nm, 2070 nm, and 4300 nm, respectively. The observed spectral features are denoted with black circle. The red solid lines are the best spectra resulting from the fitting procedure of the observed CARS signal with Eq. (3-6). The resonant CARS field resulted from PMMA film (blue lines) and nonresonant one from glass substrate (pink) as well as their cross term (green) are also displayed. For thick films of 4300 nm, the peak position and spectral shape of the observed CARS signal is almost the same to those of the resonant CARS field of PMMA. However, the CARS signal of the thin film with a thickness of 180 nm exhibited a spectral dip as well as spectral shift in peak position, which should resulted from the optical interference between very weak resonant CARS filed of PMMA and rather strong nonresonant one from the glass substrate. The contribution by the CARS field from intact PMMA film to the observed CARS signal of 180 nm PMMA film coated on glass substrate was about 7 %. Figure 4 exhibits the signal intensity resulting from only the resonant CARS field of PMMA as a function of film thickness. The logarithmic plot of the resonant CARS signal from PMMA versus the film thickness between 360 to 2250 nm is quite linear. The slope of the plot is about 2, which is in good agreement with the theoretical prediction from Eq. (1) under exact phase matching conditions (Δk=0).

It should be noted that CARS signals exhibit negative deviation from the expected straight line for the films thicker than 2300 nm. And also, the resonant CARS signal of the films with thickness less than 360 nm also exhibits apparent deviation from the linear plot with a slope of 2. To rationalize the observed negative deviation from the linear plot as shown in Figure 4, we have considered the propagation of the CARS field of PMMA thin films as a wave equation of a point source, which can be obtained by employing Green’s function. The CARS signal from a three-dimensional sample is then a coherent superposition of the field from each point source inside the sample. Following the framework of the theoretical consideration for the CARS signal proposed by Cheng et al [23], the CARS signal could be calculated from the polymer films in cylindrical coordinates with the assumption that the effect of the presence of glass substrate on the observed CARS signal is negligible. Figure 5 shows a typical normalized far-field CARS radiation pattern of thin films (n ~1.5) with incident beams co-propagating along the z-axis and polarized along the x axis. The laser beams are assumed to be focused into the center of the films with an objective lens with NA=0.9. Figure 4 displays the intensity of the CARS signal calculated at forward direction (red solid line).

The forward-detected CARS signal grows rapidly with increase in film thickness and then becomes saturated when the thickness is larger than about 2300 nm. It should be noted that the logarithmic plot of forward-detected CARS signal of PMMA films vs. the film thickness is quite linear between ca. 400 nm and 2000 nm in film thickness and the slope is ca. 2. The theoretical consideration on the CARS field for the thin films excellently reproduces the dependence of the resonant CARS signals of PMMA films coated on the glass substrate as a function of the thickness. This strongly supports the contention that analytical way to draw the resonant CARS signal from the observed multiplex-CARS spectra used in this work can fully account the thickness dependent CARS signal. To know the contribution of nonresonant CARS field generated by glass substrate to the overall CARS signal of polymer films, we have measured the CARS spectral feature of 870 nm thick film of PMMA coated on glass substrate with varying the focus in z-axis from -3600 nm to 4500 nm with a step size of 300 nm (Fig. 6(b-f)). When the laser focus is located in PMMA film (positive X-axis), the spectral feature is almost the same to that observed from thick PMMA films coated on glass substrate as shown in Fig. 3. With approaching the laser focus to the glass substrate, however, apparent spectral dip as well as changes in peak position appeared in the CARS signal. This observation reveals that nonresonant CARS field from glass substrate is profoundly interfered with the resonant CARS field from PMMA. In Fig. 6(a), the intensity of the CARS signals is displayed as a function of depth of focus. Due to the contribution by nonresonant CARS signal from glass substrate, the signal intensity increased with closing the focus into the substrate. With the same procedure employed for the analysis of thickness-dependence CARS signal, we estimate the resonant CARS signal of PMMA. The dependence of the resonant CARS signal of PMMA on the depth of focus is asymmetry in z-axis direction, which can be understood as a difference in refractive index of the environments of the PMMA films, i.e., glass substrate and air. Full width at half maximum (FWHM) of resonant CARS signal as a function of z-axis is ca. 2.1 µm for PMMA films with a thickness of 870 nm. The theoretical axial resolution of 1.4·λ_p/N.A. for current CARS microscopy [23] is ca. 1.2 µm. The CARS intensity profile as a function of z-axis is a convolution of the axial resolution of current optical scheme with the finite film thickness of 870 nm.

 

Fig. 6. Multiplex CARS intensity profile (blue solid circles) along axial direction for about 870 nm thick film of PMMA coated on slide glass (a). The intensity profile of resonant CARS signal from PMMA (black solid circles) was fitted by Gaussian function. Full width at half maximum was found to be ca. 2.1 um (red solid line). (b-f) represents specificity of depth profile at several depth positions. The experimental observation was denoted with black circle. The red (blue, green, magenta) solid lines are the best results from total (PMMA, cross term, only glass) spectral fitting using Eq. (3).

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In summary, we have systematically investigated multiplex CARS signal for PMMA thin films as a function of thickness between 180 nm to 4300 nm. With decrease in the film thickness, the observed CARS signal was mainly contributed by the interference effect associated with large nonresonant CARS field from glass substrate and the weak resonant field of PMMA films. The resonant CARS signal of PMMA thin films could be estimated from the observed spectral features by assuming that the CARS spectral features of intact glass substrate are same to that caused by nonresonant CARS field of glass substrate of the samples. It should be noted that the CARS signal intensity for PMMA thin films with a thickness of 180 nm is almost 10 times larger than the resonant term of the CARS signal intensity from PMMA films itself. We have demonstrated the analytical ability of multiplex CARS microscopy without depth-profiling to measure the PMMA thickness lower than 180 nm, which is less than one order of magnitude of the axial resolution of the current optical setup. This further reveals that multiplex-CARS is a characterization method for very thin polymer films with a great potential in addition to the advantages of CARS microscopy including concomitant chemical identification as well as rather high lateral resolution.