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A simultaneous measurement method for the total interference and self-interference of a sample is proposed. The proposed method is capable of making separate measurements of the thickness and surface profile of micro-patterned thin film. The system is an extension of a full-field wavelength scanning interferometer with a single acousto-optic tunable filter (AOTF) as a spectral imaging device. Separate measurements are realized via the polarization-sensitive diffraction of non-collinear acousto-optic interaction. That is, the diffraction angle of an AOTF is separated into different directions depending on the polarization state of the incident light. In so doing, the polarization states of a reference and a sample light were manipulated differently so that a single AOTF can generate the total interference and the self-interference signal in different directions simultaneously. Thus, a compact and light-efficient system is realized with an AOTF, a beam splitter and two CCDs. Thus, a compact system with light-efficiency of two to four times higher than the previously reported system is realized with an AOTF, a beam splitter and two CCDs. Details of the calibration procedures such as wavelength-frequency relation, image shift and registration between two CCDs are provided for the proposed setup. Experimental results are provided and compared to those using commercial equipment that demonstrate the efficiency of the proposed system for the high-speed measurements of the thickness and the surface profile of micro-patterned thin film.
©2009 Optical Society of America
1. Introduction
Optical measurement technology is widely used in the semiconductor or flat panel display industry as it is capable of fast and non-destructive measurements. Ellipsometry [1] or reflectometry [2] have been a standard procedure in the measurement of thin film thickness. Recently, higher spatial resolution is expected as the feature size under inspection decreases [3]. A smaller feature size also demands shorter depth of focus during a photolithography process. Therefore, a surface planarization of insulating layer such as SiO2 needs to be precisely inspected by measuring the thickness and the surface profile.
Researchers have attempted simultaneous measurements of the thickness and surface profile. Schnell et al. succeeded in measuring the thickness of the multilayer on a sample and the distance between a reference and the sample surface based on dispersive white-light interferometry. However, they used a single point measurement scheme with limited spatial resolution so that mechanical scanning of sample was necessary for the three-dimensional reconstruction [4]. Kim and Kim reported a three-dimensional thin film profile deposited on a micro-patterned structure with white-light scanning interferometry (z-domain) [5]. Similar results were obtained by an alternative approach known as full-field wavelength scanning interferometry (k-domain) [6, 7].
Previous investigations commonly used a least square fitting algorithm to extract the thickness and surface profile information in a manner that took a considerable amount of time for signal processing. To decouple the thickness and surface profile, a separate measurement of the self-interference from a sample and the total interference from a sample and a reference mirror was proposed to avoid this time-consuming signal processing [8, 9]. The thickness is obtained independently from the measured self-interference and is used to extract the surface profile. However, the sequential operation sacrifices the measurement time to reduce signal processing time. Ghim and Kim proposed a system that simultaneously measures the total interference and the self-interference. However, this system is bulky as it consists of three beam splitters and two spectrometers [10].
In the present study, a compact full-field wavelength scanning interferometer is proposed that can simultaneously measure the total interference and self-interference with a single AOTF, one beam splitter and two CCDs. Details of the calibration procedure and results are presented. Finally, the proposed system was used to measure the volumetric thickness profile and the results are compared to those using commercial equipment.
2. Theory
The proposed system is an extension of a full-field wavelength scanning interferometer with an AOTF as a polarization-sensitive spectral imaging device that can simultaneously measure the total interference and self-interference. Light incident to the AOTF interacts with an acoustic wave that is generated by a piezoelectric transducer attached to a birefringent (TeO2) crystal, as described in Fig. 1(a). From the non-collinear acousto-optic interaction, the polarization state and diffraction angle change depending on the polarization state of the incident light [11]. In other words, the incident ordinary polarized light changes its polarization to the extraordinary state and is diffracted in an upward direction. The extraordinary polarized light changes its polarization to the ordinary state and is diffracted in a downward direction. Thus, a single AOTF can work like two imaging spectrometers by generating two diffracted light beams at the same time in different directions depending on the polarization state of the incident light. On the other hand, the wavelength of the diffracted light (λ) is determined by the RF frequency (f) that vibrates a piezoelectric transducer [12]. The f-λ relationship is very close to being inversely proportional and is generally not the same for an ordinary and extraordinary ray, as shown in Fig. 1(b).
Fig. 1. (a). The principle of non-collinear AOTF: The polarization state becomes its opposite after the acousto-optic interaction and becomes separated from the undiffracted light, (b) the wavelength of two diffracted lights as a function of the RF frequency f.
Figure 2 shows the schematics of the proposed system. It consists of a broadband light source, a Michelson interferometer with a polarizer in each path, a visible range AOTF for the full-field spectral imaging and two CCDs. The proposed system is operated as follows. The light from the source is divided by a beam splitter into the reference and measurement paths. The polarization state of the reference light is adjusted to the ordinary state by the polarizer, is diffracted from the AOTF to an extraordinary state, and is then directed to CCD1. In contrast, the polarization of the sample light is adjusted to be in both an ordinary and extraordinary state. Thus, light containing sample information is diffracted by the AOTF to the extraordinary and ordinary state and is directed to CCD1 and CCD2, respectively. Finally, the total interference of the reference and the sample is recorded by CCD1 and the self-interference from the sample is recorded by CCD2 simultaneously.
Fig. 2. The proposed full-field wavelength scanning interferometer that can simultaneously measure the total interference (CCD1) and the self-interference from a sample (CCD2).
The light loss by beam splitters and polarizers for the proposed system is calculated and compared with the setup in reference 10. The amount of light delivered to the CCD1 (e-ray) and CCD2 (o-ray) by the proposed setup is 25% and 12.5% of incident light intensity, respectively. However, the light intensity is reduced by the reference setup to the 6.25% for both light paths.
This section explains in more detail the theory of analyzing the data acquired from the proposed system for a high-speed three-dimension thin film profile measurement. As illustrated in Fig. 2, the film thickness and upper surface profile are defined as d(x,y) and h(x,y), respectively. Here, h(x,y) indicates the distance from an imaginary reference plane to the upper surface of the thin film. The analysis method for the proposed system is focused on a faster processing time. Therefore, the procedure is as follows: First, the thickness profile d(x,y) is extracted from the self-interference signal recorded by CCD2. Subsequently, with the thickness d(x,y), the upper surface profile h(x,y) is calculated using a direct spectral phase calculation method [7]. The time-consuming least square fitting with two unknown variables d(x,y) and h(x,y) is no longer required because d(x,y) is measured independently. Details on the calculation procedure of thickness and surface profile are described in reference 9.
The total reflection coefficient R induced via multiple reflections at the transparent thin film is described by the following equation:
Here, r01, r12 are the Fresnel reflection coefficients between mediums 0 and 1 and mediums 1 and 2, respectively, where medium 0 is air, medium 1 is a thin film, and medium 2 is a substrate or patterned metal. N(k) represents the complex refractive index of the deposited thin film. The thickness information can be obtained by simply detecting the two consecutive peaks at wavenumbers k1 and k2. Equation (2) below was used to calculate the thickness d.
If the thickness of the thin film is too thin, it is possible to apply the least square fitting algorithm to analyze the thickness profile [8]. Once the thickness is obtained, the phase change ψ(k,d) is acquired as a function of only the wavenumber k. The upper surface h(x,y) is then analyzed with the previously acquired ψ(k,d). The total interference signal recorded by CCD1 can be expressed by the following equation including d(x,y) and h(x,y) in the spectral phase function ϕ(k).
Here, Er and Es represent the electric field reflected from the reference mirror and the sample, respectively, and I is the interference intensity. i0 and γ are the DC terms of the interference signal and the visibility function, respectively. The spectral phase function ϕ(k) is calculated throughout the entire wavenumber scanning range using a direct spectral phase calculation method. Finally, h(x,y) is obtained by subtracting ψ(k) from ϕ(k) using Eq. (4).
Here, k1 and k0 can be arbitrary wavenumbers as ψ(k) and ϕ(k) are both obtained as fully defined functions, respectively.
3. Calibration of the proposed system
An AOTF-based spectral imaging system must be calibrated prior to a specific measurement. The wavelengths (λ) of the ordinary and extraordinary diffracted light from an AOTF are determined by the acoustic waves inside the TeO2 crystal. Therefore, the electrical frequency (f) to operate the AOTF must be calibrated for the wavelengths of two diffracted rays separately. A grating based spectrometer with a higher resolution than the AOTF was used to measure the central wavelengths of the diffracted light from the AOTF while the frequency was scanned from 120 MHz to 170 MHz at an increment of 10 MHz. The experimental f-λ relationships are marked in Fig. 3 together with polynomial fitted graphs for the calibration.
Secondly, the angle of the diffracted light from the AOTF changes by nearly 0.6° for the entire scanning range so that the image on the CCD is shifted as shown in Fig. 4. The image shift is inevitable when using an AOTF; however, it can be calibrated with moderate accuracy. A prism can be inserted between the AOTF and the CCD to compensate the wavelength-dependent angular deviation [13]. Another method involves using a window to capture the same region of interest (ROI) moving together with the shifted image. The latter method was used here.
Fig. 4. Image shift after scanning the AOTF for (a) CCD1 and (b) CCD2: This is calibrated by shifting the window to capture the same region of interest.
Lastly, the image in ROI captured at CCD1 should be identical to that captured by CCD2. Therefore, the ROI positions on each CCD should be registered for the best correlation between the two images captured from each CCD. Finally, the shift coefficient was found by cross correlation. After applying the aforementioned calibration process, the images in ROI were recorded by CCD1 and CCD2 while scanning the AOTF, as shown in Fig. 5.
Fig. 5. (Media 1) Movie of calibrated images recorded by (a) CCD1 and (b) (Media 2) CCD2 while scanning the AOTF: Image shift is calibrated and the ROI for each CCD is registered at the same position.
Using this procedure, the calibration is carried out for the proposed system. The total interference signal between a Cr-coated glass and a reference mirror was measured after the calibration. Figure 6(a) shows the raw spectrum (dash) recorded at a single point. The raw spectrum is interpolated to an equally sampled wavenumber (k) space (solid) for the FFT analysis. A Gaussian window is multiplied with the k-spaced spectrum (dash-dot). After the FFT of the k-spaced spectrum, the narrow peak with a width that is close to the coherence length is determined, as shown in Fig. 6(b). The result confirms that the system is well calibrated.
Fig. 6. (a). Interference of the light from Cr-coated glass and reference mirror while scanning the wavelength by AOTF: The raw spectrum (dash) is interpolated to an equally sampled wavenumber (k) space (solid) and the Gaussian window is multiplied (dash-dot). (b) FFT of each spectrum in (a). The narrow peak of the k-mapping spectrum shows that the system is well calibrated.
4. Experimental results
A non-collinear AOTF was used in the proposed setup and was operated in the visible range between 470 nm and 610 nm with a spectral resolution of 1nm. Therefore, the coherence length is 1 μm. With a center wavelength of 540 nm and 1 nm of spectral resolution, the measurement range of 73 μm is calculated by Nyquist theorem (λc/4δλ). Labview-based custom-made software controls the AOTF, records CCD images at 25 frames per second, and analyzes the data at the same time. The transmittance of TeO2 crystal for the visible light is over 70%. The RF power to operate the AOTF is 1.5 Watts and the peak diffraction efficiency is 70%.
Experiments were carried out with two types of samples: a uniform thin film of thickness d and a micro-patterned thin film with thickness d(x,y) and surface profile h(x,y). First, the self-interference from SiO2 thin film (2μm and 3μm) deposited uniformly on a Si wafer was measured by CCD2. The results were compared to those obtained by commercial equipment and are summarized in Table 1. The commercial equipment used the model fitting method for accurate thickness measurements. Similar results were achieved with the peak detection algorithm. Note that the exact point-by-point comparison of the measured data was not feasible because of practical limitations. Instead, average film thickness was compared. The spot size of ellipsometer and reflectometer is 3 mm and 20 μm, respectively. For the proposed thickness-profiler, the spot size of 1.8 μm is imaged on each CCD pixel. The accuracy for the peak detection method improves as the film thickness increases [9].
Table 1. SiO2 thin film thickness measured by commercial instruments and the proposed system with self-interference detection scheme. * data is not available
A micro-patterned sample is prepared for the volumetric thickness profile measurement. The sample was fabricated in the following steps. First, SiO2 was deposited onto a Si wafer and a photo resist was then patterned to etch the SiO2 selectively to ensure that steps between the features exist. Finally, the photo resist was removed.
Fig. 7. Picture of the patterned thin film of SiO2 over the Si wafer substrate and a cross-sectional view showing the measurement parameters
The alignment procedure of the sample is as follows: First, a sample was placed on the stage and monitored by a CCD to determine the focused image when operating the AOTF at any specific frequency. The reference arm was then adjusted to induce the optical path difference of ~20 μm. The total and self-interference images were recorded by CCD1 and CCD2, respectively, while scanning the wavelength, as shown in Fig. 8.
Fig. 8. (a). (Media 3) Movie of total interference of the light reflected from the patterned thin film and the reference mirror recorded by CCD1 when scanning the wavelength by AOTF, (b). (Media 4) self-interference from the thin film recorded by CCD2
The thickness d(x,y) was extracted by applying the peak detection algorithm to the data recorded by CCD2, and the phase change ψ(k) was calculated using Eq. (1). The spectral phase function ϕ(k) was independently calculated from the total interference recorded by CCD1 using the direct spectral phase calculation method. Finally, the surface profile h(x,y) was calculated with ψ(k) and ϕ(k) from Eq. (4). The volumetric thickness profile displayed in Fig. 9 was reconstructed. A CCD pixel measures the thickness and surface profile of small area (~3 μm2). Therefore, the difference between adjacent CCD pixels for the thickness and surface profile is calculated and their standard deviation is obtained to estimate the resolution of the proposed system. The resolution of proposed system was estimated by 13 nm and 10 nm for the thickness and surface profile, respectively.
Fig. 9. (a). 3D thickness profile h(x,y) & d(x,y) and (b) line profile along y-axis at a pixel position of x=27
As a reference, the thickness and the surface step height were measured using a commercial spectroscopic reflectometer and a surface profiler, respectively. The results were then compared to those obtained using the proposed system. These results are summarized in Table 2. The surface step height of 530 nm directly measured by a surface profiler is very close to the thickness difference (d1-d2) measured by a reflectometer because the Si substrate is flat. The thickness, d1, obtained by the proposed method agrees well with the result from commercial equipment but d2 includes error that is originated from the peak detection method. [9]
Table 2. Comparison of measurement results for the thickness profile h(x,y) & d(x,y)
5. Conclusion
In conclusion, this study demonstrates that the proposed simultaneous measurement method for the total interference and the self-interference of a sample can efficiently and separately measure the thickness and surface profile of a micro-patterned thin film. The proposed system is compact and two to four times light-efficient than the previously reported system because a single AOTF can work like two imaging spectrometers and only one beam splitter is required. Separate measurements are realized via the polarization-sensitive diffraction of non-collinear acousto-optic interaction. Calibration procedures such as wavelength-frequency relation, image shift and registration between two CCDs were investigated in detail in this study. The experimental results for the uniform and patterned thin-film deposited on the Si wafer were compared to those obtained using commercial equipment and the feasibility of the proposed system was proved.
References and links
1. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light, (North-Holland, New York, 1979).
2. H. G. Tompkins and W. A. McGahan, Spectroscopic Ellipsometry and Reflectometry: A User’s Guide, (Wiley, New York, 1999).
3. S. Ye, S. H. Kim, Y. K. Kwak, H. M. Cho, Y. J. Cho, and W. Chegal, “Angle-resolved annular data acquisition method for microellipsometry,” Opt. Express 15, 18056–18065 (2007). [CrossRef] [PubMed]
4. U. Schnell, R. Dandliker, and S. Gray, “Dispersive white-light interferometry for absolute distance measurement with dielectric multilayer systems on the target,” Opt. Lett. 21, 528–530 (1996). [CrossRef] [PubMed]
5. S. -W. Kim and G. -H. Kim, “Thickness-profile measurement of transparent thin-film layers by white-light scanning interferometry,” Appl. Opt. 38, 5968–5937 (1999). [CrossRef]
6. D. Kim, S. Kim, H. J. Kong, and Y. Lee, “Measurement of the thickness profile of a transparent thin-film deposited upon a pattern structure with an acousto-optic tunable filter,” Opt. Lett. 27, 1893–1895 (2002). [CrossRef]
7. D. Kim and S. Kim, “Direct spectral phase function calculation for dispersive interferometric thickness profilometry,” Opt. Express 12, 5117–5124 (2004). [CrossRef] [PubMed]
8. Y. -S. Ghim and S. -W. Kim, “Fast, precise, tomographic measurements of thin films,” Appl. Phys. Lett. 91, 091903 (2007). [CrossRef]
9. J. W. You, S. Kim, and D. Kim, “High speed volumetric thickness profile measurement based on full-field wavelength scanning interferometer,” Opt. Express 16, 21022–21031 (2008). [CrossRef] [PubMed]
10. Y. -S. Ghim and S. -W. Kim, “Thin-film thickness profile and its refractive index measurements by dispersive white-light interferometry,” Opt. Express 14, 11885–11891 (2006). [CrossRef] [PubMed]
11. D. A. Glenar, J. J. Hillman, B. Saif, and J. Bergstralh, “Acousto-optic imaging spectropolarimetry for remote sensing,” Appl. Opt. 33, 7412–7424 (1994). [CrossRef] [PubMed]
12. P. A. Gass and J. R. Sambles, “Accurate design of a noncollinear acousto-optic tunable filter,” Opt. Lett. 16, 429–431 (1991). [CrossRef] [PubMed]
13. S. Y. Ryu, J. W. You, Y. K. Kwak, and S. Kim, “Design of a prism to compensate the image-shifting error of the acousto-optic tunable filter,” Opt. Express 16, (2008). [CrossRef] [PubMed]
