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An optical microscopy system as a non-destructive method for measuring critical dimension (CD) is widely used for its stability and fastness. In case of transparent thin film measurement, it is hard to recognize the pattern under white light illumination due to its transparency and reflectance characteristics. In this paper, the optical measurement system using multispectral imaging for CD measurement of transparent thin film is introduced. The measurement system utilizes an Acousto-Optic Tunable Filter (AOTF) to illuminate the specimen with various monochromatic lights. The relationship between spectral reflectance and CD measurement are deduced from series of measurement experiments with two kinds of Indium Tin Oxide (ITO) patterned samples. When the difference of spectral reflectance between substrate and thin film layers is large enough to yield a large image intensity difference, the thin film layer can be distinguished from substrate, and it is possible to measure the CD of transparent thin films. This paper analyzes CD measurement of transparent thin film with reflectance theory and shows that the CD measurement of transparent thin film can be performed successfully with the proposed system within a certain wavelength range filtered by AOTF.
© 2014 Optical Society of America
1. Introduction
More precise metrology techniques have arisen from the semiconductor industry especially for smaller and more complex Critical Dimensions (CD). It is a micro-scale inspection, and measurement ranges are from tens to hundreds microns. A transparent thin film based device is now widely being used, for example, in display applications. Transparency of thin film, however, usually interrupts the accuracy of CD measurements. There are various ways to measure CD patterns, and CD measurement can be classified into two categories: a destructive method and a non-destructive method. Atomic Force Microscopy (AFM) is a kind of optical profiler, and it is categorized as a destructive method. AFM usually takes several minutes to measure a sample. The weakness of destructive method is that it may leave flaws on specimen during measurements. Scanning electron microscopy (SEM) is one of the non-destructive methods. Critical dimension-scanning electron microscopy (CD-SEM) has renowned for its precision, which has lateral resolution up to sub-micron unit. Since CD-SEM is non-destructive method, there is no contact during the measurement process, however, samples may get flaws or destroyed during the preparation of the measurement.
Compared to other measuring methodologies, optical microscopy is outstanding in preserving specimen samples. Optical microscopy is the most commonly used non-destructive method, which uses a light source and a magnifying lens with pattern-recognizing and edge-detecting algorithms. Interferometry is also widely used to measure CD using optical coherence tomography [1, 2]. As aforementioned, the transparency of thin film affects measurement accuracy. The pattern cannot be distinguished at certain incident angle or wavelength of the light source during measurements. In this paper, to eliminate these drawbacks and to increase the accuracy of measurements, the illumination optics with the implementation of multispectral imaging system has been proposed. This system consists of typical microscopy with Acousto Optic Tunable Filter (AOTF) for spectral scanning.
Multispectral imaging is theoretically based on a spectral reflectance analysis. Every material shows its own characteristics of spectral reflectance due to dispersion of refractive index. Spectral reflectance is useful to distinguish one object from the other objects, especially when it comes to a transparent thin film layer. Many applications of multispectral imaging are applied to distinguish defects or classify materials [3–6].
Reflectometry and ellipsometry is also based on reflectance theory, however, they are usually used to measure the thickness and the refractive index of the transparent thin film [7–9]. The proposed method in this paper focuses on the lateral measurement in micro-scale. We combine a spectral reflectance theory and a CD measurement algorithm with multispectral imaging to measure CD of transparent thin film patterns. We examine the specimen which consists of an indium tin oxide (ITO) layer on top of a silicon nitride (SiNx) layer on a silicon substrate. The specimen is usually used for electrode applications in display panels. The pattern of this sample is usually hard to recognize under white light illumination due to its reflective characteristics. The experiment shows that it is possible to distinguish the patterns of transparent thin film on the substrate and to precisely measure the width of CD patterns by using multispectral imaging methods.
The most important advantage of the proposed technique is that it enables users to select the most proper light source for CD measurement of transparent film layers. Using the proposed method, users can choose the most effective wavelength for the CD measurement of transparent thin film layers.
2. Experimental setup
The basic setup for the optical system is shown in Fig. 1. The proposed measurement system consists of an AOTF for spectral scanning, a CCD camera for capturing 2D imaging data, a LED lamp which has wavelength range from 400 nm to 720 nm, a spectrometer for recognizing the wavelength of the filtered light, an objective lens for specimen magnification, and a beam splitter. The white light is emitted from the LED light source, and the collimated beam gets filtered by passing through the AOTF. There are two filtered beam that are generated after passing thorough the AOTF; a zeroth-order beam and a first-order beam. The first-order beam, that is filtered monochromatic light by the AOTF, is used in the multispectral system. The zeroth-order beam is the white light that is used to measure the spectral reflectance. The incident beam should be perpendicular to the sample, and the optical path of the beam can be adjusted by changing the orientation of the AOTF. The commercially available spectrometer with detection range from 200 nm to 1100 nm is used in the system. The optical fiber bridges the spectrometer and the optical system. A 50X apochromatic lens from Nikon is used as an objective lens. It is important to use an apochromatic lens because the optical system uses various monochromatic lights for measurement. The apochromatic lens reduces chromatic aberration to compensate different CD measurement results for each wavelength. A CCD camera of 640 x 480 pixel resolutions is used to capture the specimen image for the measurement. The CCD size is 7.4 by 7.4 square microns, and it makes spatial resolution as 0.148 μm per pixel. It provides satisfactory resolution for the measurement. The AOTF has a wavelength range of 420 nm to 700 nm and a transmission bandwidth of 0.3 nm at 560 nm beam. Captured images from the CCD camera are transferred to a computer for image processing to detect sub-pixel edges.
3. Methods
3.1 CD measurement method
The CD is generally the distance between two boundaries in a specimen. In the case of CD patterns in liquid crystal display (LCD) panels, the CD measurement is one of the most important inspection steps to control the quality of LCD panels. Before measuring the CD values, boundary edge extraction, should be performed at first. The precision of the measurement is decided by the image contrast of target area. Various image filters such as Sobel and LoG can be applied to extract boundaries in CD patterns. In this paper, Lee’s edge detection algorithm is applied [10, 11]. Edge is primarily detected by the 1st derivative operator with LoG algorithm for pixel level, and 1/9 sub-pixel level edge detection is performed by using Facet modeling for more precise measurement.
Figure 2 shows the image intensity and its derivative value. The applied algorithm uses the LoG mask and the derivative value to find the edge. Figure 3 demonstrates how to detect edges by using a derivative threshold and a hysteresis threshold. If the absolute value of derivative is higher than the derivative threshold, it can be considered as a candidate for the edge. For more precise measurement, only the value which is higher than the sum of derivative threshold and hysteresis threshold is determined as a strong edge.
3.2 Reflectance theory
Spectral reflectance depends on the wavelength of a light source and the refractive index of the materials. Figure 4 shows reflections and transmissions of light when there is a thin film over a substrate.
In Fig. 4, N1 is the refractive index of air (≈1), N2 is the refractive index of the thin-film layer, and N3 is the refractive index of the substrate. Every refractive index is in a complex form. θ1 is the incident angle of the light and θ2 is the refraction angle. d is the thickness of the thin film. The light experiences two state changes while penetrating two interfaces. One is the air–thin film interface and the other is the thin film-substrate interface. The reflectance coefficient can be expressed in terms of the Fresnel reflection coefficient. Equations (1) and (2) represents of an air–thin film interface case [12].
is reflection coefficient of p-wave and is reflection coefficient of s-wave at air-thin film interface. Equations (1) and (2) can be applied to the thin-film-substrate interface as and. Then the total reflection coefficients, and, for a single film are expressed as follows: where,λ is the wavelength of light, and β is the phase shift of light during the thin film penetration in Eq. (5). Reflectance coefficients mean the ratio of electromagnetic wave in Eq. (3) and Eq. (4). It is only possible to measure the intensity of the reflected light by CCD camera. Equation (6) shows the relationship between intensity of the light and electromagnetic wave [13]. and are the intensities of incident and reflected light, and and are electromagnetic waves of incident and reflected light respectively. is the total reflection coefficient from Eq. (3) and Eq. (4). The reflectance R is defined as the square of the total reflection coefficient, and it is the ratio of incident and reflective light. This shows that the reflectance is a relative value.3.3 Proposed method: correlation between image intensity and spectral reflectance
Image intensity function for the brightness in CCD pixels, , is expressed as below:
is the spectral reflectance, and it is determined by the illumination wavelength λ and the corresponding position of the sensor (pixel position x and y). E(λ) is the illuminant power of the light source, and S(λ) is the sensor spectral sensitivity(quantum efficiency). E and S are identical in every pixel on the image [14, 15]. To measure CD, intensity difference between pixels is very important. Intensity Difference (I.D) between adjacent two pixels can be expressed as follows: is the intensity of the position 1, and is the intensity of the position 2. If the light source is monochromatic, E and S terms are same in every pixel and R term only varies with the pixel position.3.4 Analysis of the relationship between spectral reflectance and thin film thickness
Figure 5 shows spectral reflectances of the Si-SiNx-ITO structure which is calculated with Fresnel reflectance coefficients [16, 17]. It can derive the relationship between ITO film thickness and spectral reflectance. The thickness of the SiNx layer is 650 nm, while the thickness of the ITO layer varies from 1 nm to 40 nm, with a 10 nm interval. As it is shown in Fig. 5, when the layer of the ITO gets thicker, the reflectance graph shifts to the right direction on the wavelength axis.
The reflectance change by the thickness variation has a great effect on the intensity difference at the boundary. By choosing the appropriate monochromatic wavelengths in the suggested system, it is possible to measure CD of various thin film samples with different film thickness. The wavelength at the peak of reflectance difference on the boundary results the successful and stable CD measurement.
The proposed system is able to save the stack of multispectral images. By applying the reflectometry theory, the thickness of the transparent film layers can be calculated based on the acquired images [18]. By picking the intensity profile about a certain pixel from the stack, the reflectance signal can be extracted. Figure 6 shows the data acquisition process with the multi-spectral system. Once spectral data acquisition process is completed, the regression method is used for searching the best-matching theoretical reflectance. The best matching theoretical reflectance gives the thickness information of the specimen [19]. If the thickness information is acquired, it can be used for finding optimal wavelength in CD measurement.
Figures 7(a) and 7(b) show the nonlinear fitting results for the samples. With the proposed system, thickness of the sample is measured; Sample 1 has 639.09 nm thickness of silicon nitride (SiNx) layer and 39.02 nm of Indium Tin Oxide (ITO) layer while sample 2 has 620.02 nm thickness of SiNx and 40.74 nm of ITO.
4. Result
To verify the reliability of the CD measurements at a given series of wavelengths, two kinds of ITO patterned CD samples are used. The wavelengths varies in 10 nm intervals from 432 nm to 702 nm. Measurement time of each frame is 1/125 sec. It takes less than 1 second for gathering multi-spectral images. Each sample consists of an ITO patterned layer on top. Below the ITO layer, there is a SiNx layer on a silicon substrate. Lee’s method is applied to detect edges [10, 11]. Specific lines of each sample are measured ten times repeatedly to yield an average value and repeatability of the measurement (3σ); σ stands for the standard deviation of the repeated measurements.
4.1 Pattern visibility of transparent thin film
There are no differences in image intensities of thin film and substrate under white light illumination. In Figs. 8(a) and 8(b), the thin film area cannot be seen under the wavelength of 532 nm, by which it is impossible to detect edges between thin film and substrate areas to measure the CD. Figures 9(a) and 9(b) are the images of the same samples as Figs. 8(a) and 8(b) under the wavelength of 562 nm through the AOTF. On the contrary of Fig. 8, A1 and A2 can be clearly distinguishable from the other area in Fig. 9. To help understanding the geometric information of samples, both samples are measured by AFM. Figures 10(a) and 10(b) present the 3D maps of sample 1 and 2, and Figs. 11(a) and 11(b) show their horizontal profiles.
Fig. 8 Images of invisible thin film pattern at sample 1 (a) and sample 2 (b) under the certain wavelength, 532 nm.
Fig. 9 Images of visible thin film pattern at sample 1 (a) and sample 2 (b) image under the certain wavelength, 562 nm: dashed lines – detected edge with high contrast, arrows – CD of the measurement target.
Spectral reflectance is measured to find the relationship between detected edge and image intensity. The spectral reflectance of two points in two different samples are compared with each other to verify the relationship. As shown in Fig. 9, one point (P1) is in the substrate area (A1), and the other point (P2) is in the thin film area (A2).
As it is shown in Figs. 12, and 13 (a) shows the reflectance of each point, and (b) shows the difference of the spectral reflectance of sample 1 and 2 respectively. is the spectral reflectance of point 1, and the reflectance of point 2. With the wavelengths of 532 nm, the reflectance differences between the substrate and the thin film areas are 0.013 in sample 1 and 0.015 in sample 2. However, with the wavelength of 562 nm, the reflectance differences are 0.033 and 0.026. As a result, the reflectance differences in 562 nm are bigger than the one in 532 nm, and thin film area can be seen as Fig. 9.
Fig. 12 (a) The spectral reflectance of sample 1, (b) The difference of the spectral reflectance between P1 and P2 in sample 1.
Fig. 13 (a) The spectral reflectance of sample 2, (b) The difference of the spectral reflectance between P1 and P2 in sample 2.
As aforementioned in the theory, edge detection is based on the derivative of the intensity profile, and it can be expressed as follows:
Edge detection can be performed via any arbitrary directions in the image: horizontal, vertical or diagonal. Although Eq. (9) only represents a derivation in the horizontal direction of the images, this equation can be applied in every direction. With white light source, there is no constant term that can be separated out from the integral in Eq. (9).In the monochromatic light, Eq. (9) can be simplified as follows:
Although E and S are the influential factors to the intensity of the pixels in Eq. (10), the reflectance difference between two points in CCD pixels is the most important term to detect edges. Therefore, by using an AOTF, it is possible to use monochromatic light in the optic system, and the wavelength can be chosen to maximize the difference of reflectances between thin film and substrate areas. The key idea is that the invisible patterns under the white light become visible under the monochromatic light at the certain wavelength.4.2 CD measurement result
The performance of the proposed system is evaluated by examining the specimen with wavelength from 432 nm to 702 nm in 10 nm interval. Figures 14 and 15 show the relationship between the difference of spectral reflectance and CD measurement in the sample 1 and 2. The dashed horizontal lines in the Fig. 14 and Fig. 15 represent the reflectance threshold for edge detection by Lee’s method. Sample 1 and 2 have different reflectance due to their distinctive layer structures, refractive indices and ITO thickness.
Fig. 14 The difference of the spectral reflectance between P1 and P2 in sample 1 and minimum difference to detect edges in CD algorithm.
Fig. 15 The difference of the spectral reflectance between P1 and P2 in sample 2 and minimum difference to detect edges in CD algorithm.
Edge detection parameters are applied identically in sample 1 and 2, however, Fig. 14 and Fig. 15 show that sample 1 and 2 have different reflectance threshold for edge detection. It is explained that reflectance is relative value which is the ratio of incident and reflective light intensities.
The edge is judged by the derivative values of the image intensity [20, 21]. Keeping the difference of the spectral reflectance as big as possible, it raises the image contrast around the edges. As shown in Figs. 14 and 15, if the difference of the spectral reflectance is above the reflectance threshold, the detection succeeds, and if not, the detection fails. In other words, the most important thing in the edge detection is that the derivative value must be higher than the sum of the derivative and hysteresis threshold of Lee’s algorithm [22]. It shows consistent result as the theory described in the previous section.
4.3 Results of the measurement repeatability
When the repeatability of the measurement is 50 nm or below, it is considered as a good measurement with an error tolerance of 0.05%. In this paper, CD patterns are measured 10 times, and the repeatability is evaluated by 3σ. Three wavelengths are selected to verify the measurement repeatability: 442 nm (B), 562 nm (G) and 622 nm (R).
Table 1 shows the result data of the measurements. As it is shown in Fig. 14, the difference of spectral reflectance is 0.012 at the wavelength of 442 nm. Since it is under the threshold of CD measurement, it results the measurement failure of sample 1. On the contrary, measurement succeeds at the wavelength of 442 nm in sample 2. The measurement repeatabilities of the selected wavelengths stay under 50 nm except at the wavelength of 442 nm in sample 1.
Table 1. Measurement Result Matrix [unit: μm]
5. Conclusion
This paper introduces the methodology of CD measurement for transparent thin film, for example, the ITO film. It is hard to detect transparent thin film patterns of sample 1 and 2 by using the conventional optic system such as interferometry and microscope with white light source. We suggest a novel method, and it is summarized as follows.
- The proposed system consists of following components: a white light source, AOTF for filtering the light, an objective lens, a CCD camera to capture images, and a spectrometer to acquire the spectral intensity of the reflected light. It is very similar to reflectometer with a CCD camera system, which can measure the thickness of the sample [19]. Therefore, the multispectral imaging system is highly applicable to other measurement systems such as Michelson interferometer by simply adding a blocking plate and AOTF.
- The change of the spectral reflectance which depends on the thickness of the ITO layer is simulated. Once we know the thickness of the layer, it is possible to find the optimal monochromatic wavelength for successful edge detection by changing spectral reflectance. The proposed system allows to manipulate the wavelength of the incident light which allows conducting CD measurement of various thin film samples.
- With the proposed system, CD measurements are conducted with multispectral imaging by using AOTF. The edge detection is the key factor that determines success or failure of the measurement. In all the succeeded edge detection cases, the measurements are stable, and the repeatabilities of the measurements stay under 50 nm.
- To investigate the reason for measurement success and failure at specific wavelengths, spectral reflectance of the substrate and the thin film area are evaluated. A measurement fails with unstable edge detection due to small derivative values of intensity, and it clearly portrays the relationship between the spectral reflectance and the image intensity profile. Thus, the wavelength at the highest derivative value should be set by using AOTF for stable CD measurement.
- The great advantage of the proposed system is the availability to measure both thickness and CD of the transparent film simultaneously. Thickness of the film can be measured by the proposed system with spectral reflectance data [19]. When the thickness of the film is given by manufacturing target, optimal wavelength can be calculated simply by spectral reflectance analysis. In this case, we can skip the thickness fitting process. If the thickness information is not given, however, thickness measurement should be conducted first, and the proper wavelength can be chosen by the measured reflectance data to measure CD.
Using multispectral imaging system, optimal wavelength can be suggested to measure CD of transparent thin-film by analyzing spectral reflectance. Then, it can measure CD patterns of various other transparent thin-films by changing monochromatic light to the proper wavelength. This can maximize the difference of reflectance. The most important advantage of the proposed technique is that it enables users to select the most proper light source for CD measurement of transparent film layers.
Acknowledgments
This work was supported in part by the Brain Korea 21 Plus, the Engineering Research Institute, Institute of Advanced Machinery and Design at Seoul National University.
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