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Abstract
We propose a new method of through-focus scanning optical microscopy (TSOM) without a reference database, i.e., a model-less TSOM method. Building a TSOM reference database is time-consuming or even impractical in some TSOM applications that involve complex structures, such as 3D NAND, or irregular shapes such as defects. The proposed model-less TSOM method was used to determine just the height of defect particles, for the first time as far as we are aware. Defect height is the only relevant dimension for the display panel application. Specifically, we analyzed 40 organic light-emitting diode (OLED) surface defects using a lab-developed motion-free TSOM tool consisting of a 50× objective lens (numerical aperture (NA) 0.55), a 532-nm light source, an imaging detector with a 7.5-µm pitch, and a deformable mirror. The tool is in-line and capable of achieving high throughput non-destructively, both relevant features for industrial applications. We investigated linear regression relations between newly defined TSOM parameters (TSOM height, TSOM area and TSOM volume) and the defect heights, which were first measured by atomic force microscopy (AFM). Following defect classification based on in-focus images, we successfully found that the AFM height has a linear correlation with 50% TSOM height (H50%) within ± 20.3 nm (1σ) error over the range of 140 to 950 nm. The one-sigma error, i.e., 20.3 nm, was approximately λ/26 or 1/43 of the depth of focus (DOF) of the applied microscope.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Through-focus scanning optical microscopy (TSOM) is an optical metrology method that can operate beyond the classic resolution limit of applied bright-field (BF) optical microscopy [1,2], often reaching nanometer dimension measurement sensitivity [3–5]. The enhanced sensitivity of the TSOM method is achieved by analyzing a stacked 3D TSOM data cube or 2D TSOM image using library-matching [5,6] or machine-learning [7]. Both methods require reference TSOM data/images that have been either experimentally or computationally collected. In this sense, the conventional TSOM method is model-based. Figure 1 provides a schematic diagram of the model-based TSOM process, which comprises four major steps: 1) through-focus scanning along the optical axis, 2) image acquisition at multiple through-focus positions during scanning, 3) TSOM data cube/image generation, and 4) TSOM data processing.
Because TSOM is a model-based metrology method, great attention has been paid to optimizing the image acquisition/simulation conditions and minimizing the dissimilarities between them [8–18]. For example, Rim et al. reported the detection of nanoscale contamination in semiconductor fabrication using TSOM [18]. However, building a TSOM reference database (DB) of complex structures, such as 3D NAND, or irregular particle defects becomes unbearably time-consuming or even impractical [19,20]. Figure 2 shows two example cases where a TSOM reference DB was hard to prepare with both experimental and simulation methods.
The main application of TSOM has been metrology and inspection (MI) in the semiconductor industry, where it was first introduced in 2008 [1]. Recently, the TSOM method has been studied for application in other areas, including displays, biotechnology, and photonics, because TSOM shows considerable promise for meeting the industrial requirements of high throughput and cost-effective 3D shape metrology [18,21]. In particular, the display panel industry has significant interest in its application for first-order classification of particle defects in panels. The method is uniquely suited for this particular challenge, where the defect of interest (DOI) is increasingly smaller, while the size of the inspection area (panel size) is increasingly larger.
In this paper, we propose a model-less TSOM method to estimate the dimensional feature size of particle defects in organic light-emitting diode (OLED) display panels, a case where it is very difficult to practically build a TSOM reference library. In particular, we are interested in the defect height rather than the lateral size/dimension because particle defects over a certain height, such as 50 nm, cause current leakage that affects the device lifespan [22,23]. The proposed method first classifies the defects types based on their in-focus images, as in previous studies [24–27] and then extracts the height information via class-based linear correlations between the measurement results and the TSOM parameters, such as 80% TSOM volume or 50% TSOM height, which are newly defined here.
2. Model-less TSOM methods
2.1 TSOM data acquisition
The image acquisition process of the proposed model-less TSOM is identical to that of the conventional model-based TSOM. In the TSOM method, a defect is scanned through the focus of an optical microscope, and conventional 2D images are acquired at various through-focus positions (one focused image and many defocused images at various through-focus positions). In this study, we employed a lab-developed motion-free TSOM tool, shown in Fig. 3 [17]. The tool consists of a 50× objective lens (numerical aperture (NA), 0.55), a white light source with a 532-nm band-pass filter, a deformable mirror, a Shack-Hartmann sensor, and an imaging detector with a 5.5-µm pitch. Table 1 lists the main parameters of TSOM operation.
Fig. 3. Motion-free TSOM tool: ① light source, ② He-Ne laser, ③ z-axis stage, ④ objective lens, ⑤ deformable mirror, ⑥ imaging detector, ⑦ Shack-Hartmann wavefront sensor, ⑧ aperture & spectral filter, and ⑨ control PC
Table 1. Main parameters of motion-free TSOM implementation
The tool provides motionless through-focus scanning using a deformable mirror to produce equivalent wavefront deformation ${\textrm{W}_{DM}}({x,\textrm{y}} )$. The deformable mirror provides defocus wavefront deformation ${\textrm{W}_{DM}}({x,\textrm{y}} )$ with a modal control signal ${\textrm{b}_4}$ as reported in a previous study [17]:
where (x,y) = coordinates in the Fourier plane of the objective lens, $\textrm{N}{\textrm{A}_o}$ = numerical aperture (NA) of the objective lens, ${\varepsilon _z}$ = amount of defocus in the object plane, R = maximum beam radius at the Fourier plane of the objective lens, ${\textrm{W}_{residual}}$ = residual aberration of the objective lens, and ${\textrm{W}_{DM}}$= wavefront deformation by a phase modulator such as a deformable mirror.
Through-focus scanning was conducted over an area of 3.63 µm × 3.63 µm centered at each defect, through a focus range of −10 µm to10 µm with 101 focus steps, producing a TSOM data cube of 33×33×101.
2.2 Model-less TSOM data analysis
The conventional TSOM method extracts nanometer sensitive feature information by analyzing the differences between a target TSOM data cube/image $(TSO{M_{Target}})$ and a set of reference TSOM data cubes/images called a TSOM library ($TSO{M_{Reference}})$. The most common criteria is the mean squared difference (MSD) as given by
The proposed method aims to estimate the heights of defect particles with no TSOM library. We first calculated the TSOM parameters from a measured TSOM data cube. The parameters, such as Ratio, TSOM volume, TSOM area, and TSOM height of a surface defect, are newly defined in this study in the following paragraph. Then we estimated the height of the defect via linear regression relations with the calculated TSOM parameters. Figure 4 shows a schematic diagram of the defect height estimation using the model-less TSOM process.
In the process we first define the relative intensity ratio (Ratio) at each volume pixel within the TSOM data cube with respect to the minimum (Min) and maximum (Max) intensity values:
We then define the TSOM volume, TSOM area, and TSOM height based on the Ratio. We define TSOM volume as the volume occupied by pixels with a ratio larger than a certain value. The TSOM area is the area of a cross-section of the TSOM volume or TSOM image. The TSOM height is the height of the TSOM image along the vertical axis. For example, 50% TSOM volume means the volume of pixels whose pixel values are higher than half of the highest difference. Similarly, 50% TSOM area and 50% TSOM height are the corresponding area and height of the 50% TSOM volume. We note them as V50%, A50%, and H50%, respectively.
In this approach, we can estimate the height of a defect ($\hat{H}$) via a linear regression with a calculated TSOM parameter value ($P$) of the defect, which is later chosen to be the 50% of the TSOM height (H50%) of the defect. We can express the relationship between the estimated height (${\hat{H}_i}$) and its TSOM parameter value (${P_i}$) for a defect with an index number i as below.
where a and b are the slope and offset values of the linear regression, respectively, and can be calculated from the true or measured values (H) of a group of N sample defects.Then we can evaluate the validity of the estimation using the standard deviation (σ) of the fitting error over the sample group, given as below.
2.3 First-order verification via numerical simulation
In the case of OLED panel displays, a particle defect can cause current leakage, affecting lifespan, only when its defect height is above a certain value, such as 50 nm, regardless of its lateral size or shape [22,23]. For this purpose, we need to measure or estimate the heights of defects with an axial resolution better than ∼ 50 nm, which is approximately one seventieth of the Rayleigh axial resolution (${\textrm{R}_{Axial}})\; $ of the applied microscope, given as [28]
We first tested the validity of the proposed method for estimating defect heights using a first-order numerical simulation. Even though OLED particle defects are irregular, as in Fig. 2 and Fig. 7, a significant amount of defects can be represented by elliptical hemispheric domes as shown in Fig. 5. First we modeled 45 elliptical hemispehric domes with five base diameters (0.5, 0.75, 1.0, 1.25, and 1.5 µm) and nine height steps in 0.1 µm increments from 0.1 to 0.9 µm. The numerical simulation was performed using the Fourier modal method [13] with the TSOM image acquisition conditions presented in Table 1. Figure 5 shows some geometries of the analysis models and their example in-focus (or BF) and TSOM images simulated with height = 0.3 µm. The analysis results were normalized to have a peak intensity of 1.0.
Fig. 6. TSOM parameters for three ratio values (20%, 50% and 80%) vs. model defect heights. D is the base diameter in µm of the elliptical hemispheric dome.
Figure 6 plots the model heights versus the TSOM parameters (volume, area, and height) for three ratio values (20%, 50%, and 80%). We investigated the linear regression relations between the TSOM parameters and the model defect heights as described in Section 2.2. After grouping the models into two groups, one with a diameter greater than 1 µm and the other smaller, we found that 50% TSOM height (H50%) was the proper TSOM parameter for estimating the defect height in a linear regression manner. As in the following experiments, we called each group circular spots and donuts based on their bright-field images. Table 2 lists the linear regression relationship between H50% and the model defect heights, which resulted in the height estimation with H50% within ± 11.5 nm (one sigma) after type classification.
Table 2. Linear regression relationships between H50% versus model defect heights after type classification
3. Experiments & results
3.1 Defect samples
We sampled 40 particle defects found on an OLED display panel surface, supplied by Samsung Display (Ltd). The defect samples were independently measured by atomic force microscopy (AFM) prior to the TSOM observation. Figure 7 shows the BF and AFM images of the particle defects. The heights of the defects measured by AFM, referred to as AFM height, varied from 140 to 950 nm. Similarly, we called the measured radius or diameter the AFM radius or AFM diameter.
All of the defects were then TSOM scanned using the acquisition conditions presented in Table 1, and 3D data cubes were constructed accordingly. As mentioned in Section 2.2, we defined the TSOM parameters (volume, area, and height) with an intensity ratio R. Figure 8 shows example plots of the TSOM areas and volumes for three different ratios (20%, 50%, and 80%). As the ratio increased, the TSOM area and volume became smaller around the defect center. Figure 9 shows the 50% TSOM volumes and areas of all the defects.
3.2 Prior type classification
Prior to estimating defect height in the OLED panel inspection we first classified the defect type as recommended by prior research [27,28], and as confirmed by our first-order verification study in Section 2.3. The prior system classified the defects into three types: circular spots (type 1), donuts (type 2) and cylinder-like random (type 3). Figure 10 shows in-focus/AFM/TSOM images of each representative defect type.
3.3 Defect height estimation
Figure 11 plots the AFM heights versus various TSOM parameters for three different ratios (20%, 50%, and 80%). In the plots in Fig. 11, defects are marked with t type symbols (‘+’, ‘*’, and ‘o’).
Figure 12 plots the estimation error (σ) determined in Eq. (8) as the ratio was varied from 20% to 80% with three TSOM parameters (volume, area, and height) applied as regression variables, respectively. Figure 12 shows that H50% has the minimum height estimation error, even in real defect applications, as predicted by the first-order simulation study in Section 2.3.
Figure 13 plots the H50% versus the AFM height with a dotted best-fit line for the three defect classes. Table 3 lists the linear regression relationship between H50% and the AFM defect heights. The overall estimation error (1 σ, sigma) was 20.3 nm, which is better than the initial goal of our study, i.e. 50 nm. It was noted that the slopes of the best-fitted lines were somewhat different than those in the model analysis results in Table 2. We suspect that defects are of a different material than we used in the analysis, i.e., Si (silicon), since the material’s properties, such as refractive index, would change the slopes.
Table 3. Linear regression relationships between H50% versus real defect heights after type classification
The data scattering still seems to be relatively high in Fig. 13. First, some data scattering occurs intrinsically due to the shape and material randomness of the OLED defects, and inaccuracies in the type of classification due to the limited resolution of the applied in-focus (BF) images. The estimation error could be further reduced by reducing instrument noise or instability, such as the image noise reduction. In addition, a further reduction may be possible by investigating ways to improve TSOM data analysis, such as combined-analysis of multi-NA TSOM datacubes [29].
4. Conclusion
The conventional TSOM method extracts information below the diffraction limit using BF optical microscopy. The conventional TSOM method is model-based optical metrology, where the nano-sensitive information is acquired by analyzing the differences between a measured TSOM data cube/images and a reference TSOM library. We often encounter cases where the construction of a reference TSOM library is too time-consuming or even impossible, as in 3D NAND memory or OLED panel defect inspection.
In this paper, we propose a model-less TSOM method which extracts dimensional feature information using only the measured TSOM data cube. In this study we employed the method to estimate the dimensional feature size of particle defects below the level of optical resolution, particularly their height. As a first step in implementing the model-less TSOM method, we defined three TSOM parameters (volume, area, and height). The TSOM volume is the volume/space occupied by pixels having a relative intensity ratio larger than a certain value. The TSOM area and height are the cross-section/area and vertical height of the TSOM volume.
As a first application, we successfully applied the proposed method to estimate the heights of 40 OLED panel particle defects ranging from 140 to 950 nm following a first-order numerical study confirming the concept. After investigating the correlation between the heights obtained by AFM and the measured TSOM parameters, we estimated the defect heights using 50% TSOM height (H50%), and the results were within ± 20.3 nm measurement error (1σ), which is ∼ λ/26 or 1/43 of the depth of focus (DOF) of the applied microscope. Future research will investigate steps to further reduce the estimation error, by minimizing instrumental instability or noises and also by employing other analysis methods such as combined-analysis of multi-NA TSOM datacubes.
Funding
Kongju National University (2021); Samsung Display.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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