Motion-free TSOM using a deformable mirror

Through-focus scanning optical microscopy (TSOM) is a model-based optical metrology method that involves the scanning of a target through the focus of an optical microscope. Unlike a conventional optical microscope that directly extracts the diffraction-limited optical information from a single in-focus image, the TSOM method extracts nanometer scale sensitive information by matching the target TSOM data/image to reference TSOM data/images that are either experimentally or computationally collected. Therefore, the sensitivity and accuracy of the TSOM method strongly depends on the similarities between the conditions in which the target and reference TSOM images are taken or simulated, especially the lateral instability during through-focus scanning. As a remedy to the lateral instability, we proposed the application of adaptive optics to the through-focus scanning operation and initially developed a closed-loop system with a tip/tilt mirror and a Shack-Hartmann sensor, with which we were able to keep the plane position within peak-to-valley (PV) 33 nm. We then further developed a motion-free TSOM tool reducing the instability down to practically zero by the replacement of the tip/tilt mirror with a deformable mirror that performs through-focus scanning by deforming its mirror surface. The motion-free TSOM tool with a × 50 (NA 0.55) objective lens could provide a scanning range of up to± 25 μm with a minimum step of 25 nm at a maximum update rate of 4 kHz. The tool was demonstrated to have a recognition accuracy of < 4 nm for critical dimension (CD) values in the range of 60 ∼ 120 nm with a reference TSOM image library generated by a Fourier modal method matching various observations conditions. © 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement


Introduction
Through-focus scanning optical microscopy (TSOM) is an optical model-based metrology method that was developed to overcome the classical resolution limit due to diffraction in optical microscopy [1][2][3]. This bright-field microscopy technique uses an ordinary optical reflection microscope but produces nanometer dimensional measurement sensitivity [4][5][6][7][8][9]. In comparison to a conventional bright-field microscope, which directly extracts the diffraction-limited optical information from a single in-focus image, TSOM indirectly extracts nanometer scale sensitive information by analyzing stacked through-focus (TF) images as a whole (TSOM data cube) or a cross-sectional image along the scanning direction, which is referred to as a TSOM image. The TSOM data analysis typically includes library-matching [4][5][6][7][8][9] or machine-learning methods [10,11]. Both methods require reference TSOM data/images that are either experimentally or computationally collected. Therefore, the sensitivity and accuracy of the TSOM method strongly depends on the similarities between the conditions in which the target and reference TSOM data/images are acquired or simulated. Figure 1 provides a schematic diagram of the TSOM process describing four major steps: 1) through-focus scanning along the optical axis, 2) image acquisition at multiple through-focus positions during the scanning process, 3) TSOM data cube/image generation, and 4) TSOM data processing. It should be emphasized again that TSOM is a nanodetection technique but does not provide real improved resolving power such as fluorescent stimulated emission depletion microscopy (STED) [12]. The nanometer sensitivity is obtained with great care paid in optimizing the image acquisition conditions such as averaging, noise reduction, and calibration, and in normalizing the images so that they can be compared with each other or with a library of images from a reference library [3,[13][14]. In particular, major efforts have been focused on mitigation of the dissimilarity in the through-focus scanning and illumination conditions in which the target and reference TSOM images are taken or simulated [15][16][17][18][19][20][21][22][23].
Regarding the mitigation efforts for the instability issue, several approaches have been proposed: 1) a z-axis scanning-free strategy utilizing the residual chromatic aberration of an objective lens [15,16]; 2) temporal averaging by the exposure time increment [17]; 3) instability correction with Fourier transform [18,19]; and 4) active compensation by the use of adaptive optics technology [20][21][22]. The first approach requires precise knowledge of the residual chromatic aberration, which is not typically provided and it prohibits the use of monochromatic light sources such as lasers desired for high volume metrology and inspection applications [24]. The second approach averages out the random position instability by increasing the exposure time of the camera, which sacrifices the efficacy or the throughput. In addition, the slow lateral movement such as drift cannot be removed out even after the temporal averaging. The third approach, i.e. lateral movement correction using Fourier transform, effectively decreases the lateral movement of the pattern image due to the optical and mechanical noise, simultaneously. But this approach requires precise knowledge of the target structure and material properties and the increased TSOM data processing time. The use of adaptive optics [25,26] was initially proposed to compensate the lateral jitter motion with a tip/tilt mirror close-looped with a Shack-Hartmann wavefront sensor in the imaging path of the microscope [20][21][22]. However, due to the limited angular resolution of the Shack-Hartmann sensor, the lateral position error is small but still non-zero, i.e. 33 nm in peak-to-valley (PV) value [22].
We here propose further improvement from the tip/tilt compensated TSOM, i.e. a motion-free TSOM. The motion-free TSOM reduces the instability down to practically zero by replacing the tip/tilt mirror with a deformable mirror which performs through-focus scanning by deforming its mirror surface.

Understanding of through-focus scanning process
2.1. Optical understanding of through-focus scanning Figure 2 shows a schematic diagram of an infinite-conjugate microscope consisting of an objective lens, a tube lens, and a phase modulator located at the Fourier plane of the microscope, which is a deformable mirror in our study. In terms of geometrical optics, an object plane at the focus of the objective lens is conjugated to the image plane located at the focus of the tube lens with lateral magnification M and longitudinal magnification M z as follows: (2) f 0 and f T are the focal lengths of the objective and tube lens. x 0 , y 0 , z 0 and x i , y i , z i are the coordinate systems of the object and image space with the origins at each focus, respectively.

Fig. 2. Schematic diagram of an infinite-conjugate microscopy
When the object plane is shifted along the optical axis by an amount ε z , the conjugated image plane is accordingly shifted along the optical axis by an amount −M 2 ε z . Without the corresponding shift of either the object plane or image plane, the imaging is referred to as defocused. In terms of wave optics, the wavefront aberration W (x, y) of the defocused imaging is given as where: (x,y) = coordinate in the Fourier plane NA o = numerical aperture (NA) of the objective lens ε z = amount of defocus in the object plane R = maximum beam radius at the Fourier plane of the objective lens W residual = residual aberration of the objective lens W DM = wavefront deformation by a phase modulator such as a deformable mirror Therefore, the through-focus scanning can be done by changing either the object or image distances or by generating equivalent optical aberrations by chromatic sweeping or active phase modulation. Attotta thoroughly reviewed over 15 types of through-focus image acquisition methods potentially suitable for TSOM [27]: scanning the sample stage along the focus axis, scanning the objective lens along the focus axis, scanning the image plane along the focus axis, multifocal plane microscopy, wavelength scanning method, flexible-membrane liquid lens, liquid-tunable lens, adaptive optics, multifocus microscopy, aperture-scanning Fourier ptychography, confocal microscopy, light sheet microscopy, light field microscopy, phase retrieval techniques, and digital holography microscopy. Among the reported methods, sample stage scanning is most widely used in the TSOM studies by adopting a manual or motorized z-axis stage [2,[4][5][6][7][8][9][10][11]13,14,16,19,23].

Numerical simulation of through-focus scanning
Many studies numerically simulated the through-focus scanning process by iterative calculation of the light field with movement of the target [2,[4][5][6][7][8][9][11][12][13][14][15][16][17]. Recently, a Fourier modal method (FMM) was proposed to improve the computational efficiency by applying a once-solved scattering matrix in the frequency domain to obtain field distributions at any z-position [18], which was used for building up reference TSOM images in this study.

Necessity of stable through-focus scanning mechanism
The use of the mechanical scanning inevitably incurs positional ambiguity and instability, mostly in the lateral direction across the through-focus scanning direction. First, sub-pixel position ambiguity naturally exists due to the use of a finite sized detector which fundamentally limits the accuracy of the TSOM method. Second, it is very costly to remove relevant random jitter and slow drift during the z-axis stage operation, especially when dealing with targets of nanometer feature size. It was reported that the slow-drift or tilt in the TSOM image can also occur due to non-uniform angular illumination asymmetry (ANILAS) across the field-of-view [28,29]. Figure 3 shows conceptual TSOM image stacks with the lateral positional ambiguity and instability and corresponding exemplary simulated TSOM images.  Table 1. Figure 4 shows the mean square differences (MSD) variations due to CD change and various positional errors of a 60 nm linewidth single line fin pattern. The MSD value of 31.2 × 10 −4 corresponds to the 10% CD difference, i.e. 6 nm. For securing 10% CD measurement accuracy, the sub-pixel position ambiguity, random jitter, and liner drift should be smaller than 15 nm, 12 nm, and 0.4 degree, respectively. Therefore, it is obviously necessary to reduce the positional errors for achieving nm measurement sensitivity in the TSOM method.

Adaptive optics supported TSOM
Adaptive optics is an optical technology that removes the wavefront distortion introduced by a turbulent medium by introducing a controllable counter wavefront distortion that both spatially and temporally follows that of the disturbance [25,30]. The use of adaptive optics technology was proposed to actively compensate the lateral instability via two approaches [20][21][22]. The first approach uses a simple tip/tilt mirror to compensate any optical-axis instability while moving the wafer stage. The second approach uses a deformable mirror to optically perform the through-focus scanning without any mechanical movement. Figure 5 presents schematic diagrams of the two approaches.

Experience with a tip/tilt correction TSOM implementation
The first approach was implemented on an optical bench with commercial off-the-shelf components. The technical details of the implementation are tabulated in Table 2. The motorized z-axis stage experienced center beam movement of 4.1 µm over the 3.0 µm z-axis scanning, as seen in Fig. 6(a). With the help of the active tip/tilt compensation, the beam movement was dramatically reduced down to 33 nm in PV (peak-valley), as presented in Fig. 6(b). However, considering the results of section 2.3, further reduction of the positional error is still desired.

Motion-free TSOM with a deformable mirror
There are several types of deformable mirrors (DMs) including stacked array, bimorph, voice-coil actuator, micro electro-mechanical system (MEMS), and optically addressed DMs [30,31]. Among them, a bimorph DM is chosen in our study since it provides excellent correction or formation of most common optical aberrations, especially focus [32,33]. The wavefront deformation of the deformable mirrors can be controlled via either zonal or modal control approaches. In the modal control approach, each control channel corresponds to one optical mode, which is often a Zernike polynomial. The wavefront deformation W DM (x, y) is then expressed by where Z i (x, y) is the i th Zernike polynomial and b i the corresponding control signal. Defocus corresponds to the 4 th Zernike polynomial Z 4 (x, y), as given below [34]: Therefore, the target movement (ε z ) along the optical axis can be optically modulated by equivalent wavefront deformations with the control signal b 4 or the peak-to-valley (PV) physical stroke S of the DM at the DM maximum aperture R max , given as Figure 7 shows a motion-free TSOM tool developed with the technical details in Table 3. As expected from Eq. (8), the tool could provide a through-focus range of ± 25 µm with a 25 nm step for a × 50 (NA 0.55) objective lens. The illumination NA and spectrum could be simply changed by changing the aperture and spectral filter in the illumination path, marked as in Fig. 7.

Experiments with single line fin patterns
The sub-nanometer scale sensitivity of the motion-free TSOM tool was tested with four single line fin patterns having design width 60, 80, 100, and 120 nm with a height of 50 nm, which were measured to have CDs of 55.2, 78.9, 94.7, and 110.4 nm, respectively, by a scanning electron microscope (SEM), as shown in Fig. 8. Figure 9 shows the experimentally measured and corresponding simulated TSOM images of the four single line fin patterns. Each measured TSOM image was compared with reference TSOM images featuring sub-nanoscale linewidth variations in terms of the MSD. The linewidth (CD) could be estimated at the minimum point of the MSD under a reliable tolerance level of 0.1 nm [18]. The estimated line widths were all within 4 nm from the SEM measured values, as listed in Table 4.

Conclusion
TSOM is a nanodetection technique that overcomes the resolution limit but the nanometer sensitivity only is obtained with great care paid in optimizing the image acquisition conditions and minimizing the dissimilarity in the through-focus scanning and illumination conditions in which the target and reference TSOM images are taken or simulated. Adaptive optics techniques were introduced to stabilize the through-focus scanning process. The first implementation with a tip/tilt mirror successfully reduced the PV lateral position error from 4 µm to 33 nm. However, it was necessary to further reduce the residual to a few nanometers. A motion-free TSOM by the use of a deformable mirror (DM) was then proposed. A motion-free TSOM tool with a bimorph mirror was developed and it could provide a through-focus range of ± 25 µm with a 25 nm increment for a ×50 (NA 0.55) objective lens. We demonstrated that the motion-free TSOM tool estimated the critical dimension (CD) values of single line fin patterns in the range of 60 ∼ 120 nm with accuracy of < 4 nm based on the minimum MSD approach.

Funding
Ministry of Trade, Industry and Energy (10048720).

Disclosures
The authors declare no conflicts of interest.