Optical Metrology Tool Research Articles

Stitching Locally Fitted T-Splines for Fast Fitting of Large-Scale Freeform Point Clouds.

Parametric splines are popular tools for precision optical metrology of complex freeform surfaces. However, as a promising topologically unconstrained solution, existing T-spline fitting techniques, such as improved global fitting, local fitting, and split-connect algorithms, still suffer the problems of low computational efficiency, especially in the case of large data scales and high accuracy requirements. This paper proposes a speed-improved algorithm for fast, large-scale freeform point cloud fitting by stitching locally fitted T-splines through three steps of localized operations. Experiments show that the proposed algorithm produces a three-to-eightfold efficiency improvement from the global and local fitting algorithms, and a two-to-fourfold improvement from the latest split-connect algorithm, in high-accuracy and large-scale fitting scenarios. A classical Lena image study showed that the algorithm is at least twice as fast as the split-connect algorithm using fewer than 80% control points of the latter.

Co‐Generation of Orthogonal Soliton Pair in a Monolithic Fiber Resonator with Mechanical Tunability

AbstractSoliton frequency combs generated in microresonators offer powerful tools for optical metrology, due to the high time‐frequency resolution. Here, via exciting the intracavity Brillouin laser in a high Q monolithic fiber resonator, a pair of orthogonal Kerr soliton combs is generated, which share the same repetition (frep ≈ 1.001 GHz) due to the soliton trapping but different central wavelengths (≈ 9.278 GHz). They offer rich dual‐comb beat notes with minimum phase noise down to −166.5 dBc Hz−1@1 MHz. Thanks to the geometric flexibility of the monolithic fiber resonator, the orthogonal soliton pair is found to be mechanically controllable with high precision. Specifically, by applying external stress on the microcavity in a range of ≈ 0–7.33 mN, the difference of their carrier‐envelope‐offset frequencies (Δfceo) is linearly tunable with a response of 0.3 kHz µN−1, meanwhile, tunability of the frep reaches 0.4 kHz µN−1. Such an orthogonally polarized dual soliton with stress controllability combining Brillouin excitation and parametric oscillation can offer a miniature all‐in‐fiber tool for wide applications ranging from frequency‐adjustable photonic microwave sources to highly sensitive gyroscopes.

Mueller Matrix Ellipsometric Approach on the Imaging of Sub-Wavelength Nanostructures

Conventional spectroscopic ellipsometry is a powerful tool in optical metrology. However, when it comes to the characterization of non-periodic nanostructures or structured fields that are much smaller than the illumination spot size, it is not well suited as it integrates the results over the whole illuminated area. Instead, imaging ellipsometry can be applied. Especially imaging Mueller matrix ellipsometry is highly useful in nanostructure characterization and defect inspection, as it is capable to measure the complete Mueller matrix for each pixel in a microscope image of the sample. It has been shown that these so-called Mueller matrix images can help to distinguish geometrical features of nanostructures in the sub-wavelength regime due to visible differences in off-diagonal matrix elements. To further investigate the sensitivity of imaging Mueller matrix ellipsometry for sub-wavelength sized features, we designed and fabricated a sample containing geometrical nanostructures with lateral dimensions ranging from 50 to 5,000 nm. The structures consist of square and circular shapes with varying sizes and corner rounding. For the characterization of their Mueller matrix images, we constructed an in-house Mueller matrix microscope capable of measuring the full Mueller matrix for each pixel of a CCD camera, using an imaging system and a dual-rotating compensator configuration for the ellipsometric system. The samples are illuminated at 455 nm wavelength and the measurements can be performed in both transmission and reflection. Using this setup, we systematically examine the sensitivity of Mueller matrix images to small features of the designed nanostructures. Within this contribution, the results are compared with traceable atomic force microscopy measurements and the suitability of this measurement technique in optical nanometrology is discussed. AFM measurements confirm that the fabricated samples closely match their design and are suitable for nanometrological test measurements. Mueller matrix images of the structures show close resemblance to numerical simulations and significant influence of sub-wavelength features to off-diagonal matrix elements.

Polarization-Dependent All-Dielectric Metasurface for Single-Shot Quantitative Phase Imaging.

Phase retrieval is a noninterferometric quantitative phase imaging technique that has become an essential tool in optical metrology and label-free microscopy. Phase retrieval techniques require multiple intensity measurements traditionally recorded by camera or sample translation, which limits their applicability mostly to static objects. In this work, we propose the use of a single polarization-dependent all-dielectric metasurface to facilitate the simultaneous recording of two images, which are utilized in phase calculation based on the transport-of-intensity equation. The metasurface acts as a multifunctional device that splits two orthogonal polarization components and adds a propagation phase shift onto one of them. As a proof-of-principle, we demonstrate the technique in the wavefront sensing of technical samples using a standard imaging setup. Our metasurface-based approach fosters a fast and compact configuration that can be integrated into commercial imaging systems.

Use of smartphones as optical metrology tools for surface wear detection

Proper wear level information and early wear detection are crucial goals in many engineering applications and industrial components in order to improve efficiency and reduce production, maintenance, or replacements costs. Furthermore, this should ideally be achieved with a user-friendly, low-cost, and easy to implement methodology for wear level monitoring and detection. In this work, we present the design of a new approach to accomplish early wear detection that is implemented by means of a stand-alone smartphone device and application providing real-time online metrology. The online monitoring is done by means of optical measurements and image processing based on the advanced smartphone vision system technology currently available in commercial devices. The developed mobile App works in continuous mode without interrupting the wear process. Specifically, it traces surface changes and monitors the progression of wear enabling just-in-time warning alarms for “significant wear” and “critical wear” detection. We demonstrate that critical wear of a surface prior to fatal rupture can be detected, which is the main objective in many industrial applications.

34.4: Applications of Electron Beam Review System for AMOLED Patterning Process Control

As the development of display technologies, much smaller critical dimension design is an inevitable trend and much tighter statistical process control is needed and necessary. Electron Beam Review System can provide much more precise critical dimension measurement without glass to be broken compared with traditional optical metrology tools. Besides, taper CD or taper angle is a critical parameter for display product quality control and Electron Beam Review System is the only tool in display Fabs that can provide such information.

Impact of coherence length on the field of view in dark-field holographic microscopy for semiconductor metrology: theoretical and experimental comparisons

Semiconductor manufacturers continue to increase the component densities on computer chips by reducing the device dimensions to less than 10 nm. This trend requires faster, more precise, and more robust optical metrology tools that contain complex and high-precision optics with challenging imaging requirements. Here, we present dark-field digital holographic microscopy as a promising optical metrology technique that uses optics with acceptable complexity. A theoretical analysis and an experimental demonstration of this technique are presented, showing the impact of the coherence length of the light source on the field of view. Finally, we also present the first holographically obtained images of metrology targets.

Parallel spectroscopic ellipsometry for ultra-fast thin film characterization.

Spectroscopic ellipsometer (SE) is an essential optical metrology tool commonly used to characterize thin films and monitor fabrication processes. However, it relies on mechanical rotation of a polarizer or a photo-elastic phase modulator which are limited in speed and prone to errors when handling dynamic processes. The constant trend of micro-electronics dimensions shrinkage and increase of the wafer area necessitates faster and more accurate tools. A fast SE design based on parallel snapshot detection of three signals at different polarizations is proposed and demonstrated. Not relying on mechanical rotation nor serial phase modulation, it is more accurate and can reach acquisition rates of hundreds of measurements per second.

Correlation Study of Bulk Si Stress and Lithography Defects Using Polarized Stress Imager

Polarized Stress Imaging is an excellent method for monitoring bulk stress distribution in silicon wafers. In this study, the correlation of bulk Si stress and lithography defects are shown using Semilab’s Polarized Stress Imager (PSI) system. 300 mm diameter samples with 7 nm advanced node FinFET devices were investigated with PSI optical imaging metrology tool and AMAT’s UVision wafer inspection tool. Two sets of samples were analyzed after shallow trench isolation etch and after gate etch. Results show that stress imaging can detect process deviations that lead to high defectivity and may have uses in failure analysis to pinpoint root causes of failures.

Stitching sub-aperture in digital holography based on machine learning.

Sub-aperture stitching in digital holography (DH) is a very important issue both for the spatial resolution improvement as well as for measuring larger aperture through synthetic enlargement of numerical aperture. In fact, sub-apertures stitching permits to greatly expand the capabilities of optical metrology thus allowing to accurately measure complex optical surfaces such as large spherical and aspheric. Stitching operations can be difficult and cumbersome depending on geometric parameters of specific objects under test. However, here we show that machine learning can definitively aid this process. In fact, here we propose for the first time, to the best of our knowledge, a novel sub-aperture stitching approach based on machine learning applied to an array of different phase-maps sub-apertures recorded by an off-axis digital holographic systems. Essentially, we construct a network according to computation model of sub-aperture stitching and remove the alignment errors and system aberration of sub-aperture maps by training the network. Correct measurement of the surface topography of hemisphere surface is demonstrated thus validating the proposed learning approach. Reported results demonstrate that machine learning can be a useful tool for simplifying the process and for making it a reliable and accurate tool in optical metrology.

Diagnostic of graphene on Ge(100)/Si(100) in a 200 mm wafer Si technology environment by spectroscopic ellipsometry/reflectometry

Comprehensive diagnostics is a prerequisite for the application of graphene in semiconductor technologies. Here, the authors present long-term investigations of graphene on 200-mm Ge(100)/Si(100) wafers under clean room environmental conditions. Diagnostic of graphene was performed by a fast and nondestructive metrology method based on the combination of spectroscopic ellipsometry and reflectometry (SE/R), realized within a wafer optical metrology tool. A robust procedure for unambiguous thickness monitoring of a multilayer film stack, including graphene, interface layer GeOx underneath graphene, and surface roughness is developed and applied for process control. The authors found a relationship between the quality of graphene and the growth of GeOx beneath graphene. Enhanced oxidation of Ge beneath graphene was registered as a long-term process. SE/R measurements were validated and complemented using atomic force microscopy, scanning electron microscopy, Raman spectroscopy, and secondary ion mass spectrometry. This comparative study shows a high potential for optical metrology of graphene deposited on Ge/Si structures, due to its great sensitivity, repeatability, and flexibility, realized in a nondestructive way.

Broadband electro-optic frequency comb generation in a lithium niobate microring resonator.

Optical frequency combs consist of equally spaced discrete optical frequency components and are essential tools for optical communication, precision metrology, timing and spectroscopy1-9. At present, combs with wide spectra are usually generated by mode-locked lasers10 or dispersion-engineered resonators with third-order Kerr nonlinearity11. An alternative method of comb production uses electro-optic (EO) phase modulation in a resonator with strong second-order nonlinearity, resulting in combs with excellent stability and controllability12-14. Previous EO combs, however, have been limited to narrow widths by a weak EO interaction strength and a lack of dispersion engineering in free-space systems. Here we overcome these limitations by realizing an integrated EO comb generator in a thin-film lithium niobate photonic platform that features a large EO response, ultralow optical loss and highly co-localized microwave and optical fields15, while enabling dispersion engineering. Our measured EO comb spans more frequencies than the entire telecommunications L-band (over 900 comb lines spaced about 10 gigahertz apart), and we show that future dispersion engineering can enable octave-spanning combs. Furthermore, we demonstrate the high tolerance of our comb generator to modulation frequency detuning, with frequency spacing finely controllable over seven orders of magnitude (10 hertz to 100 megahertz), and we use this feature to generate dual-frequency combs in a single resonator. Our results show that integrated EO comb generators are capable of generating wide and stable comb spectra. Their excellent reconfigurability is a powerful complement to integrated Kerr combs, enabling applications ranging from spectroscopy16 to optical communications8.

Digital correction method for realizing a phase-stable dual-comb interferometer

A phase-stable dual-comb interferometer measures materials' broadband optical response functions, including amplitude, frequency, and phase, making it a powerful tool for optical metrology. Normally, the phase-stable dual-comb interferometer is realized via tight phase-locking methods. This paper presents a post-correction algorithm that can compensate for carrier wave phase noise and interferogram timing jitter. The compensating signal is a beat between two combs using a free-running continuous wave laser as an optical intermediary. In our experiment, sub-hertz relative linewidth, ~1 ns relative timing jitter, and 0.2 rad precision in the carrier phase is demonstrated.

Evaluation of adaptively enhanced two-shot fringe pattern phase and amplitude demodulation methods.

Phase-shifting interferometry is a standard tool in optical metrology. Most frequently, it needs three or more interferograms to solve the system of fringe equations for phase or amplitude retrieval, which limits its time resolution. Recently, the topic of two-shot, arbitrary-phase-step fringe pattern phase and amplitude demodulation has been flourishing and attracting attention with several novel and interesting methods being proposed. In this work, we evaluate six up-to-date two-shot phase-shifting methods analyzing their main error sources and proposing efficient ways to minimize their influence by adaptive filtering using the Hilbert-Huang transform.

Enhanced spectral sensitivity of a chip-scale photonic-crystal slow-light interferometer.

We experimentally demonstrate that the spectral sensitivity of a Mach-Zehnder (MZ) interferometer can be enhanced through structural slow light. We observe a 20-fold resolution enhancement by placing a dispersion-engineered, slow-light, photonic-crystal waveguide in one arm of a fiber-based MZ interferometer. The spectral sensitivity of the interferometer increases roughly linearly with the group index, and we have quantified the resolution in terms of the spectral density of interference fringes. These results show promise for the use of slow-light methods for developing novel tools for optical metrology and, specifically, for compact high-resolution spectrometers.

Numerical tools for the characterization of microelectromechanical systems by digital holographic microscopy

Digital holography (DH) in microscopy became an important interferometric tool in optical metrology when camera sensors reached a higher pixel number with smaller size and high-speed computers became able to process the acquired images. This allowed the investigation of engineered surfaces on microscale, such as microelectromechanical systems (MEMS). In DH, numerical tools perform the reconstruction of the wave field. This offers the possibility of retrieving not only the intensity of the acquired wavefield, but also the phase distribution. This review describes the principles of DH and shows the most important numerical tools discovered and applied to date in the field of MEMS. Both the static and the dynamic regimes can be analyzed by means of DH. Whereas the first one is mostly related to the characterization after the fabrication process, the second one is a useful tool to characterize the actuation of the MEMS.

Nonlinear Cavity and Frequency Comb Radiations Induced by Negative Frequency Field Effects.

Optical Kerr frequency combs (KFCs) are an increasingly important optical metrology tool with applications ranging from ultraprecise spectroscopy to time keeping. KFCs may be generated in compact resonators with extremely high quality factors. Here, we show that the same features that lead to high quality frequency combs in these resonators also lead to an enhancement of nonlinear emissions that may be identified as originating from the presence of a negative frequency (NF) component in the optical spectrum. While the negative frequency component of the spectrum is naturally always present in the real-valued optical field, it is not included in the principal theoretical model used to model nonlinear cavities, i.e., the Lugiato-Lefever equation. We therefore extend these equations in order to include the contribution of NF components and show that the predicted emissions may be studied analytically, in excellent agreement with full numerical simulations. These results are of importance for a variety of fields, such as Bose-Einstein condensates, mode-locked lasers, nonlinear plasmonics, and polaritonics.

Improving holographic reconstruction by automatic Butterworth filtering for microelectromechanical systems characterization.

Digital holographic microscopy is an important interferometric tool in optical metrology allowing the investigation of engineered surfaces with microscale lateral resolution and nanoscale axial precision. In particular, microelectromechanical systems (MEMS) surface analysis, conducted by holographic characterization, requires high accuracy for functional testing. The main issues related to MEMS inspection are the superficial roughness and the complex geometry resulting from the several fabrication steps. Here, an automatic procedure, particularly suited in the case of high-roughness surfaces, is presented to selectively filter the spectrum, providing very low-noise reconstructed images. The numerical procedure is based on Butterworth filtering, and the obtained results demonstrate a significant increase in the images' quality and in the accuracy of the measurements, making our technique highly applicable for quantitative phase imaging in MEMS analysis. Furthermore, our method is fully tunable to the spectrum under investigation and automatic. This makes it highly suitable for real-time applications. Several experimental tests show the suitability of the proposed approach.

Dimensional metrology of lab-on-a-chip internal structures: a comparison of optical coherence tomography with confocal fluorescence microscopy.

The characterization of internal structures in a polymeric microfluidic device, especially of a final product, will require a different set of optical metrology tools than those traditionally used for microelectronic devices. We demonstrate that optical coherence tomography (OCT) imaging is a promising technique to characterize the internal structures of poly(methyl methacrylate) devices where the subsurface structures often cannot be imaged by conventional wide field optical microscopy. The structural details of channels in the devices were imaged with OCT and analyzed with an in-house written ImageJ macro in an effort to identify the structural details of the channel. The dimensional values obtained with OCT were compared with laser-scanning confocal microscopy images of channels filled with a fluorophore solution. Attempts were also made using confocal reflectance and interferometry microscopy to measure the channel dimensions, but artefacts present in the images precluded quantitative analysis. OCT provided the most accurate estimates for the channel height based on an analysis of optical micrographs obtained after destructively slicing the channel with a microtome. OCT may be a promising technique for the future of three-dimensional metrology of critical internal structures in lab-on-a-chip devices because scans can be performed rapidly and noninvasively prior to their use.

Characterization of wafer geometry and overlay error on silicon wafers with nonuniform stress

Process-induced overlay errors are a growing problem in meeting the ever-tightening overlay requirements for integrated circuit production. Although uniform process-induced stress is easily corrected, nonuniform stress across the wafer is much more problematic, often resulting in noncorrectable overlay errors. Measurements of the wafer geometry of free, unchucked wafers give a powerful method for characterization of such nonuniform stress-induced wafer distortions. Wafer geometry data can be related to in-plane distortion of the wafer pulled flat by an exposure tool vacuum chuck, which in turn relates to overlay error. This paper will explore the relationship between wafer geometry and overlay error by the use of silicon test wafers with deliberate stress variations, i.e., engineered stress monitor (ESM) wafers. A process will be described that allows the creation of ESM wafers with nonuniform stress and includes many thousands of overlay targets for a detailed characterization of each wafer. Because the spatial character of the stress variation is easily changed, ESM wafers constitute a versatile platform for exploring nonuniform stress. We have fabricated ESM wafers of several different types, e.g., wafers where the center area has much higher stress than the outside area. Wafer geometry is measured with an optical metrology tool. After fabrication of the ESM wafers including alignment marks and first level overlay targets etched into the wafer, we expose a second level resist pattern designed to overlay with the etched targets. After resist patterning, relative overlay error is measured using standard optical methods. An innovative metric from the wafer geometry measurements is able to predict the process-induced overlay error. We conclude that appropriate wafer geometry measurements of in-process wafers have strong potential to characterize and reduce process-induced overlay errors.