KEYWORDS: Phase shifting, Phase measurement, Measurement uncertainty, Model based design, Interferometers, Data modeling, Distance measurement, Signal intensity
An electro-optic comb has a wide frequency mode spacing of more than several tens of GHz, making it possible to resolve each comb mode by using commercial spectrometers. The individual frequency modes of the electro-optic comb can be employed as the multiple stabilized lasers required for a multi-wavelength interferometer in absolute distance measurements. For absolute distance measurements, the phase information for each frequency mode, i.e., wavelength, is necessary for determining the absolute distance using the excess fraction method, and this requires a phase shifting process. Typically, the phase shifting is implemented through the sequential translation of a reference mirror by an equal distance. However, since the wavelength values corresponding to every frequency mode are different, even the same amount of shifting of the reference mirror generates different phase change for each wavelength. In such a situation, to accurately measure the phase for each wavelength, a model-based analysis method for phase shifting intensity signals itself was adopted. In the model-based analysis of phase shifting intensity signals, the phase determination uncertainty can vary depending on the number of the phase shifting step. Therefore, in this study, we aim to estimate the phase determination uncertainty according to the number of the phase shifting step through numerical simulations.
Absolute distance measurement has been widely required not only in various industrial fields such as semiconductors, displays, and heavy industry, but also in fundamental and applied research sites. Among the various optical methods for measuring absolute distances, the most widely used method with high precision is multi-wavelength interferometry. In general, multi-wavelength interferometry uses three or more frequency-stabilized lasers to solve the phase ambiguity problem from a large amount of phase information corresponding to several wavelengths. However, despite the high measurement precision of multi-wavelength interferometers, it is practically not easy to install and maintain several frequency-stabilized lasers in terms of cost and maintenance. In this work, we aim to implement a multi-wavelength interferometer using an electro-optic comb with wide spacing between frequency modes. Because the frequency mode spacing of the electro-optic comb is wide enough to be resolved by commercial spectrometers, each frequency mode can be considered as a single frequency-stabilized laser. Through this concept, several frequency-stabilized lasers for multiwavelength interferometer can be replaced with a single electro-optic comb. Absolute distance measurement was performed using the proposed method, and measurement uncertainty evaluation was also performed to evaluate the proposed method. When the electro-optic comb is stabilized by being locked to an atomic clock being traceable to the time standard, so it is expected that it can be easily used to realize length standards or measure ultra-precise absolute distances in the future.
A multi-layered structure is being extensively applied in the high-tech devices fabrication in the semiconductor and display industries. For measuring the thin-film thicknesses of the multi-layered structure, various techniques like spectral reflectometry, spectral ellipsometry, and SEM/TEM have been used depending on the application fields. Among them, the spectral reflectometry is being widely used because of the advantages of simple configuration, non-destructive characteristics, and high-speed measurement. In spectral reflectometry, the reliability of the reflectance model is very important, because the higher the agreement of the modeled reflectance to the measured one, the lower the measurement uncertainty of the thin-film thicknesses determined by the reflectance model. In case of the single-layer thin-film sample, the thickness can be verified using a certified reference material, but the multi-layer thicknesses are not easy to be verified unlike single-layer case. In this study, to check the reliability of the multi-layer reflectance model, two different methods were used; (1) the extension of the single-layer model and (2) the multi-layer model based on the transfer matrix. The first one is to sequentially determine the thin-film thicknesses from layer to layer. The second one is to simultaneously determine all the thin-film thicknesses of a multi-layer structure. By applying two methods to double-layered thin-film sample(SiO2-SiN), the thin-film thicknesses of both layers were determined and compared to each other by considering the measurement uncertainty. The applicability of the theoretical reflectance model can be confirmed according to whether the thin-film thickness measurement results are agreed within the uncertainty.
We propose an optical system capable of simultaneously measuring physical thickness, group refractive index, and surface profile of a single-layer substrate based on a spectral domain interferometer. Specifically, the proposed method can be functionally divided into two parts; one is the Mach-Zehnder configuration for thickness and refractive index measurements, the other is the Michelson configuration for surface profile measurement. To integrate two different configurations into a single system, two fiber components of an optical circulator and a 2-by-1 optical coupler were installed for the purpose of acquiring both signals reflected from and transmitted through the sample. In addition, the Michelson configuration was realized by replacing a right-angle turning mirror with a beamsplitter and adding a reference mirror in the Mach-Zehnder layout. For feasibility test of the proposed method, a 100-mm-diameter silicon wafer was laterally scanned within a square area of 50 mm2 using a two-axis motorized linear stage. The reference mirror for surface profile measurement was suitably positioned along the optical axis to prevent the overlap between the optical path differences. As a result, the distribution maps of physical thickness, group refractive index, and surface profile were successfully measured over the target area of the silicon wafer. In the proposed setup, the measured surface profile of a plane-parallel substrate like a silicon wafer represents the bending information in its natural state. The proposed method is highly applicable to the semiconductor or display devices inspection where thickness and surface profile measurement should be monitored simultaneously.
Absolute distance measurement technique can be a useful tool for solving the challenging issues such as large optics fabrication and alignment. An optical system free from non-measurable range of spectral-domain interferometer was proposed by using dual reference paths with orthogonal polarizations. The problem of non-measurable range caused by sampling limit of an interference spectrum having very small optical path difference has already been overcome by making the dual reference path with a pre-determined offset in the previous study. However, the interference signal between the two reference paths could cause the measurement error when it overlaps with the distance measurement signal. In this study, to remove the interference signal between the two reference paths, polarization-based spectral-domain interferometer was proposed and realized. For feasibility test of the proposed method, the absolute distances to the target mirror were measured within the scan range of 200 μm, and the measurement results were compared with those obtained using the commercial laser interferometer simultaneously. As a result, it was verified that the distance measurement error was significantly reduced through the proposed method.
Optical interferometry is one of the suitable methods which can be used to measure the physical thicknesses of microscale structures because this approach can measure optical path differences accurately with a non-contact method. In this paper, on the basis of the simultaneous measurement of the physical thickness and refractive index of an optically transparent plane-parallel plate, a spectral-domain interferometer capable of measuring the physical thickness and refractive index of separate layers in a step-shaped structure with two layers was proposed and realized. For a feasibility test, a microfluidic channel mold with two layers was selected as a sample. For verification of the measured thickness in a double-layered region, a contact-type surface profilometer equipped with laser interferometers on the x-y-z axes was used for a thickness comparison. However, it is never simple to compare measured thicknesses due to positioning errors and the different measuring sizes of each method. For these reasons, the corresponding thickness value was defined as an offset between height values at center points of the single-layered and double-layered region in a specific area of 5 mm × 5 mm. For an accurate determination of the offset, the slopes of the surface profile were removed. The assumption that the surface profile of the bottom layer in the double-layered region is very flat was applied to calculate the thickness from the measured surface profile, and this assumption was checked as to whether it is acceptable or not in this study. In conclusion, the physical thicknesses according to a surface profilometer and by the proposed method were determined to be 106.332 μm and 106.304 μm, respectively, in good agreement within the respective uncertainty values.
The optical interferometry is a non-contact dimensional measurement technique which is capable of ultra-high-precision measurements. Fundamentally, it provides the optical path difference instead of the geometrical path difference. For thickness measurements of glass panels, the physical thickness can be extracted from the optical thickness when the refractive index of the glass panel is precisely given. Otherwise, the precision of an optical interferometer cannot be maintained owing to errors in the refractive index. To overcome this problem, several studies based on optical interferometry for simultaneously measuring the physical thickness and refractive index have been proposed and realized. For in-line inspections, the vibration problem becomes serious with increased dimensions of thin glass panels. When delivering large glass panels, a large amount of vibration is inevitable. In this paper, a transmission-type spectral-domain interferometer for determining physical thicknesses and group refractive indices of large glass panel, which can be operated even under vibration conditions is introduced. For an in-line inspection, large tilt angles of glass panels are created by swing motion when delivering these glass panels at a high-speed. Even if the proposed method determines physical thickness values successfully under the severe vibration condition used here, the measurement error caused by the vibration effect should be investigated and analyzed to correct the measured thickness values. To do this, a theoretical analysis of the error was performed by mathematical modeling. Moreover, the error of the physical thickness was experimentally analyzed at various tilt angles of the large glass panel. The uncertainty was evaluated to be about 436 nm based on the results of these investigations.
With the advent of smart devices, the semiconductor packaging process has been proposed to realize devices that have
high performance devices and compact size. Several silicon wafers are stacked vertically to create 3 dimensional devices
with a high degree of integration. In this process, we measured two important parameters: the thickness of the silicon
wafers and the depth and diameter of the through-silicon vias, which are vertical electrical connection lines between the
stacked silicon wafers. To avoid pattern distortion and failure during the optical lithography process, the absolute value
of the thickness as well as the thickness uniformity needed to be measured. The proposed method directly extracts the
geometrical thickness from optical thickness. Because short through-silicon vias lead to disconnection between the
silicon wafers, and narrow though-silicon vias may cause voids, the depth and diameter of the through-silicon vias must
also be measured accurately. For these purposes, we propose two high-speed optical interferometers based on spectrum-domain
analysis. The light source was a femtosecond pulse laser which has the advantages of a wide-spectral bandwidth,
high peak power and long coherence length. The measurement uncertainty of the thickness was estimated to be 100 nm
(k=2) in the range of 100 mm. The depth and diameter of the through-silicon vias were measured at the same time with a
measurement resolution of 10 nm and 100 nm, respectively. It is expected that the proposed interferometers will be used
for on-line metrology and inspection as well as new metrological methods for dimensional standards.
The uncertainties of measuring the geometrical thickness and refractive index of silicon wafers were evaluated. Both quantities of the geometrical thickness and refractive index were obtained using the previously proposed method based on spectral domain interferometry using the optical comb of a femtosecond pulse laser. The primary uncertainty factor was derived from the determination process of the optical path differences (OPDs) including the phase calculation, measurement repeatability, refractive index of air, and wavelength variation. The uncertainty for the phase calculation contains a Fourier transform in order to obtain the dominant periodic signal as well as an inverse Fourier transform with windowed filtering in order to calculate the phase value of the interference signal. The uncertainty for the measurement repeatability was estimated using the standard deviation of the measured optical path differences. During the experiments, the uncertainty of the refractive index of air should be considered for wavelengths in air because light travels through air. Because the optical path difference was determined based on the wavelength in use, the variation of the wavelength could also contribute to the overall measurement uncertainty. In addition, the uncertainty of the wavelength depends on the wavelength measurement accuracy of the sampling device, i.e. the optical spectrum analyzer. In this paper, the details on the uncertainty components are discussed, and future research for improving the performance of the measurement system is also proposed based on the uncertainty evaluation.
We describe a method to simultaneously measure both thickness profile and refractive index distribution of a silicon wafer based on a lateral scanning of the wafer itself. By using dispersive interferometer principle based on a broadband source, which is a femtosecond pulse laser with 100 nm spectral bandwidth, both thickness profile and refractive index distribution can be measured at the same time using a single scanning operation along a lateral direction. The proposed measurement system was tested using an approximately 90 mm range with a 0.2 mm step along the center-line, except for the rim area in a ϕ100 silicon wafer. As a result, the thickness profile was determined to have a wedge-like shape with an approximately 2 μm difference at an averaged thickness of 478.03 μm. Also, the mean value of the refractive index distribution was 3.603, with an rms value of about 0.001. In addition, the measurement uncertainty of the thickness profile was evaluated by considering two uncertainty components that are related to the scanning operation, like the yaw motion of the motorized stage and the long-term stability of an optical path difference in an air path. The measurement reliability of both the thickness profile and refractive index distribution can be increased through several methods such as an analysis of the correlation between the thickness profile and the refractive index distribution and a comparative measurement using a contact-type method; these potential methods are the subject of our future work.
A high level of immunity to vibration required for on-machine measurements is demonstrated by the continuous phaseshifting
interferometer described in this work. Phase measurement errors caused by environmental disturbance and
mechanical instability are eliminated by Fourier analysis on a few hundreds of fringes captured by a high-speed CMOS
camera. For the purpose, phase shifting is applied in a continuous mode. The proposed continuous phase-scanning
method is proposed to apply the phase-extraction principle on a specific heterodyne frequency generated from multiple
cycles of 2π-scanning by the uniform translation of PZT-driven stage. As a result, inherent drawbacks of conventional
PSI algorithms, such as nonlinearity errors of PZT, measurement speed, complexity of phase analysis algorithm, can be
overcome effectively. The experimental results about surface measurement of 1" spherical concave mirror show that
superior phase reconstruction performance with good quality can be achieved even under severe vibration circumstances
simulated by target excitation along a lateral direction.
We present a new type of point-diffraction interferometer specially designed for industrial use with high immunity to external vibration encountered in the course of measurement process. The proposed interferometer uses thermally-expanded fibers instead of conventional pinholes as the point-diffraction source to obtain a high quality reference wave with an additional advantage of relatively easy alignment of optical components. Vibration desensitization is realized through a common-path configuration that allows the influence of vibration to affect both the reference and measurement waves identically so that it is subsequently cancelled out during the interference of the two waves. A spatial phase shifter is added to capture four phase-shifted interferograms simultaneously without time delay using a single camera to avoid vibration effects. Experimental results demonstrate that the proposed interferometer is capable of providing stable measurements with a level of fringe stabilization of less than 1 nanometer in a typical workshop environment equipped with no excessive ground isolation for anti-vibration.
We present a new type of point-diffraction interferometer specially designed for industrial use to obtain high immunity to external vibration encountered in the course of measurement process. The proposed interferometer uses thermally- expanded fibers instead of conventional pinholes as the point-diffraction source to obtain a high quality reference wave with an additional advantage of relatively easy alignment of interferometric optical setup. Vibration desensitization is realized through a common-path configuration that allows the influence of vibration to identically affect both the reference wave and the measurement wave and be subsequently cancelled out during the interference of the two waves. A new spatial phase shifter is also added to capture four phase-shifted interferograms simultaneously without time delay using a single camera to avoid vibration effect. Experimental results for a spherical concave mirror prove that the proposed interferometer is capable of providing stable measurements with a level of fringe stabilization of less than 1 nanometer in a typical workshop environment equipped with no excessive ground isolation for anti-vibration. Also, we verify that the proposed interferometer using a short coherence source is applicable to the surface metrology for defect inspection of transparent substrates such as liquid crystal display panels.
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