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.
In semiconductor manufacturing process, thin film thickness must be precisely controlled. Because it requires fast and precise thickness measurement, studies have been conducted to analyze the thicknesses of thin films by applying deep learning algorithms to spectral reflectometry. The reflectance spectrum of a thin film sample, which varies according to the film thickness, can be calculated with well-known theoretical equation. A theoretical dataset being used to train a deep learning algorithm for thin film thickness analysis is generated by the theoretical equation. For the practical use of the trained deep learning algorithm, performance evaluation using actual measured data is essential, but it is not easy because the exact thickness of the film sample is not known. Recently, a study that proposed an uncertainty evaluation of thin film thickness measurement using a deep learning model by utilizing the certified reference materials (CRMs) was published. In this study, the measurement uncertainty of a deep learning algorithm for thin film thickness measurement using data augmentation was evaluated. Referring to previous studies, a multilayer perceptron algorithm was designed and trained by theoretical reflectance spectra of silicon dioxide thin film on silicon substrate with thin film thickness varying from 1 nm to 110 nm in visible band. Considering the intensity fluctuation of the light source used in the reflectometry, a noise with a normal distribution of 1% standard deviation was applied to the training dataset. Then, the reflectance spectrum of the silicon dioxide thin film CRMs measured in the wavelength range of 355 nm to 657 nm was analyzed with the trained model. Based on the thickness analysis results, a measurement uncertainty evaluation was performed by considering several uncertainty factors of the offset of the analysis result from the certified value, the uncertainty of the CRMs itself, and the measurement repeatability.
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.
Thin films have been widely used in advanced high-technology manufacturing processes such as semiconductors, displays, and batteries. A representative method among non-destructive thickness measurement methods is a spectral reflectometer. An optical layout of the spectral reflectometer is compact with only a few optical components, and a mathematical model for analysis is also relatively simple. However, in order to find a thickness solution based on the model-based analysis, an initial value should be well chosen to cover. In addition, the analysis time takes longer for improving the thickness resolution due to large numbers of comparison. To overcome this practical difficulty, an artificial neural network algorithm with several different conditions such as number of hidden layers and nodes were designed and trained within a thickness range around 100 nm. The training data set and the validation data set were used by theoretically generating an interference spectrum based on the Fresnel equation. In this work, the spectral reflectometer was realized in a wavelength range of 355 nm to 657 nm based on our previous work. For quantitative analysis in this measurement, certified reference materials having a nominal thickness of 10 nm, 30 nm, 50 nm, and 100 nm silicon dioxide thin film was measured, and an uncertainty analysis was performed on the thickness measurement value determined through this. Uncertainty factors include measurement uncertainties related to the calibration of the spectral reflectometer in use, measurement repeatability, and artificial neural network algorithms.
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 laser radar (LADAR) system with a Geiger mode avalanche photodiode (GAPD) is used extensively due to its high
detection sensitivity. However, this system requires a certain amount of time to receive subsequent signals after detecting
the previous one. This dead time, usually 10 ns to 10 μs, is determined by the material composition of the detector and
the design of the quenching circuits. Therefore, when we measure objects in close proximity to other objects along the
optical axis using the LADAR system with GAPD, it is difficult to separate them clearly owing to the dead time problem.
One example for that is a case of hidden objects behind partially transparent blinds. In this paper, we suggested a
modified LADAR system with GAPD to remove the dead time problem by adopting an additional linear mode avalanche
photodiode (LAPD) as a complementary detector. Because the LAPD does not have dead time while still maintaining
relatively low detection sensitivity, the proposed system can measure an object placed within the dead time with high
detection sensitivity. Light is emitted from the pulsed laser of a light source and is delivered into a fast photodiode to
generate a start signal. Most of laser pulses are directed onto the target and scattered from the surfaces of targets. The
scattered light in the field-of-view of the system is divided by a polarizing beam splitter, after which it becomes incident
to two different types of APDs, the GAPD and the LAPD. The GAPD receives the signals from the target with high
sensitivity, and the signals scattered in the dead time zone are then detected by the LAPD. The obtained signals are
analyzed at the same time. In this way, the signals scattered from objects placed within the dead time can be
distinguished clearly.
We propose a microscopic system which could be applied to three-dimensional surface profile measurement. In the
system, a two-dimensional pinhole array is imaged onto the surface under measurement by an objective lens. These spots
act as discrete object points which are then imaged to the CCD chip by the microscope which contains two orthogonal
cylindrical lenses. Due to the astigmatism of the two cylindrical lenses, the shape of the image of object points on the
CCD camera becomes oval unless the object point is located at a position which satisfies the best imaging condition. By
calculating the focus error signal using the intensities measured at a group of CCD cells, the information on the distance
of the corresponding object point could be found out.
The basic concept of the system was checked by computer simulation on the point spread function of various object
points. A preliminary measurement system which consists of the same optical components used in the computer
simulation has been set up for verification of the idea. Since this system requires only one image to analyze the surface
profile, it is a one-shot measurement system, and is insensitive to environmental noises such as mechanical vibration.
High harmonic generation is a well-established optical method to produce coherent short-wavelength light in the
ultraviolet and soft-X ray range. This nonlinear conversion process requires ultrashort pulse lasers of strong intensity
exceeding the threshold of 1013 Wcm-2 to ionize noble gas atoms. Chirped pulse amplification (CPA) is popularly used to
increase the intensity power of a femtosecond laser produced from an oscillator. However, CPA requires long cavities
for multi-staged power amplification, restricting its practical uses due to hardware bulkiness and fragility. Recently, we
successfully exploited the phenomenon of localized surface plasmon resonance for high harmonic generation, which
enables replacing CPA with a compact metallic nanostructure. Surface plasmon resonance induced in a well-designed
nanostructure allows for intensity enhancement of the incident laser field more than 20 dB. For experimental validation,
a 2D array of gold bowtie nanostructure was fabricated on a sapphire substrate by the focused-ion-beam process. By
injection of argon and xenon gas atoms onto the bowtie nanostructure, high harmonics up to 21st order were produced
while the incident laser intensity remains at only 1011 Wcm-2. In conclusion, the approach of exploiting surface plasmons
resonance offers an important advantage of hardware compactness in high harmonic generation.
When a metallic nanostructure is illuminated by ultrashort light pulses, the excitation of surface plasmons is observed
along with subsequent strong enhancement of the electric field in the vicinity of the nanostructure. This localized surface
plasmonic resonance is exploited to generate coherent extreme ultraviolet light and soft-X ray by interacting noble gas
atoms with femtosecond laser pulses. The resulting field enhancement is much affected by the 3-D shape of the used
nanostructure, so various nanostructure shapes are examined through finite-difference time-domain analysis to predict
their performance in high harmonic generation.
We report an exploitation of the optical comb of a femtosecond pulse laser as the wavelength ruler for the task of absolute length calibration of gauge blocks. To that end, the optical comb was stabilized to an Rb atomic clock and an optical frequency synthesizer was constructed by tuning an external single-frequency laser to the optical comb. The absolute height of gauge blocks was measured by means of multi-wavelength interferometry using multiple beams of different wavelengths consecutively provided by the optical frequency synthesizer. The wavelength uncertainty was measured 1.9 × 10-10 that leads to an overall calibration uncertainty of 17 nm (k=1) in determining the absolute length of gauge blocks of 25 mm nominal length.
Possibilities of using recently-developed femtosecond pulse lasers for advanced precision length metrology are
investigated. Special emphasis is placed on the use of femtosecond lasers particularly for absolute distance
measurements with sub-micrometer accuracy over extensive ranges. This investigation reveals that femtosecond lasers
are capable of providing a suitable means of nanometrology by implementing dispersive comb interferometry in
combination with synthetic wavelength interferometry and heterodyne interferometry.
Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks.
You are receiving this notice because your organization may not have SPIE eBooks access.*
*Shibboleth/Open Athens users─please
sign in
to access your institution's subscriptions.
To obtain this item, you may purchase the complete book in print or electronic format on
SPIE.org.
INSTITUTIONAL Select your institution to access the SPIE Digital Library.
PERSONAL Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.