Thickness is a typical parameter related to length, of which measurements are conducted in various industrial fields, such as the automotive, aviation, ship-building, semiconductor, and display industries. Among various measurement techniques, optical interferometry is very attractive in terms of reliability owing to the direct realization of the metre. Moreover, the nature of this non-contact method is such that it does not damage samples. In this review, optical interferometric methods for measuring thicknesses of thick transparent layers are introduced through a discussion of basic principles and applications. With consideration of optical layouts and analysis methods of interference signals, monochromatic laser interferometry, low-coherence interferometry, and spectral interferometry are introduced and discussed in chapters 2, 3 and 4, respectively. With regard to spectral interferometry, the two different key technologies of spectrally resolved interferometry and wavelength-scanning interferometry are covered in different subsections of chapter 4.

A Review of Thickness Measurements of Thick Transparent Layers Using Optical Interferometry

In the field of dimensional metrology, significant technical challenges have been encountered with regard to large-scale object assembly, satellite positioning, control of the long-distance precision stage, and inspections of large steps or deep holes on semiconductor devices and multi-layered display panels. The key elements required are high speeds, a long dynamic measurable range, and good precision of measurements, and conventional methods can scarcely meet such requirements simultaneously. Promisingly, the advent of the optical comb has opened up numerous possibilities to break through practical limits by exploiting several of its unique features. These include inter-mode interference, a wide spectral bandwidth with a long coherence length and well-defined longitudinal modes. In this review, various dimensional metrological methods using the optical comb are introduced, describing their basic principles and applications in scientific as well as industrial areas.

https://iopscience.iop.org/article/10.1088/0957-0233/27/2/022001/pdf

Dimensional metrology using the optical comb of a mode-locked laser

We propose and realize a modified spectral-domain interferometer to measure the physical thickness profile and group refractive index distribution of a large glass substrate simultaneously. The optical layout was modified based on a Mach-Zehnder type interferometer, which was specially adopted to be insensitive to mechanical vibration. According to the measurement results of repeated experiments at a length of 820 mm along the horizontal axis, the standard deviations of the physical thickness and group refractive index were calculated to be 0.173 μm and 3.4 × 10(-4), respectively. To verify the insensitivity to vibration, the physical thickness values were monitored at a stationary point while the glass panel was swung at an amplitude exceeding 20 mm. The uncertainty components were evaluated, and the combined measurement uncertainty became 161 nm (k = 1) for a glass panel with a nominal thickness of 0.7 mm.

Vibration-insensitive measurements of the thickness profile of large glass panels.

In this paper, a ranging system using dispersive interferometry is developed with a femtosecond pulse laser, aiming to eliminate the measurement dead zones by using a greatly unbalanced Mach–Zehnder interferometer. The distance can be measured by the frequency of the spectral modulation. We indicate that the integer number of the pulse-to-pulse length can be determined by changing the repetition frequency. In the short distance measurement, the results show an agreement within 1.5 μm compared with an incremental He-Ne laser in the 1 m measurement range. We do large-scale experiments on a long optical rail using a typical Michelson interferometer, and an agreement well within 25 μm is obtained in a range up to 75 m, corresponding to a relative precision of 3.3 × 10−7. Additionally, we experimentally optimize the system set-up to minimize the measurement uncertainty.

https://iopscience.iop.org/article/10.1088/0957-0233/27/1/015202/pdf

Absolute distance measurement in a combined-dispersive interferometer using a femtosecond pulse laser

With the help of the optical comb of a femtosecond pulse laser, a spectral-domain interferometer has been utilized for measuring absolute distances. Even if the technique can measure distances at a high speed and with good precision, it has two fundamental problems: non-measurable range and directional ambiguity. First, the non-measurable range arises due to the sampling limit of the interference spectra at very short distances or the integer multiple of a double non-ambiguity range. Second, the peak corresponding to the desired distance in the Fourier domain has a directional ambiguity owing to the repeated property of the optical comb. Therefore, due to these two fundamental problems, most previous works never measure the absolute distances by itself in a single operation. In this letter, an interferometric method for measuring arbitrary absolute distances based on a spectral-domain interferometer operating with two reference mirrors is proposed and demonstrated. The two reference mirrors generate two d...

Absolute distance measurement method without a non-measurable range and directional ambiguity based on the spectral-domain interferometer using the optical comb of the femtosecond pulse laser

We developed an optical interferometric probe for measuring the geometrical thickness and refractive index of silicon wafers based on a Fizeau-type spectral-domain interferometer, as realized by adopting the optical fiber components of a circulator and a sheet-type beam splitter. The proposed method enables us to achieve a much simpler optical composition and higher immunity to air fluctuations owing to the use of fiber components and a common-path configuration as compared to a bulk-type optical configuration. A femtosecond pulse laser having a spectral bandwidth of 80 nm at a center wavelength of 1.55 µm and an optical spectrum analyzer having a wavelength uncertainty of 0.02 nm were used to acquire multiple interference signals in the frequency domain without a mechanical phase-shifting process. Among the many peaks in the Fourier-transformed signals of the measured interferograms, only three interference signals representing three different optical path differences were selected to extract both the geometrical thickness and group refractive index of a silicon wafer simultaneously. A single point on a double-sided polished silicon wafer was measured 90 times repetitively every two seconds. The geometrical thickness and group refractive index were found to be 476.89 µm and 3.6084, respectively. The measured thickness is in good agreement with that of a contact type method within the expanded uncertainty of contact-type instruments. Through an uncertainty evaluation of the proposed method, the expanded uncertainty of the geometrical thickness was estimated to be 0.12 µm (k = 2).

Fizeau-type interferometric probe to measure geometrical thickness of silicon wafers

Certified reference materials (CRMs) have been used to calibrate surface profilers for reliable measurements In this paper, we present a newly designed step height CRM which has a step height pattern with two different widths and various special patterns for checking radial magnification, distortion of optical viewing systems, etc Especially, it could be useful for multi-probe inspection instruments in the manufacturing lines The fabrication was done by conventional optical lithography and dry etching process with optimized conditions To verify the step height values, a white-light scanning interferometer was used with objective lenses having magnification of and  CRMs with nominal step heights of , , , , , and were fabricated and the uniformity of these CRMs was evaluated to be less than 3 nm ()

Design and Fabrication of a Step Height Certified Reference Material for Multi-probe Inspection Instruments

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.

Dimensional metrology on a semiconductor packaging process using an optical comb

We have proposed a modified method to improve the measurement uncertainty of the geometrical thickness and refractive index of a silicon wafer. Because measurement resolution based on Fourier domain analysis depends on the spectral bandwidth of a light source directly, a femtosecond pulse laser having the broad spectral bandwidth of about 100 nm was adopted as a new light source. A phase detection algorithm in Fourier domain was also modified to minimize the effect related to environmental disturbance. Since the wide spectral bandwidth may cause a dispersion effect in the optical parts of the proposed interferometer, it was considered carefully through numerical simulations. In conclusion, the measurement uncertainty of geometrical thickness was estimated to be 48 nm for a double-polished silicon wafer having the geometrical thickness of 320.7 μm, which was an improvement of about 20 times that obtained by the previous method.

Uncertainty improvement of geometrical thickness and refractive index measurement of a silicon wafer using a femtosecond pulse laser

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Fizeau-type interferometric probe to measure geometrical thickness of silicon wafers

Design and Fabrication of a Step Height Certified Reference Material for Multi-probe Inspection Instruments

Dimensional metrology on a semiconductor packaging process using an optical comb

Uncertainty improvement of geometrical thickness and refractive index measurement of a silicon wafer using a femtosecond pulse laser