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.
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.
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.
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.