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 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
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.
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.
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 10<sup>13</sup> Wcm<sup>-2</sup> 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 21<sup>st</sup> order were produced
while the incident laser intensity remains at only 10<sup>11</sup> Wcm<sup>-2</sup>. In conclusion, the approach of exploiting surface plasmons
resonance offers an important advantage of hardware compactness 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<sup>-10</sup> 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.