On Regression Methods for Virtual Metrology in Semiconductor Manufacturing

Virtual metrology (VM) aims to predict metrology values using sensor data from production equipment and physical metrology values of preceding samples. VM is a promising technology for the semiconductor manufacturing industry as it can reduce the frequency of in-line metrology operations and provide supportive information for other operations such as fault detection, predictive maintenance and run-to-run control. The prediction models for VM can be from a large variety of linear and nonlinear regression methods and the selection of a proper regression method for a specific VM problem is not straightforward, especially when the candidate predictor set is of high dimension, correlated and noisy. Using process data from a benchmark semiconductor manufacturing process, this paper evaluates the performance of four typical regression methods for VM: multiple linear regression (MLR), least absolute shrinkage and selection operator (LASSO), neural networks (NN) and Gaussian process regression (GPR). It is observed that GPR performs the best among the four methods and that, remarkably, the performance of linear regression approaches that of GPR as the subset of selected input variables is increased. The observed competitiveness of high-dimensional linear regression models, which does not hold true in general, is explained in the context of extreme learning machines and functional link neural networks.

Picosecond metrology of laser-driven proton bursts

Tracking primary radiation-induced processes in matter requires ultrafast sources and high precision timing. While compact laser-driven ion accelerators are seeding the development of novel high instantaneous flux applications, combining the ultrashort ion and laser pulse durations with their inherent synchronicity to trace the real-time evolution of initial damage events has yet to be realized. Here we report on the absolute measurement of proton bursts as short as 3.5±0.7 ps from laser solid target interactions for this purpose. Our results verify that laser-driven ion acceleration can deliver interaction times over a factor of hundred shorter than those of state-of-the-art accelerators optimized for high instantaneous flux. Furthermore, these observations draw ion interaction physics into the field of ultrafast science, opening the opportunity for quantitative comparison with both numerical modelling and the adjacent fields of ultrafast electron and photon interactions in matter.

Characterization of human and instrument related measurement errors

Measurement is the act or the result of a quantitative comparison between a given quantity and a quantity of the same kind chosen as a unit. It is generally agreed that all measurements contain errors. In a measuring system where both a measuring instrument and a human being taking the measurement using a preset process, the measurement error could be due to the instrument, the process or the human being involved. The first part of the study is devoted to understanding the human errors in measurement. For that, selected person related and selected work related factors that could affect measurement errors have been identified. Though these are well known, the exact extent of the error and the extent of effect of different factors on human errors in measurement are less reported. Characterization of human errors in measurement is done by conducting an experimental study using different subjects, where the factors were changed one at a time and the measurements made by them recorded. From the pre‐experiment survey research studies, it is observed that the respondents could not give the correct answers to questions related to the correct values [extent] of human related measurement errors. This confirmed the fears expressed regarding lack of knowledge about the extent of human related measurement errors among professionals associated with quality. But in postexperiment phase of survey study, it is observed that the answers regarding the extent of human related measurement errors has improved significantly since the answer choices were provided based on the experimental study. It is hoped that this work will help users of measurement in practice to better understand and manage the phenomena of human related errors in measurement.

Redefinition of the kilogram, ampere, kelvin and mole: a proposed approach to implementing CIPM recommendation 1 (CI-2005)

The International System of Units (SI) is founded on seven base units, the metre, kilogram, second, ampere, kelvin, mole and candela corresponding to the seven base quantities of length, mass, time, electric current, thermodynamic temperature, amount of substance and luminous intensity. At its 94th meeting in October 2005, the International Committee for Weights and Measures (CIPM) adopted a recommendation on preparative steps towards redefining the kilogram, ampere, kelvin and mole so that these units are linked to exactly known values of fundamental constants. We propose here that these four base units should be given new definitions linking them to exactly defined values of the Planck constant h, elementary charge e, Boltzmann constant k and Avogadro constant NA, respectively. This would mean that six of the seven base units of the SI would be defined in terms of true invariants of nature. In addition, not only would these four fundamental constants have exactly defined values but also the uncertainties of many of the other fundamental constants of physics would be either eliminated or appreciably reduced. In this paper we present the background and discuss the merits of these proposed changes, and we also present possible wordings for the four new definitions. We also suggest a novel way to define the entire SI explicitly using such definitions without making any distinction between base units and derived units. We list a number of key points that should be addressed when the new definitions are adopted by the General Conference on Weights and Measures (CGPM), possibly by the 24th CGPM in 2011, and we discuss the implications of these changes for other aspects of metrology.

Interference filters and coatings for mid-infrared astronomy (8-30µm)

The VISIR instrument for the European Southern Observatory (ESO) Very Large Telescope (VLT) is a thermal-infrared imager and spectrometer currently being developed by the French Service d'Astrophysique of CEA Saclay, and Dutch NFRA ASTRON Dwingeloo consortium. This cryogenic instrument will employ precision infrared bandpass filters in the N-( =7.5-14µm) and Q-( =16-28µm) band mid-IR atmospheric windows to study interstellar and circumstellar environments crucial for star and planetary formation theories. As the filters in these mid-IR wavelength ranges are of interest to many astronomical cryogenic instruments, a worldwide astronomical filter consortium was set up with participation from 12 differing institutes, each requiring instrument specific filter operating environments and optical metrology. This paper describes the design and fabrication methods used to manufacture these astronomical consortium filters, including the rationale for the selection of multilayer coating designs, temperature-dependant optical properties of the filter materials and FTIR spectral measurements showing the changes in passband and blocking performance on cooling to <50K. We also describe the development of a 7-14µm broadband antireflection coating deposited on Ge lenses and KRS-5 grisms for cryogenic operation at 40K

Comparative analysis between a CAD model design and physical models obtained by manufacturing additive technologies using optical scan

This article presents a detailed study of the application of different additive manufacturing technologies (sintering process, three-dimensional printing, extrusion and stereolithographic process), in the design process of a complex geometry model and its moving parts. The fabrication sequence was evaluated in terms of pre-processing conditions (model generation and model STL SLI), generation strategy and physical model post-processing operations. Dimensional verification of the obtained models was undertook by projecting structured light (optical scan), a relatively new technology of main importance for metrology and reverse engineering. Studies were done in certain manufacturing time and production costs, which allowed the definition of an more comprehensive evaluation matrix of additive technologies.

Measuring the impact of quality infrastructure in Latin America: Experiences, achievements and limitations

This document, which is partly based on by the study Impacto de la Infraestructura de la Calidad en América Latina, is a second joint effort by the Economic Commission for Latin America and the Caribbean (ECLAC) and the German National Metrology Institute (PTB) to move towards a more detailed understanding of the role played by the Quality Infrastructure in opening up possibilities for the countries in the region to innovate and compete. Through methodological analysis and the realization of case studies at the national level in certain countries in the region, the document seeks to offer a more comprehensive picture of the impact of the Quality Infrastructure and its importance for the economic and social development of countries. The document analyzes various QI related aspects, with particular emphasis on a review of conceptual elements, the role of the QI in the innovation systems of countries and a brief analysis of a set of case studies in Latin American countries. It also identifies a series of challenges and limitations for carrying out impact studies. These elements are taken up again in the final conclusions of the book, where a number of policy recommendations are outlined.

High precision astrometry mission for the detection and characterization of nearby habitable planetary systems with the Nearby Earth Astrometric Telescope (NEAT)

A complete census of planetary systems around a volume-limited sample of solar-type stars (FGK dwarfs) in the Solar neighborhood (d a parts per thousand currency signaEuro parts per thousand 15 pc) with uniform sensitivity down to Earth-mass planets within their Habitable Zones out to several AUs would be a major milestone in extrasolar planets astrophysics. This fundamental goal can be achieved with a mission concept such as NEAT-the Nearby Earth Astrometric Telescope. NEAT is designed to carry out space-borne extremely-high-precision astrometric measurements at the 0.05 mu as (1 sigma) accuracy level, sufficient to detect dynamical effects due to orbiting planets of mass even lower than Earth's around the nearest stars. Such a survey mission would provide the actual planetary masses and the full orbital geometry for all the components of the detected planetary systems down to the Earth-mass limit. The NEAT performance limits can be achieved by carrying out differential astrometry between the targets and a set of suitable reference stars in the field. The NEAT instrument design consists of an off-axis parabola single-mirror telescope (D = 1 m), a detector with a large field of view located 40 m away from the telescope and made of 8 small movable CCDs located around a fixed central CCD, and an interferometric calibration system monitoring dynamical Young's fringes originating from metrology fibers located at the primary mirror. The mission profile is driven by the fact that the two main modules of the payload, the telescope and the focal plane, must be located 40 m away leading to the choice of a formation flying option as the reference mission, and of a deployable boom option as an alternative choice. The proposed mission architecture relies on the use of two satellites, of about 700 kg each, operating at L2 for 5 years, flying in formation and offering a capability of more than 20,000 reconfigurations. The two satellites will be launched in a stacked configuration using a Soyuz ST launch vehicle. The NEAT primary science program will encompass an astrometric survey of our 200 closest F-, G- and K-type stellar neighbors, with an average of 50 visits each distributed over the nominal mission duration. The main survey operation will use approximately 70% of the mission lifetime. The remaining 30% of NEAT observing time might be allocated, for example, to improve the characterization of the architecture of selected planetary systems around nearby targets of specific interest (low-mass stars, young stars, etc.) discovered by Gaia, ground-based high-precision radial-velocity surveys, and other programs. With its exquisite, surgical astrometric precision, NEAT holds the promise to provide the first thorough census for Earth-mass planets around stars in the immediate vicinity of our Sun.

Spin coherent states in NMR quadrupolar system: experimental and theoretical applications

Working with nuclear magnetic resonance (NMR) in quadrupolar spin systems, in this paper we transfer the concept of atomic coherent state to the nuclear spin context, where it is referred to as pseudonuclear spin coherent state (pseudo-NSCS). Experimentally, we discuss the initialization of the pseudo- NSCSs and also their quantum control, implemented by polar and azimuthal rotations. Theoretically, we compute the geometric phases acquired by an initial pseudo-NSCS on undergoing three distinct cyclic evolutions: (i) the free evolution of the NMR quadrupolar system and, by analogy with the evolution of the NMR quadrupolar system, that of (ii) single-mode and (iii) two-mode Bose-Einstein Condensate like system. By means of these analogies, we derive, through spin angular momentum operators, results equivalent to those presented in the literature for orbital angular momentum operators. The pseudo-NSCS description is a starting point to introduce the spin squeezed state and quantum metrology into nuclear spin systems of liquid crystal or solid matter.

Nuclear charge radius determination of 7,10 Be and the one-neutron halo nucleus 11 Be

The only nuclear model independent method for the determination of nuclear charge radii of short-lived radioactive isotopes is the measurement of the isotope shift. For light elements (Z < 10) extremely high accuracy in experiment and theory is required and was only reached for He and Li so far. The nuclear charge radii of the lightest elements are of great interest because they have isotopes which exhibit so-called halo nuclei. Those nuclei are characterized by a a very exotic nuclear structure: They have a compact core and an area of less dense nuclear matter that extends far from this core. Examples for halo nuclei are 6^He, 8^He, 11^Li and 11^Be that is investigated in this thesis. Furthermore these isotopes are of interest because up to now only for such systems with a few nucleons the nuclear structure can be calculated ab-initio. In the Institut für Kernchemie at the Johannes Gutenberg-Universität Mainz two approaches with different accuracy were developed. The goal of these approaches was the measurement of the isotope shifts between (7,10,11)^Be^+ and 9^Be^+ in the D1 line. The …first approach is laser spectroscopy on laser cooled Be^+ ions that are trapped in a linear Paul trap. The accessible accuracy should be in the order of some 100 kHz. In this thesis two types of linear Paul traps were developed for this purpose. Moreover, the peripheral experimental setup was simulated and constructed. It allows the efficient deceleration of fast ions with an initial energy of 60 keV down to some eV and an effcient transport into the ion trap. For one of the Paul traps the ion trapping could already be demonstrated, while the optical detection of captured 9^Be^+ ions could not be completed, because the development work was delayed by the second approach. The second approach uses the technique of collinear laser spectroscopy that was already applied in the last 30 years for measuring isotope shifts of plenty of heavier isotopes. For light elements (Z < 10), it was so far not possible to reach the accuracy that is required to extract information about nuclear charge radii. The combination of collinear laser spectroscopy with the most modern methods of frequency metrology …finally permitted the …first-time determination of the nuclear charge radii of (7,10)^Be and the one neutron halo nucleus 11^Be at the COLLAPS experiment at ISOLDE/ CERN. In the course of the work reported in this thesis it was possible to measure the absolute transition frequencies and the isotope shifts in the D1 line for the Be isotopes mentioned above with an accuracy of better than 2 MHz. Combination with the most recent calculations of the mass effect allowed the extraction of the nuclear charge radii of (7,10,11)^Be with an relative accuracy better than 1%. The nuclear charge radius decreases from 7^Be continuously to 10^Be and increases again for 11^Be. This result is compared with predictions of ab-initio nuclear models which reproduce the observed trend. Particularly the "Greens Function Monte Carlo" and the "Fermionic Molecular Dynamic" model show very good agreement.

Virtual Instruments in Dimensional Metrology

During the last five years, in order to improve understanding of content related to "Coordinate Metrology", the Laboratorio de Metrología y Metrotecnia (LMM) from the Polytechnic University of Madrid offers its PhD students, as a course work, the construction of a virtual instrument. This virtual instrument simulates the imaging of a part to be measured by optical dimensional metrology instruments (microscopes, profile projectors, vision machines). The LMM provides students with images similar to those they would obtain with real instrumentation for the instrument adjustment and calibration process. Working with these images, students should determine the adjustment parameters of the virtual instrument. Once these parameters are set, the student can perform the proper calibration of the virtual instrument. Beyond this process, the instrument is already able to perform traceable measurement. In order to do that, LMM offers students some images of parts. Students should perform some measurements using those images and estimate the corresponding uncertainties.

Uncertainty in ellipse fitting using a flatbed scanner: development and experimental verification

In the field of dimensional metrology, the use of optical measuring machines requires the handling of a large number of measurement points, or scanning points, taken from the image of the measurand. The presence of correlation between these measurement points has a significant influence on the uncertainty of the result. The aim of this work is the development of an estimation procedure for the uncertainty of measurement in a geometrically elliptical shape, taking into account the correlation between the scanning points. These points are obtained from an image produced using a commercial flat bed scanner. The characteristic parameters of the ellipse (coordinates of the center, semi-axes and the angle of the semi-major axis with regard to the horizontal) are determined using a least squares fit and orthogonal distance regression. The uncertainty is estimated using the information from the auto-correlation function of the residuals and is propagated through the fitting algorithm according to the rules described in Evaluation of Measurement Data—Supplement 2 to the ‘Guide to the Expression of Uncertainty in Measurement’—Extension to any number of output quantities. By introducing the concept of cut-off length, it can be observed how it is possible to take into account the presence of the correlation in the estimation of uncertainty in a very simple way while avoiding underestimation.

Uncertainty Estimation for Performance Evaluation of a Confocal Microscope as Metrology Equipment

Both in industry and research, the quality control of micrometric manufactured parts is based on the measurement of parameters whose traceability is sometimes difficult to guarantee. In some of these parts, the confocal microscopy shows great aptitudes to characterize a measurand qualitatively and quantitatively. The confocal microscopy allows the acquisition of 2D and 3D images that are easily manipulated. Nowadays, this equipment is manufactured by many different brands, each of them claiming a resolution probably not in accord to their real performance. The Laser Center (Technical University of Madrid) has a confocal microscope to verify the dimensions of the micro mechanizing in their own research projects. The present study pretends to confirm that the magnitudes obtained are true and reliable. To achieve this, a methodology for confocal microscope calibration is proposed, as well as an experimental phase for dimensionally valuing the equipment by 4 different standard positions, with its seven magnifications and the six objective lenses that the equipment currently has, in the x–y and z axis. From the results the uncertainty will be estimated along with an effect analysis of the different magnifications in each of the objective lenses.