Commutators, Spectral Trace Identities, and Universal Estimates for Eigenvalues

Using simple commutator relations, we obtain several trace identities involving eigenvalues and eigenfunctions of an abstract self-adjoint operator acting in a Hilbert space. Applications involve abstract universal estimates for the eigenvalue gaps. As particular examples, we present simple proofs of the classical universal estimates for eigenvalues of the Dirichlet Laplacian (Payne-Polya-Weinberger, Hile-Protter, etc.), as well as of some known and new results for other differential operators and systems. We also suggest an extension of the methods to the case of non-self-adjoint operators.Comment: 21 pages; revised version: minor misprints correcte

Topological Semimetals

This thesis describes two topological phases of matter, the Weyl semimetal and the line node semimetal, that are related to but distinct from topological insulator phases. These new topological phases are semimetallic, having electronic energy bands that touch at discrete points or along a continuous curve in momentum space. These states are achieved by breaking time-reversal symmetry near a transition between an ordinary insulator and a topological insulator, using a model based on alternating layers of topological and ordinary insulators, which can be tuned close to the transition by choosing the thicknesses of the layers. The semimetallic phases are topologically protected, with corresponding topological surface states, but the protection is due to separation of the band-touching points in momentum space and discrete symmetries, rather than being protected by an energy gap as in topological insulators. The chiral surface states of the Weyl semimetal give it a non-zero Hall conductivity, while the surface states of the line node semimetal have a flat energy dispersion in the region bounded by the line node. Some transport properties are derived, with a particular emphasis on the behaviour of the conductivity as a function of the impurity concentrations and the temperature

Statistical Techniques and Non-Destructive Testing Methods for Copper Wire Bond Reliability Investigation

Microelectronic devices require packaging for mechanical protection and electrical interconnections. Reliability challenges in microelectronics packaging are becoming more severe, as applications demand smaller package sizes and operation in harsher environments, such as in automotive applications. At the same time, manufacturers are seeking to reduce production costs by using new materials, for example in wire bonding by replacing costly gold wire with more economical copper. Because microelectronic devices are expected to function reliably for years or even decades, depending on the application, reliability testing is commonly accelerated, e.g. by using elevated temperature and/or humidity. Even so, testing is often time consuming, requiring weeks or months for product qualification. Furthermore, although standard test conditions exist, little guidance is available in the literature to indicate how long products passing these tests will survive in operation. Non-destructive testing methods provide a great deal of information regarding product degradation and reliability. With proper statistical analysis, strong conclusions can be made about device reliability with relatively short test durations, since testing need not continue until all samples fail. However, data analysis techniques used in the electronics packaging literature are often limited, with statistical analyses and confidence bounds rarely presented. Analysis of incomplete or censored data requires specialized techniques from the field of survival analysis. The contributions of this thesis can be divided in two topics. The first topic is the equipment and techniques used to obtain new reliability results, including a method for temperature calibration of the miniature ovens used, a modification of those ovens for use as environmental chambers with humidity control, and procedures for optimization of wire bonding processes. Second, statistical techniques for analysis of reliability data are demonstrated, using accelerated failure time models to analyze resistance data from copper wire bonds in high temperature storage testing. In doing so, new information was provided to answer an important open question in the field of copper wire bonding, namely, the maximum temperature at which one can expect copper wire bonds on aluminum metallization to perform reliably. In particular, ball bonds made from 25 µm diameter palladium-coated copper wire are estimated to be highly reliable up to at least 167 °C in a clean environment without encapsulation, with failure rate of only 1 ppm after 12000 h. PCC wires were more reliable than bare Cu wires when unencapsulated or when encapsulated in silicone. Conversely, bare Cu was more reliable than PCC when encapsulated in epoxy. The best-performing encapsulated bonds tested were bare Cu wire with a highly heat tolerant epoxy, which are estimated to survive 12000 h with 1 ppm failure probability at 159 °C. Effects of several other factors on bond reliability were also investigated, namely the cleaning process, Al bond pad thickness, and the bonded ball size. Sample and environmental cleanliness were found to be critical to good reliability. Bond pad thickness and bonded ball size had only minor effects on reliability, suggesting that these factors can be safely chosen to satisfy other requirements such as bond pad pitch or current-carrying requirements

Application of tilt correlation statistics to anisoplanatic optical turbulence modeling and mitigation

Atmospheric optical turbulence can be a significant source of image degradation, particularly in long range imaging applications. Many turbulence mitigation algorithms rely on an optical transfer function (OTF) model that includes the Fried parameter. We present anisoplanatic tilt statistics for spherical wave propagation. We transform these into 2D autocorrelation functions that can inform turbulence modeling and mitigation algorithms. Using these, we construct an OTF model that accounts for image registration. We also propose a spectral ratio Fried parameter estimation algorithm that is robust to camera motion and requires no specialized scene content or sources. We employ the Fried parameter estimation and OTF model for turbulence mitigation. A numerical wave-propagation turbulence simulator is used to generate data to quantitatively validate the proposed methods. Results with real camera data are also presented

HOw patients view extended half‐life products: impressions from real‐world experience (The HOPE study)

Introduction Extended half‐life (EHL) clotting factors have been shown to offer people with haemophilia (PwH) protection from bleeding with fewer infusions, which might reduce treatment burden. Aim The HOw Patients view Extended half‐life products (HOPE) study aimed to explore, understand and describe patient expectations around the prophylactic use of EHL products and to establish whether these expectations were met through individual follow‐up analysis. Methods The HOPE study was a prospective, qualitative cohort study conducted among PwH who had switched to Fc fusion protein EHL products in routine clinical care and who had not been recruited to clinical trials of these products. Semi‐structured audio‐recorded interviews were undertaken over two time points; transcripts were analysed to systematically generate theory from data that contains both inductive and deductive thinking. Results Forty‐three interviews were conducted with 25 participants. Most participants were positive about EHL treatment and intended to continue using them. Reduced frequency of infusions meant lives were less disrupted or dominated by haemophilia, and there was less perceived stress on overused veins. For those PwH who did not reduce infusion frequency, there were other perceived benefits from EHLs with respect to greater protection with higher trough levels and fewer bleeds. Conclusion Patients switching to EHL treatments believe these products will result in fewer infusions and less disruption of everyday life, leaving them feeling more protected with fewer bleeds and increased activity levels, as well as enhanced well‐being and mental health. Understanding patient expectation and experience around using products adds real‐world data to clinical trial experience

Wire bonding on glass substrates via vapour deposition of Ag-Ti film

The final publication is available at Elsevier via https://doi.org/10.1016/j.mejo.2019.05.009. © 2019. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/Circuits on glass technology have recently developed in applications such as interposers, fibre optics, and displays. We report an automatable method towards interconnecting to glass circuits via wire bonding with maintained transparency. The method is based on wire bonding Au-Ag, using 25 μm diameter 99.99% pure Au wire. A 5 nm Ti and 500 nm Ag base film are initially deposited via e-beam evaporation onto a standard glass slide, where after wire bonding is preformed. The metal film is then etched from the substrate via ion-milling; remaining intact only in areas shielded from the beam. Cross-sections of the bonded balls before and after metallization removal show high quality continuous interfaces with no intermetallic or micro void formations. Good reliability was indicated by shear testing, remaining above 100 MPa for at least 8 days of ageing at 200 °C. Strong wire bonds were thus obtained on a glass substrate by deposition and selective removal of a Ag-Ti film.We acknowledge financial support from Microbonds, Inc. and the Natural Sciences and Engineering Research Council (NSERC) of Canada. We are grateful for the use of equipment at the University of Waterloo in the Centre for Advanced Materials Joining, the Quantum NanoFab, and WATLab. This infrastructure would not be possible without the significant contributions of CFREF, CFI, Industry Canada, the Ontario Ministry of Research & Innovation and Mike & Ophelia Lazaridis. Their support is gratefully acknowledged

Deep learning for anisoplanatic optical turbulence mitigation in long-range imaging

We present a deep learning approach for restoring images degraded by atmospheric optical turbulence. We consider the case of terrestrial imaging over long ranges with a wide field-of-view. This produces an anisoplanatic imaging scenario where turbulence warping and blurring vary spatially across the image. The proposed turbulence mitigation (TM) method assumes that a sequence of short-exposure images is acquired. A block matching (BM) registration algorithm is applied to the observed frames for dewarping, and the resulting images are averaged. A convolutional neural network (CNN) is then employed to perform spatially adaptive restoration. We refer to the proposed TM algorithm as the block matching and CNN (BM-CNN) method. Training the CNN is accomplished using simulated data from a fast turbulence simulation tool capable of producing a large amount of degraded imagery from declared truth images rapidly. Testing is done using independent data simulated with a different well-validated numerical wave-propagation simulator. Our proposed BM-CNN TM method is evaluated in a number of experiments using quantitative metrics. The quantitative analysis is made possible by virtue of having truth imagery from the simulations. A number of restored images are provided for subjective evaluation. We demonstrate that the BM-CNN TM method outperforms the benchmark methods in the scenarios tested