There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

(1991). Applied Linear Regression Models. Journal of Quality Technology: Vol. 23, No. 1, pp. 76-77.

Applied Linear Regression Models

IEEE transactions on computer-aided design of integrated circuits and systems : a publication of the IEEE Circuits and Systems Society

Micromachining and micro-electromechanical system (MEMS) technologies can be used to produce complex structures, devices and systems on the scale of micrometers. Initially micromachining techniques were borrowed directly from the integrated circuit (IC) industry, but now many unique MEMS-specific micromachining processes are being developed. In MEMS, a wide variety of transduction mechanisms can be used to convert real-world signals from one form of energy to another, thereby enabling many different microsensors, microactuators and microsystems. Despite only partial standardization and a maturing MEMS CAD technology foundation, complex and sophisticated MEMS are being produced. The integration of ICs with MEMS can improve performance, but at the price of higher development costs, greater complexity and a longer development time. A growing appreciation for the potential impact of MEMS has prompted many efforts to commercialize a wide variety of novel MEMS products. In addition, MEMS are well suited for the needs of space exploration and thus will play an increasingly large role in future missions to the space station, Mars and beyond. (Some figures in this article are in colour only in the electronic version)

https://iopscience.iop.org/article/10.1088/0964-1726/10/6/301/pdf

Microelectromechanical systems (MEMS):fabrication, design and applications

Traditional software-based diagnosis of failing chips typically identifies several lines where the failure is believed to reside. However, these lines can span across multiple layers and can be very long in length. This makes physical failure analysis difficult. hi contrast, there are emerging diagnosis techniques that identify both the faulty lines as well as the neighboring conditions for which an affected line becomes faulty, hi this paper, an approach is presented to improve failure localization by automatically analyzing the information associated with the outcome of diagnosis. Experimental results show a significant improvement in failure localization when this method is applied to 106 real IC failures.

Precise failure localization using automated layout analysis of diagnosis candidates

A built-in self-test technique that is applicable to symmetric microsystems is described. A combination of existing layout features and additional circuitry is used to make measurements from symmetrically located points. In addition to the normal sense output, self-test outputs are used to detect the presence of layout asymmetry that are caused by local, hard-to-detect defects. Simulation results for an accelerometer reveal that our self-test approach is able to distinguish misbehavior resulting from local defects and global manufacturing process variations. A mathematical model is developed to analyze the efficacy of the differential built-in self-test method in characterization of a wide range of local manufacturing variations affecting different regions of a device and/or wafer. Model predictions are validated by simulation. Specifically, it has been shown that by using a suitable modulation scheme, sensitivity to etch variation along a particular direction is improved by nearly 30%.

Built-in self-test of MEMS accelerometers

We propose a methodology that effectively estimates the defect-type distribution that affects a design fabricated in a given manufacturing process. Understanding the distribution can improve design quality, test quality, and the manufacturing process itself. The methodology is composed of i) an improved approach for identifying the signal lines relevant to defect activation at each site reported by diagnosis, ii) a new behavior attribution method, and iii) a novel approach to estimate the defect-type distribution. The efficacy of this methodology is validated using circuit-level simulation experiments. The results show that the method achieves an average accuracy of 94% in identifying signal lines that are relevant to the activation of a defect. When estimating defect-type distribution for a population affected by a variety of defects, the average estimation accuracy is 92% with ideal diagnosis. With a realistic diagnosis (i.e., the inherent ambiguity of diagnosis is accounted for), the estimated defect-type distribution is 85% accurate, on average.

Estimating defect-type distributions through volume diagnosis and defect behavior attribution

A multiple defect diagnosis methodology consisting of a defect site identification and elimination method, a path-based defect site elimination method, and a defect site selection and ranking method is described. The flexibility of the diagnosis method in handling various defect behaviors and arbitrary failing pattern characteristics is demonstrated through extensive simulations. Unlike some competing approaches, the search space of the diagnosis method does not grow exponentially with the number of defects. Results from over 1700 simulated and 131 failing ICs show that this method can effectively diagnose circuits that are affected by a large (>20) or small number of defects of various types. Specifically, when diagnosing circuits with more than 20 defects, our method identifies 65% of them, and the number of sites reported per actual defective site is, on average, 1.17. For circuits affected by two defects, these numbers change to 86% and 1.85, respectively. Finally, 84% of our top-ranked sites are actual defect sites.

An Effective and Flexible Multiple Defect Diagnosis Methodology Using Error Propagation Analysis

This paper describes a multiple-defect diagnosis methodology that is flexible in handling various defect behaviors and arbitrary failing pattern characteristics. Unlike some other approaches, the search space of the diagnosis method does not grow exponentially with the number of defects. Results from extensive simulation experiments and real failing integrated circuits show that this method can effectively diagnose circuits that are affected by a large (>20) or small number of defects of various types. Moreover, this method is capable of accurately estimating the number of defective sites in the failing circuit.

R.D. Blanton

Papers

Precise failure localization using automated layout analysis of diagnosis candidates

Built-in self-test of MEMS accelerometers

Estimating defect-type distributions through volume diagnosis and defect behavior attribution

An Effective and Flexible Multiple Defect Diagnosis Methodology Using Error Propagation Analysis

Diagnosis of Integrated Circuits With Multiple Defects of Arbitrary Characteristics