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

Logic diagnosis analyzes the observed failing circuit responses to derive the potential defect sites. This paper describes a method for improving diagnosis through failing behavior identification (FBI). FBI captures defect behavior (i.e., activation conditions of the defect) by identifying the signal lines related to defect activation. This additional information allows the root cause to be estimated in order to improve yield, design quality, and test quality, as well as guide PFA to perform faster defect localization. FBI is accomplished by: 1) deriving the neighborhood states of the defect site, i.e., the actual values on the signal lines within logical or physical proximity to the defect site, and 2) identifying the signal lines that are most relevant to defect activation. The efficacy of FBI is validated using circuit-level and logic-level simulation experiments. The results show that FBI achieves an average accuracy of 94% in identifying signal lines that are relevant to defect activation, a 28% improvement over an existing approach. Moreover, by analyzing the neighborhood states of each defect site reported by logic diagnosis, sites that are not likely to be defective can be eliminated, which leads to improvement in diagnosis resolution. Experiment results show that with little influence on diagnosis accuracy, the number of incorrect defective sites reported by logic diagnosis can be reduced by 64%, on average.

Improving Diagnosis Through Failing Behavior Identification

MEMS structures rendered defective by particles are modeled at the schematic-level using existing models of fault-free MEMS primitives within the nodal simulator NODAS. We have compared the results of schematic-level fault simulations with low-level finite element analysis (FEA) and demonstrated the efficacy of such an approach. Analysis shows that NODAS achieves a 60X speedup over FEA with little accuracy loss in modeling defects caused by particles.

High-Level Fault Modeling in Surface-Micromachined MEMS

As integrated circuit (IC) manufacturing entered the nano-scale era, defect observability has greatly diminished. As a result, test-fail data diagnosis and mining are playing an indispensable role in providing feedback for yield learning. Accurate simulation of defect behavior is vital to this process but, unfortunately, cannot be achieved with simulation at the logic-level alone. This work proposes a framework to enable fast and accurate defect simulation, by making use of existing and well-developed mixed-signal simulation technology (traditionally used for design verification). While previous work has considered this topic before, the innovation here centers on two aspects: (i) accuracy resulting from defect injection taking place at the layout level, (ii) speedup resulting from careful and automatic partitioning of the circuit into digital and analog domains for mixed-signal simulation, and (iii) complete automation that involves defect injection, design partitioning, netlist extraction, mixed-signal simulation, and test-data extraction. The mixed-signal framework developed can be applied in a variety of settings that include diagnosis resolution improvement, defect localization, fault model evaluation, and virtual failure data creation. Experiments demonstrate that the proposed framework is scalable to handle large designs efficiently. A second set of experiments demonstrates how defect localization can be dramatically improved (> 53%) by more accurate defect simulation.

SLIDER: A fast and accurate defect simulation framework

A technique to derive test vectors that exercise the worstcase delay effects in a domino circuit in the presence of crosstalk is described. A model for characterizing the delay of a domino gate in the presence of crosstalk is developed and exploited by a new efJicient timing analysis algorithm. The algorithm uses a single, breadth-jirst traversal to compute delays in the presence of crosstalk. Thus, it avoids the iterative methods commonly employed for static CMOS circuits. The timing analysis technique is used to generate test input vectors that exercise the worst-case delays of a multiplier circuit implemented using domino logic. Hspice simulation results demonstrate that the technique identiJes test vectors that produce circuit delay that satisfy the targeted value in the presence of crosstalk.

Path delay test generation for domino logic circuits in the presence of crosstalk

Systematic defects due to design-process interactions are a significant component of integrated circuit (IC) yield loss in nano-scale technologies. Test structures do not adequately represent the product in terms of feature diversity and feature volume, and therefore are unable to identify all the systematic defects that will affect a product over its manufacturing lifetime. This paper describes a comprehensive methodology that addresses the prevention and identification of systematic defects. For prevention, a method called RADAR (Rule Assessment of Defect-Affected Regions) has been developed for measuring the effectiveness of design-for-manufacturability (DFM) rules in preventing systematic defects that is based on volume diagnosis data. A second method called LASIC (Layout Analysis for Systematic Identification using Clustering), also based on volume diagnosis data, has been developed for identifying systematic defects that escape DFM. To validate RADAR and LASIC, a fast and accurate defect simulation framework called SLIDER (Simulation of Layout-Injected Defects for Electrical Responses) has been developed. SLIDER generates virtual failure data with known defect characteristics. Experiments involving two industrial chips and virtual failure data from SLIDER demonstrate the effectiveness of RADAR and LASIC.

R.D. Blanton

Papers

Improving Diagnosis Through Failing Behavior Identification

High-Level Fault Modeling in Surface-Micromachined MEMS

SLIDER: A fast and accurate defect simulation framework

Path delay test generation for domino logic circuits in the presence of crosstalk

Physically-aware analysis of systematic defects in integrated circuits