scholarly journals Layout and Thermal Analysis of Power Devices Using a PC/XC

1990 ◽  
Vol 14 (2) ◽  
pp. 95-109
Author(s):  
J. N. Avaritsiotis ◽  
G. Eleftheriades
Keyword(s):  
Thermal Analysis ◽  
Integrated Circuits ◽  
High Reliability ◽  
Linear Equations ◽  
Single Layer ◽  
High Density ◽  
Computer Work ◽  
Bottom Surface ◽  
Systems Of Linear Equations ◽  
New Treatment

Thermal analysis during the design process is an essential step towards the achievement of high reliability in modern high density hybrid and integrated circuits. Thermal analysis is also essential for modern, high density PCBs. Traditionally, a solution of the thermal problem is obtained by either the method of finite differences or the method of finite elements. Both methods, however, require a fine 3-D partition of the substrate, leading to large systems of linear equations the solution of which demands substantial computing power provided by number crunching machines and/or powerful computer work-stations.The widespread use of personal computers, however, dictates the development of new approaches to the thermal problems so that a design engineer can solve them in reasonable time with a PC. A new treatment of steady-state thermal analysis combined with a layout editor is proposed in this paper, which makes use of the analytical solution for the temperature distribution in a single-layer substrate with heat sources on the surface, and having an isothermal bottom surface. In this way the mathematical complexity of the problem is dramatically reduced allowing the thermal analysis of Multi Chip Modules (M.C.M.s) and complex hybrid circuits with the use of a PC/XT or compatible.

Failure Analysis With the Scanning Electron Microscope

1972 ◽  
Vol 30 ◽  
pp. 482-483
Author(s):  
John R. Devaney
Keyword(s):  
Electron Microscope ◽  
Scanning Electron Microscope ◽  
Integrated Circuits ◽  
Failure Analysis ◽  
High Reliability ◽  
Military Applications ◽  
Small Structure ◽  
Useful Life ◽  
Insight Into ◽  
Scanning Electron

Occasionally in history, an event may occur which has a profound influence on a technology. Such an event occurred when the scanning electron microscope became commercially available to industry in the mid 60's. Semiconductors were being increasingly used in high-reliability space and military applications both because of their small volume but, also, because of their inherent reliability. However, they did fail, both early in life and sometimes in middle or old age. Why they failed and how to prevent failure or prolong “useful life” was a worry which resulted in a blossoming of sophisticated failure analysis laboratories across the country. By 1966, the ability to build small structure integrated circuits was forging well ahead of techniques available to dissect and analyze these same failures. The arrival of the scanning electron microscope gave these analysts a new insight into failure mechanisms.

On Some Properties of Semi-rings

2018 ◽  
pp. 35-50
Author(s):  
A. I. Belousov
Keyword(s):  
Linear Equations ◽  
Oriented Graph ◽  
Theoretical Computer Science ◽  
Alternative Methods ◽  
Main Role ◽  
Cost Matrix ◽  
Sequential Elimination ◽  
The Matrix ◽  
Systems Of Linear Equations ◽  
The Cost

The main objective of this paper is to prove a theorem according to which a method of successive elimination of unknowns in the solution of systems of linear equations in the semi-rings with iteration gives the really smallest solution of the system. The proof is based on the graph interpretation of the system and establishes a relationship between the method of sequential elimination of unknowns and the method for calculating a cost matrix of a labeled oriented graph using the method of sequential calculation of cost matrices following the paths of increasing ranks. Along with that, and in terms of preparing for the proof of the main theorem, we consider the following important properties of the closed semi-rings and semi-rings with iteration.We prove the properties of an infinite sum (a supremum of the sequence in natural ordering of an idempotent semi-ring). In particular, the proof of the continuity of the addition operation is much simpler than in the known issues, which is the basis for the well-known algorithm for solving a linear equation in a semi-ring with iteration.Next, we prove a theorem on the closeness of semi-rings with iteration with respect to solutions of the systems of linear equations. We also give a detailed proof of the theorem of the cost matrix of an oriented graph labeled above a semi-ring as an iteration of the matrix of arc labels.The concept of an automaton over a semi-ring is introduced, which, unlike the usual labeled oriented graph, has a distinguished "final" vertex with a zero out-degree.All of the foregoing provides a basis for the proof of the main theorem, in which the concept of an automaton over a semi-ring plays the main role.The article's results are scientifically and methodologically valuable. The proposed proof of the main theorem allows us to relate two alternative methods for calculating the cost matrix of a labeled oriented graph, and the proposed proofs of already known statements can be useful in presenting the elements of the theory of semi-rings that plays an important role in mathematical studies of students majoring in software technologies and theoretical computer science.

scholarly journals Millisecond lattice gasification for high-density CO2- and O2-sieving nanopores in single-layer graphene

2021 ◽  
Vol 7 (9) ◽  
pp. eabf0116
Author(s):  
Shiqi Huang ◽  
Shaoxian Li ◽  
Luis Francisco Villalobos ◽  
Mostapha Dakhchoune ◽  
Marina Micari ◽  
...  
Keyword(s):  
Single Layer ◽  
High Density ◽  
Single Layer Graphene ◽  
Pore Density ◽  
Vacancy Defects ◽  
Carbon Gasification ◽  
Layer Graphene ◽  
Gas Molecules ◽  
Good Agreement

Etching single-layer graphene to incorporate a high pore density with sub-angstrom precision in molecular differentiation is critical to realize the promising high-flux separation of similar-sized gas molecules, e.g., CO2 from N2. However, rapid etching kinetics needed to achieve the high pore density is challenging to control for such precision. Here, we report a millisecond carbon gasification chemistry incorporating high density (>1012 cm−2) of functional oxygen clusters that then evolve in CO2-sieving vacancy defects under controlled and predictable gasification conditions. A statistical distribution of nanopore lattice isomers is observed, in good agreement with the theoretical solution to the isomer cataloging problem. The gasification technique is scalable, and a centimeter-scale membrane is demonstrated. Last, molecular cutoff could be adjusted by 0.1 Å by in situ expansion of the vacancy defects in an O2 atmosphere. Large CO2 and O2 permeances (>10,000 and 1000 GPU, respectively) are demonstrated accompanying attractive CO2/N2 and O2/N2 selectivities.

scholarly journals A Brief Overview of On-Chip Voltage Regulation in High-Performance and High-Density Integrated Circuits

IEEE Access ◽  
2021 ◽  
Vol 9 ◽  
pp. 813-826
Author(s):  
Farid Uddin Ahmed ◽  
Zarin Tasnim Sandhie ◽  
Liaquat Ali ◽  
Masud H. Chowdhury
Keyword(s):  
Integrated Circuits ◽  
High Performance ◽  
Voltage Regulation ◽  
High Density ◽  
On Chip

scholarly journals A Globally Convergent Parallel SSLE Algorithm for Inequality Constrained Optimization

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Zhijun Luo ◽  
Lirong Wang
Keyword(s):  
Constrained Optimization ◽  
Optimization Problems ◽  
Linear Equations ◽  
Coefficient Matrix ◽  
Descent Direction ◽  
Constrained Optimization Problems ◽  
Inequality Constrained Optimization ◽  
Globally Convergent ◽  
Variable Distribution ◽  
Systems Of Linear Equations

A new parallel variable distribution algorithm based on interior point SSLE algorithm is proposed for solving inequality constrained optimization problems under the condition that the constraints are block-separable by the technology of sequential system of linear equation. Each iteration of this algorithm only needs to solve three systems of linear equations with the same coefficient matrix to obtain the descent direction. Furthermore, under certain conditions, the global convergence is achieved.

Mutual Embeddings

2015 ◽  
Vol 15 (01n02) ◽  
pp. 1550001
Author(s):  
ILKER NADI BOZKURT ◽  
HAI HUANG ◽  
BRUCE MAGGS ◽  
ANDRÉA RICHA ◽  
MAVERICK WOO
Keyword(s):  
Iterative Methods ◽  
Lower Bounds ◽  
Linear Equations ◽  
Graph Embedding ◽  
Open Problems ◽  
Linear Arrays ◽  
Systems Of Linear Equations

This paper introduces a type of graph embedding called a mutual embedding. A mutual embedding between two n-node graphs [Formula: see text] and [Formula: see text] is an identification of the vertices of V1 and V2, i.e., a bijection [Formula: see text], together with an embedding of G1 into G2 and an embedding of G2 into G1 where in the embedding of G1 into G2, each node u of G1 is mapped to π(u) in G2 and in the embedding of G2 into G1 each node v of G2 is mapped to [Formula: see text] in G1. The identification of vertices in G1 and G2 constrains the two embeddings so that it is not always possible for both to exhibit small congestion and dilation, even if there are traditional one-way embeddings in both directions with small congestion and dilation. Mutual embeddings arise in the context of finding preconditioners for accelerating the convergence of iterative methods for solving systems of linear equations. We present mutual embeddings between several types of graphs such as linear arrays, cycles, trees, and meshes, prove lower bounds on mutual embeddings between several classes of graphs, and present some open problems related to optimal mutual embeddings.

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