Tensor Computation: A New Framework for High-Dimensional Problems in EDA

Many critical EDA problems suffer from the curse of dimensionality, i.e. the very fast-scaling computational burden produced by large number of parameters and/or unknown variables. This phenomenon may be caused by multiple spatial or temporal factors (e.g. 3-D field solvers discretizations and multi-rate circuit simulation), nonlinearity of devices and circuits, large number of design or optimization parameters (e.g. full-chip routing/placement and circuit sizing), or extensive process variations (e.g. variability/reliability analysis and design for manufacturability). The computational challenges generated by such high dimensional problems are generally hard to handle efficiently with traditional EDA core algorithms that are based on matrix and vector computation. This paper presents "tensor computation" as an alternative general framework for the development of efficient EDA algorithms and tools. A tensor is a high-dimensional generalization of a matrix and a vector, and is a natural choice for both storing and solving efficiently high-dimensional EDA problems. This paper gives a basic tutorial on tensors, demonstrates some recent examples of EDA applications (e.g., nonlinear circuit modeling and high-dimensional uncertainty quantification), and suggests further open EDA problems where the use of tensor computation could be of advantage.Comment: 14 figures. Accepted by IEEE Trans. CAD of Integrated Circuits and System

Modellierung, Simulation und Optimierung integrierter Schaltkreise

[no abstract available

SCEE 2008 book of abstracts : the 7th International Conference on Scientific Computing in Electrical Engineering (SCEE 2008), September 28 – October 3, 2008, Helsinki University of Technology, Espoo, Finland

This report contains abstracts of presentations given at the SCEE 2008 conference.reviewe

Custom Integrated Circuits

Contains reports on twelve research projects.Analog Devices, Inc.International Business Machines, Inc.Joint Services Electronics Program (Contract DAAL03-86-K-0002)Joint Services Electronics Program (Contract DAAL03-89-C-0001)U.S. Air Force - Office of Scientific Research (Grant AFOSR 86-0164)Rockwell International CorporationOKI Semiconductor, Inc.U.S. Navy - Office of Naval Research (Contract N00014-81-K-0742)Charles Stark Draper LaboratoryNational Science Foundation (Grant MIP 84-07285)National Science Foundation (Grant MIP 87-14969)Battelle LaboratoriesNational Science Foundation (Grant MIP 88-14612)DuPont CorporationDefense Advanced Research Projects Agency/U.S. Navy - Office of Naval Research (Contract N00014-87-K-0825)American Telephone and TelegraphDigital Equipment CorporationNational Science Foundation (Grant MIP-88-58764

An Efficient Integrated Circuit Simulator And Time Domain Adjoint Sensitivity Analysis

In this paper, we revisit time-domain adjoint sensitivity with a circuit theoretic approach and an efficient solution is clearly stated in terms of device level. Key is the linearization of the energy storage elements (e.g., capacitance and inductance) and nonlinear memoryless elements (e.g., MOS, BJT DC characteristics) at each time step. Due to the finite precision of computation, numerical errors that accumulate across timesteps can arise in nonlinear elements

Custom Integrated Circuits

Contains reports on nine research projects.Analog Devices, Inc.International Business Machines, Inc.Joint Services Electronics Program (Contract DAALO03-86-K-0002)U.S. Air Force - Office of Scientific Research (Grant AFOSR 86-0164)Rockwell International CorporationOKI SemiconductorU.S. Navy - Office of Naval Research (Contract N00014-81-K-0742)Charles Stark Draper LaboratoryDARPA/U.S. Navy - Office of Naval Research (Contract N00014-80-C-0622)DARPA/U.S. Navy - Office of Naval Research (Contract N00014-87-K-0825)National Science Foundation (Grant ECS-83-10941)AT&T Bell Laboratorie

Efficient Procedure Improving Precision of High Conditioned Matrices in Electronic Circuits Analysis

In this article, we propose several improvements that could be done to SPICE simulator. The first is based on a functional implementation of device models. The advantages of functional implementation are demonstrated on basic Shichman-Hodges model of MOS transistor. It starts with a description of primary algorithms used in SPICE simulator for the solution of circuits with nonlinear devices and identify the problems that can occur during simulations.Main part of the article is devoted to improved factorization procedure for simulation of the nonlinear electronic circuits. The primary intention of the proposed method is to increase final precision of the result in a case of high condition linear systems. The procedure is based on a use of the iterative methods for solution of nonlinear and linear equations. Utilizing those methods for one iterative process helps to reduce memory consumption during simulation computation, and it can significantly improve simulation precision. The procedure allows to use enumeration with definable precision in a very efficient way

Circuit-level modelling and simulation of carbon nanotube devices

The growing academic interest in carbon nanotubes (CNTs) as a promising novel class of electronic materials has led to significant progress in the understanding of CNT physics including ballistic and non-ballistic electron transport characteristics. Together with the increasing amount of theoretical analysis and experimental studies into the properties of CNT transistors, the need for corresponding modelling techniques has also grown rapidly. This research is focused on the electron transport characteristics of CNT transistors, with the aim to develop efficient techniquesto model and simulate CNT devices for logic circuit analysis.The contributions of this research can be summarised as follows. Firstly, to accelerate the evaluation of the equations that model a CNT transistor, while maintaining high modelling accuracy, three efficient numerical techniques based on piece-wise linear, quadratic polynomial and cubic spline approximation have been developed. The numerical approximation simplifies the solution of the CNT transistor’s self-consistent voltage such that the calculation of the drain-source current is accelerated by at least two orders of magnitude. The numerical approach eliminates complicated calculations in the modelling process and facilitates the development of fast and efficient CNT transistor models for circuit simulation.Secondly, non-ballistic CNT transistors have been considered, and extended circuit-level models which can capture both ballistic and non-ballistic electron transport phenomena, including elastic scattering, phonon scattering, strain and tunnelling effects, have been developed. A salient feature of the developed models is their ability to incorporate both ballistic and non-ballistic transport mechanisms without a significant computational cost. The developed models have been extensively validated against reported transport theories of CNT transistors and experimental results.Thirdly, the proposed carbon nanotube transistor models have been implemented on several platforms. The underlying algorithms have been developed and tested in MATLAB, behaviourallevel models in VHDL-AMS, and improved circuit-level models have been implemented in two versions of the SPICE simulator. As the final contribution of this work, parameter variation analysis has been carried out in SPICE3 to study the performance of the proposed circuit-level CNT transistor models in logic circuit analysis. Typical circuits, including inverters and adders, have been analysed to determine the dependence of the circuit’s correct operation on CNT parameter variation