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  • International Series on Advances in Solid State Electronics and Technology(ASSET)

    Founding Editor: Chih-Tang Sah


    Modern Semiconductor Quantum Physics

    by Li Ming-Fu

    Topics in Growth and Device Processing of III-V Semiconductors

    by Stephen John Pearton, Cammy R. Abernathy & Fan Ren

    Ionizing Radiation Effects in MOS Oxides

    by Timothy R. Oldham

    MOSFET Modeling for VLSI Simulation: Theory and Practice

    by Narain Arora


    The Physics and Modeling of MOSFETS: Surface-Potential Model HiSIM

    by Mitiko Miura-Mattausch, Hans Jrgen Mattausch & Tatsuya Ezaki

    BSIM4: Theory and Engineering of MOSFET Modeling for IC Simulation

    by Weidong Liu & Chenming Hu

    Steven - MOSFET Modeling.pmd 12/11/2006, 10:13 AM2

  • ASSETInternational series on Advances in solid state Electronics and Technology

    Found ing Ed i to r : ch ih -Tang sah




    WORLD SCIENTIFICnew jersey . london . s ingapore . be i j ing . shanghai . hong kong . ta ipe i . chennai

  • British Library Cataloguing-in-Publication DataA catalogue record for this book is available from the British Library.

    For photocopying of material in this volume, please pay a copying fee through the CopyrightClearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission tophotocopy is not required from the publisher.

    ISBN-13 978-981-256-810-6ISBN-10 981-256-810-7

    Disclaimer: This book was prepared by the authors. Neither the Publisher nor its Series Editorthereof, nor any of their employees, assumes any legal liability or responsibility for the accuracy,completeness, or usefulness of any information. The contents, views, and opinions of the authorsexpressed herein do not necessarily state or reflect those of the Publisher, its Series Editor, and theiremployees.

    All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means,electronic or mechanical, including photocopying, recording or any information storage and retrievalsystem now known or to be invented, without written permission from the Publisher.

    Copyright 2007 by World Scientific Publishing Co. Pte. Ltd.

    Published by

    World Scientific Publishing Co. Pte. Ltd.

    5 Toh Tuck Link, Singapore 596224

    USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601

    UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE

    Printed in Singapore.

    MOSFET MODELING FOR CIRCUIT ANALYSIS AND DESIGNInternational Series on Advances in Solid State Electronics and Technology

    Steven - MOSFET Modeling.pmd 12/11/2006, 10:13 AM1

  • v

    To To To To MarleneMarleneMarleneMarlene and R and R and R and Ritaitaitaita

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  • Foreword The purpose of this compact modeling monograph series is to provide an archival

    reference on each specific MOS transistor compact model as described by the originators or the veterans of each compact model. The monograph idea came about when this editor was looking into the literature to prepare for a keynote address, invited by the Founder of the Workshop on Compact Modeling, Professor Xing Zhou of Nanyang Technology University, and his program committee, to be presented at its 4th Workshop on May 10, 2005. The topic was on the history of MOS transistor compact modeling, a subject this editor could not find a reference or book that provided the descriptions of each of the dozen or more MOS transistor compact models, which had been extensively developed for the first-generation computer-aided circuit design applications during 1995-2005, such as the use of the Berkeley BSIM and SPICE. A second purpose is to serve as textbooks for graduate students and reference books for practicing engineers, to rapidly distribute the detailed design methodologies and underlying physics in order to meet the ever faster advances in the design of silicon semiconductor MOS and bipolar-junction-transistor integrated circuits, which contain hundreds or thousands of transistors per circuit or circuit function. I am especially thankful to the authors of the four startup monograph volumes who concurred with me and agreed to take up the chore to write their books in the very short time of less than six months in order to be published in one year, which we try as a rapid response to document the latest advances. It is also the objective of this monograph series to provide timely updates via website exchanges between the readers and authors, for public distribution, and for new editions when sufficient materials are accummulated by the authors.

    We are very pleased to publish the graduate course lecture notes taught by Professors Carlos Galup-Montoro and Mrcio C. Schneider of the Federal University of Santa Catarina, Brazil, as the first monograph of original unpublished work of this series on MOS transistor compact modeling. It is the first textbook and reference book using the next generation surface potential approach to develop compact MOS transistor models by ways of the inversion charge in the surface channel of the conduction carriers, electron (hole) channel for the n-channel (p-channel) MOS transistor. It starts out with a concise definition of the inversion charge in terms of the integrals of the surface potential variable which no other publications have provided as the starting point. This provides the mathematical rigor on the meaning of the inversion charge.

    I would like to thank all the WSPC editors and this monograph volumes copyeditor Mr. Steven Patt (Singapore), led by Dr. Yubing Zhai (New Jersey) for their timely efforts, and Professor Kok-Khoo Phua, Founder and Chairman of WSPC, for his support, all of which have made it possible to attain a less-than-one-year turn-around time to print each monograph volume, in order to meet our intention of responding to the rapid advances of the state of the art of computer-aided integrated circuit design. Chih-Tang Sah Gainesville, San Diego, Singapore December 31, 2006


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  • ix


    Complementary metal-oxide semiconductor (CMOS) technology is the

    leading electronics technology and will continue to be for the next few

    years. The metal-oxide-semiconductor field-effect transistor (MOSFET)

    is the basic building block in CMOS technologies and, as a consequence,

    the predominant device of integrated circuits. Therefore, MOSFET

    modeling plays an important role in interfacing the circuit design

    community with the device and technology community.

    In order to be of practical usefulness for circuit designers, MOSFET

    models should be compact, i.e., they should provide efficient and

    accurate algorithms to calculate charges, currents, and their derivatives.

    The compact modeling of MOS transistors for integrated circuit design

    has, for many years, been driven by the needs of digital circuit

    simulation. However, the trend which started in the late 1970s toward

    mixed analog-digital design generated the necessity for MOSFET models

    appropriate for analog and radio-frequency (RF) design as well. As a

    result, two types of advanced models are currently considered as

    adequate for circuit analysis and design, inversion charge and surface

    potential-based models. In the former approach, currents and charges are

    expressed in terms of the inversion charge densities at the source and

    drain ends of the transistor channel. In the latter, drain current and

    charges are related to the surface-potential at the ends of the channel.

    This book provides both an overview of the basic physics theory

    required to build compact MOSFET models and a unified treatment of

    inversion-charge and surface-potential models. The text presents a fresh

    view of compact modeling, having completely abandoned the regional

    modeling approach. Regional models are presented as asymptotic cases

    of the all-region model, with the main objective of developing the

    understanding of the reader regarding transistor operation in that

    particular region. Compact expressions for hand analysis or for automatic


    by Galup-Montoro and Schneider x

    synthesis, valid in all the operating regions, are presented throughout the

    book. Most of the accurate expressions for computer simulation used in

    the new generation compact models are derived.

    The book starts with a short introduction to MOSFET transistor

    modeling. Chapter 2 presents the two- and three-terminal MOS

    structures. Because it forms the basis of MOS compact models, the

    equivalent capacitive circuit of the MOS structure is carefully derived. A

    rigorous definition of pinch-off based on charge is given. Chapter 2

    includes a thorough treatment of the unified charge control model

    (UCCM) which is at the center of the so-called charge-based models.

    The long-channel MOSFET theory is the subject of Chap. 3. Compact

    drain current models based on either surface potential or inversion charge

    are rigorously derived from the exact Pao and Sah double-integral

    formula. The chapter finishes with the introduction of a current-based

    model appropriate for design and parameter extra