Compound Semiconductor Device Modelling

294 Pages·1993·12.233 MB·English

by  Eric A. B. Cole (auth.), Christopher M. Snowden BSc, MSc, PhD, CEng, MIEE, Sen. Mem. IEEE, Robert E. Miles BSc, ARCS, PhD, CEng, MIEE, MIEEE (eds.)

Compound Semiconductor Device Modelling
C.M. Snowden and R.E. Miles (Eds.)
Compound Semiconductor
Device Modelling
With 130 Figures
Springer-Verlag
London Berlin Heidelberg New York
Paris Tokyo Hong Kong
Barcelona Budapest
Christopher M. Snowden, BSc, MSc, PhD, CEng, MIEE, Sen. Mem. IEEE
Robert E. Miles, BSc, ARCS, PhD, CEng, MIEE, MIEEE
Microwave Solid State Group, Department of Electronic and Electrical Engineering,
University of Leeds, Leeds LS2 9JT, UK
Cover illustraJion: Plots from a microwave transistor simulation (HEMT)
ISBN-13: 978-1-4471-2050-6 e-ISBN-13: 978-1-4471-2048-3
DOl: 10.1007/978-1-4471-2048-3
British Library Cataloguing in Publication Data
A catalogue record for this book is available from the British Library
Library of Congress Cataloging-in-Publication Data
A catalog record for this book is available from the Library of Congress
Apart from any fair dealing for the purposes of research or private study, or criticism or review, as
permitted under the Copyright, Designs and Patents Act 1988, this publication may only be
reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing
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should be sent to the publishers.
Text except Chapter 13 C Springer-Verlag London Limited 1993
Chapter 13 C University of Leeds 1993
Softcover reprint ofthe hardcover 1st edition 1993
The publisher makes no representation, express or implied, with regard to the accuracy of the
information contained in this book and cannot accept any legal responsibility or liability for any errors
or omissions that may be made.
Typesetting: Camera ready by contributors
69/3830-543210 Printed on acid-free paper
Contents
Preface .............................................................................. vii
List of Contributors ............................................................. ix
1. Numerical Methods and their Application to Device Modelling
Eric A.B. Cole ..................................................................... 1
2. MESFET Modelling
Christopher M. Snowden.......................................................... 26
3. HEMT Modelling
Michael Shur and Tor A. Fjeldly................................................ 56
4. HDT Modelling
Robert E. Miles .................................................................... 74
S. Guon Diode and IMPA TT Diode Modelling
Michael Shur ....................................................................... 89
6. Introduction to Quantum Modelling
Robert E. Miles.............................. ...................................... 104
7. Modelling of Distributed Feedback Lasers
Geert Morthier and Roel Baets .................................................. 119
8. Equivalent Circuit Modelling
Stavros Iezekiel .................................................................... 149
9. Large-Signal Models
Robert J. Trew ..................................................................... 170
10. Noise Modelling
Alain Cappy ........................................................................ 194
11. Monte Carlo Models and Simulations
Paulo Lugli ......................................................................... 210
12. Quasi-Two-Oimensional Models for MESFETs and HEMTs
Alain Cappy ........................................................................ 232
13. Application of Modelling to Microwave CAD
D. Michael Brookbanks .......................................................... 246
14. Industrial Relevance of Device Modelling
Anthony J. Holden ................................................................ 270
Subject Index ...................................................................... 281
Preface
Compound semiconductor devices form the foundation of solid-state microwave and
optoelectronic technologies used in many modern communication systems. In common
with their low frequency counterparts, these devices are often represented using
equivalent circuit models, but it is often necessary to resort to physical models in order
to gain insight into the detailed operation of compound semiconductor devices. Many of
the earliest physical models were indeed developed to understand the 'unusual'
phenomena which occur at high frequencies. Such was the case with the Gunn and
IMPATI diodes, which led to an increased interest in using numerical simulation
methods. Contemporary devices often have feature sizes so small that they no longer
operate within the familiar traditional framework, and hot electron or even quantum
mechanical models are required. The need for accurate and efficient models suitable for
computer aided design has increased with the demand for a wider range of integrated
devices for operation at microwave, millimetre and optical frequencies. The apparent
complexity of equivalent circuit and physics-based models distinguishes high frequency
devices from their low frequency counterparts ..
Over the past twenty years a wide range of modelling techniques have emerged
suitable for describing the operation of compound semiconductor devices. This book
brings together for the first time the most popular techniques in everyday use by
engineers and scientists. The book specifically addresses the requirements and techniques
suitable for modelling GaAs, InP. ternary and quaternary semiconductor devices found
in modern technology. Beginning with a review of essential numerical methods and their
application to device modelling, the text continues with a chapter on equivalent circuit
models and their derivation, for popular microwave and optoelectronic devices.
MESFETs, HEMTs, HBTs, Gunn and IMPATI diodes are discussed in detail in separate
chapters, with particular emphasis on physical models. Optoelectronic devices are dealt
with as a distinct topic, highlighting the modelling of laser diodes. Large-signal and
noise-modelling, critical to the development of many high frequency communication
circuits, receives special attention. The Monte Carlo technique, which forms the basis
of many models for semiconductor material transport parameters is presented together
with its application to device simulation. Quantum models, suitable for describing many
of the emerging innovative structures is included, with a particularly pragmatic treatment
oriented towards engineering solutions. The modern requirements for computer aided
design are addressed in chapters on highly efficient physical models (quasi-two
dimensional simulations) and the application of modelling to CAD. The text concludes
with a discussion of the relevance of modelling to industry.
The inspiration for this book came from the short course on Compound
Semiconductor Device Modelling held at the University of Leeds, in the Spring of 1993.
This was the latest in a series of courses held in earlier years, which had previously dealt
with the more general topic of semiconductor device modelling. The success of our
viii
previous edited text, published in 1989, and the interest expressed by many in industry
and universities throughout the world, led us to put together this unique collection of
monographs.
We have been fortunate in obtaining contributions to this text from distinguished
engineers and scientists, who are internationally recognised for their expertise. We are
particularly grateful to them for finding the time, from busy schedules, to compile their
chapters. We hope that this text will form a useful foundation in compound
semiconductor device modelling for the novice and will also act as an essential reference
for the more experienced modeller.
Christopher M. Snowden
Robert E. Miles University of Leeds, 1992
Contributors
Roel Baets
Laboratory for Electromagnetism and Acoustics, University of Gent-IMEC, Sint-Pietersoieuwsraat 41,
D-9000 Gent, Belgium
D. Michael Brookbanks
GEC-Marconi Materials Resarch Ltd., Caswell, Towcester, NN12 SEQ. UK
Alain Cappy
D6partement Hyperfr6quences et Semiconducteun, IDsitut d'alectronique at de Micro6lectronique du
Nord, Universit6 des Sciences et techniques de une, S96SS Villeneuve D'A scq, Fnmce
Eric A.B. Cole
School of Mathematics, University of Leeds, Leeds, LS2 9JT. UK
Tor A. Fjeldly
Division of Physical Electronics, The Norwegian Institute of Technology, University of Trondheim, N
7034 Trondheim-NTH, Norway
Anthony J. Holden
GEC-Marconi Materials Research Ltd., Caswell, Towcester, NN12 SEQ. UK
Stavros Iezekiel
Microwave Solid State Group, Department of Electrical and Electronic Engineering, University of Leeds,
Leeds, LS2 9JT. UK
Paulo Lugli
Dip. di Ingengniera Meccanica, II Universita' di Roma "Tor Vergata", Roma via Carnevale 6. Italy
Robert E. Miles,
Microwave Solid State Group, Department of Electrical and Electronic Engineering, University of Leeds,
Leeds, LS29JT. UK
Geert Morthier
Laboratory for Electromagnetism and Acoustics, University of Gent-IMEC, Sint-Pietersoieuwsraat 41, D-
9000 Gent, Belgium
Michael J. Shur
Department of Electrical Engineering, School of Engineering and Applied Science, University of Virginia,
Charlottesville, VA 22901. USA
x
Christopher M. Snowden
Microwave Solid State Group, Department of Electrical and Electronic Engineering, University of Leeds,
Leeds, LS2 9JT. UK
Robert J. Trew
Department of Electrical and Computer Engineering, North Carolina State University, Box 7911, Raleigh,
NC 27695-7911. USA
Numerical Methods and their Application
to Device Modelling
Eric A.B. Cole
University of Leeds
1. INTRODUCfION
The numerical modelling of devices involves the solution of sets of coupled
partial differential equations, which in turn involve the solution of
simultaneous nonlinear equations after discretisation has taken place. It is
not possible in a single paper to fully describe all the numerical techniques
involved in this process, and in this paper we will concentrate on
the finite difference approach. Descriptions of the Finite Element
method (Selberherr 1984, Mobbs 1989), the Boundary Element method
and the Multigrid method (Ingham 1989) can be found elsewhere. Motivation for
considering certain techniques will be given by examining the equations
involved in the modelling of a two-dimensional MESFET. Finite differences are
introduced in section 2, the solution of simultaneous equations discussed in
section 3, and the discretisation of the current continuity equations and
energy equation discussed in section 4. In section 5 we give details of the
implementation for the case of the MESFET , and for a one-dimensional p-n
junction. Finally in section 6 we discuss parameter determination.
To motivate the mathematical discussion we introduce the equations
governing the simulation of a planar sub-micron gate length GaAs MESFET It
is taken as the unipolar device whose cross section in the x-y plane is shown
in figure I, with the ends of the source, gate and drain at x=s, s, g g,
o 1 0, 1
do and d( The electron density n, electron temperature Te and potential I/J
will all be functions of x, y and time t. The equations are:
(il the Poisson equation
2 q
'J I/J = -(N - n) 0)
C d
where C is the product of the permittivity of the vacuum and the relative
permittivity of the semiconductor. This equation is to be solved with the
boundary conditions I{J=V on the source, I{J=V on the drain, I{J=V +IP on the
• d g b
gate where tPb is the built-in potential, and 81/J/8fJ = 0 at other parts of the
2
y
__ _._-_
subst --_. .-.......... _s... u _... b.... strat..e. _.. . ........ " .........
active layer
x
s 0 s 1 go g1 d 0 d 1
source gate dra in
Fig. l. Cross section of the MESFET.
boundary (In this paper, ~ will represent the unit vector normal to the
surface). The electric field is
£: = -VI/J • (2)
(ii) The current continuity equation is, neglecting recombination,
an =
.!.V.J (3)
at q ~
where the current density! has the form
(4)
where ks is Boltzmann's constant, 11 is the mobility, and a 'and bare
constants. Tang(l984) has taken a=b=l, McAndrew, Singhal and Hease11(1985)
and Selberherr(l984) have taken a=1/2, b=O, while Snowden and Loret(l987) and
Feng and Hintz(l988) have taken a=l and b=O. The boundary conditions taken
here are n=2.5N on the source and drain, n=O on the gate, and anlan=O
d
elsewhere.
(iii) The energy transport equation is
aw (W-Wo)
J.E - --- - V.s (5)
IT
T(~)
where ~ is the (position and time-dependent) average electron energy, W=n~,
T(~) is the energy-dependent relaxation time, and
(6)
is the energy flux. The electron energy is given by
~ = ~k T + -1m • v 2 (7)
2 S e 2
•
where m is the average effective mass and v is the velocity. The kinetic