Table Of ContentSolid-State Circuits
by
G. J. PRIDHAM
B.SC. (ENG.), C. ENG., M.I.E.E., M.I.E.R.E.
Principal Lecturer, Middlesex Polytechnic
PERGAMON PRESS
OXFORD · NEW YORK · TORONTO
SYDNEY·BRAUNSCHWEIG
Pergamon Press Ltd., Headington Hill Hall, Oxford
Pergamon Press Inc., Maxwell House, Fairview Park, Elmsford,
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Vieweg & Sohn GmbH, Burgplatz 1, Braunschweig
Copyright © 1973 G. J. Pridham
All Rights Reserved. No part of this publication may be
reproduced, stored in a retrieval system, or transmitted, in any
form or by any means, electronic, mechanical, photocopying,
recording or otherwise, without the prior permission of
Pergamon Press Ltd.
First edition 1973
Library of Congress Cataloging in Publication Data
Pridham, G. J.
Solid-state circuits.
(The Commonwealth and international library.
Electrical engineering division)
1. Transistor circuits. I. Title.
TK7871.9.P68 1973 621.3815'3 72-10295
ISBN 0-08-016932-5
ISBN 0-08-016933-3 (pbk)
Printed in Germany
This book is sold subject to the condition
that it shall not, by way of trade, be lent,
resold, hired out, or otherwise disposed
of without the publisher's consent,
in any form of binding or cover
other than that in which
it is published.
Introduction
The purpose of this book is to provide an introduction to modern
semiconductor theory and practice. It is a sequel to Semiconductor
Circuits written by the author in conjunction with Mr. J. R. Abra-
hams, but while embodying certain features of that book it also lays
considerable emphasis on field effect transistors and integrated
circuits.
The text is divided into three sections. The first section of four
chapters is concerned with the basic physics of bulk semiconductors,
diodes, and transistors, and the construction and characteristics of
devices and integrated circuits. Physics is kept to the minimum
necessary for the understanding of devices, and the reader requires
no special physics background.
The next four chapters are devoted to the fundamental use of
semiconductors in rectifier, amplifier, and oscillator circuits. One
chapter specifically deals with the high frequency use of transistors,
and in all examples designs from device characteristics are included.
The final section of three chapters develops the equivalent circuits
of transistors. This approach highlights the a.c. operation of devices,
and the opportunity is taken here to illustrate some of the more
sophisticated circuits using semiconductor devices.
vu
List of Symbols
A Area (m2).
A Gain of an amplifier.
ß Feedback ratio.
C Capacitance (F).
ε Base of natural logarithms.
e Charge on electron (1-6 x lO"19 C).
f Frequency (Hz).
Sm Mutual conductance (mA/V).
h. Short-circuit current gain of a transistor with output
short-circuited.
h Input resistance of transistor with output short-circuited.
t
K Output conductance of transistor with input open-
circuited.
K Voltage feedback ratio of transistor with input open-
circuited.
1 Current (A).
Leakage current in common base (A).
·* co
I1 Leakage current in common emitter (A).
*co
K Coefficient of coupling.
L Inductance (H).
μ Amplification factor.
M Mutual inductance (H).
N Number of acceptor impurity atoms per m3.
A
N Number of donor impurity atoms per m3.
D
N Number of free electrons per m3.
E
N Number of free holes per m3.
M
Ni Number of carriers in intrinsic semiconductor.
Q Charge (C).
ix
X LIST OF SYMBOLS
Resistivity (Ω-m).
Q
R Resistance (Ω).
rei rb> rc T parameters
rb'ei rbb'9 Hybrid-π parameters.
Y cb'i ?ce
Drain resistance.
V Potential difference (V).
v Maximum value of potential difference (V).
m
v Drift velocity of electron.
E
Drift velocity of holes.
VH
y% Input admittance with output short circuit (S).
y Output admittance with input short circuit (S).
0
ys Forward transfer admittance with output short circuit (S).
y Reverse transfer admittance with input short circuit (S).
r
z Impedance (Ω).
ω Angular frequency (rad/s).
Where subscripts are used, upper case denotes d.c. values and lower
case r.m.s. values.
Chapter 1
Basic Physical Concepts
ALTHOUGH it is relatively easy to plunge into the realms of advanced
physics, an understanding of solid-state devices can be obtained from
a few basic concepts. These will be discussed in this chapter and
applied in later chapters to practical devices.
1.1. Composition of Matter
Since the operation of solid-state devices relies on the movement
of electrons, the relation between electrons and their parent atoms
must be considered. This is illustrated by Fig. 1.1, where a stationary
nucleus, composed of protons and neutrons, is shown with electrons
rotating in circular or elliptical orbits. Every element has a different
number of electrons which are arranged in tight shells so as to leave
a maximum number of eight valence electrons. This is illustrated
for a single atom of germanium with thirty-two electrons by Fig. 1.2.
Protons and neutrons
FIG. 1.1. The atom.
1
2 SOLID-STATE CIRCUITS
It is the valence electrons, i.e. those which are outside complete shells,
that decide the chemical and physical properties of any material.
In general, elements with one or two valence electrons are good
conductors, while those with a large number of valence electrons
are good insulators. Elements with complete shells comprise the
4 Valence
electrons
Complete M shell
(18 electrons)
Complete L shell
(8 electrons)
Nucleus Complete K shell
(2 electrons)
FIG. 1.2. The germanium atom.
group known as the inert gases, and germanium and silicon—with
four valence electrons—are the basic semiconductor materials. These
remarks are an oversimplification but are sufficient at this stage.
1.2. Conduction of Electricity
An electric current is due to the movement of charge, and for the
purpose of this book it is the charge associated with an electron
that is important. As an example, consider a good conductor, i.e.
copper with a total of twenty-nine electrons. Twenty eight of these
occupy complete K, L and M shells leaving one electron available for
conduction per atom of copper. Under the influence of an applied
field, these electrons drift through the conductor with a velocity v
E
so that the current (I) flowing is given by:
/ = charge passing a given point per second,
= charge density x volume swept out per second,
= N ev A,
E E
BASIC PHYSICAL CONCEPTS 3
where N is the number of free electrons per unit volume, e is the
E
charge on an electron, and A is the cross-sectional area presented to
the flow of electrons. The drift velocity v is directly proportional to
E
the applied field.
In the case of insulators, with six or seven valence electrons, the
electrons available for conduction are mainly due to small traces of
impurities. The electrons of the insulating material itself are tightly
bound to their parent atoms, and the current is small until the applied
voltage is sufficient to cause breakdown.
FIG. 1.3. Intrinsic semiconductor material.
Conduction in semiconductor devices is decided by the amount
of added impurities, and, initially, the difference between pure
(intrinsic) and doped (extrinsic) materials should be considered. In
an intrinsic bulk semiconductor, atoms share electrons such that
each atom has eight electrons under its influence. This is illustrated
by Fig. 1.3, where nine atoms are shown. Electrons A and B are
shared between atoms (2) and (5), C and D between atoms (6) and (5),
E and F between atoms (8) and (5), and electrons G and H between
atoms (4) and (5). In this way, atom no. (5) has eight electrons under
4 SOLID-STATE CIRCUITS
its influence giving the stable inert gas structure with few electrons
available for conduction. Those that are available are produced by
external energy (typically thermal energy) breaking the bonds between
atoms. The bonds themselves are produced by interaction between
two electrons, say A and B, and their parent atoms (2) and (5). When
a bond is broken, two effects must be considered as illustrated in
Fig. 1.4. Besides the free electron available for conduction there is
Free electron
attracted to
positive electrode
Bond broken to
produce hole
electron pair
Electron 'jumps'
Final position
of hole before
attraction to
negative electrode
FIG. 1.4. Conduction in an intrinsic semiconductor material.
a hole produced in the covalent bond. An electron will jump into this
hole, and by a succession of electron jumps the hole will move to-
wards the negative electrode. The hole may thus be regarded as a
positive charge carrier and the total current is due to negative (electron)
charge carriers and positive (hole) charge carriers. The holes drift
with a lower velocity (v ) than electrons since they are due to a succes-
H
sion of electron jumps, whereas electrons may travel a number of
atomic spacings before suffering collision.
BASIC PHYSICAL CONCEPTS 5
The total current / flowing in a sample of intrinsic semiconductor
is then the charge swept out per second, i.e.
/ = N ev A + N ev A,
E E H H
where N is the number of holes and v their drift velocity. In fact
H H
the number of holes must be equal to the number of electrons for an
intrinsic semiconductor, i.e.
Therefore
I = Njev A + NjeV A
E H
= N^VE + vH)A.
The operation of a practical device depends on the amount of
impurity added to the intrinsic semiconductor material. The impurity
may be trivalent, i.e. with three valence electrons, to give p-type
material, or pentavalent, i.e. with five valence electrons, to produce
Electron available
for conduction
o o
O
Electrons absorbed!
Pentavalent impurity in covalent bonds
atom
Ö Q
FIG. 1.5. Conduction in a pentavalent semiconductor.
