Breakdown Phenomena in Semiconductors and Semiconductor Devices: Breakdown Phenomena in Semiconductors and Semiconductor Devices.pdf

Preface
One form of avalanche breakdown has been known to mankind from ancient times:
lightning, the terrifying gas discharge, the fear of which is inscribed in the tales and
myths of all primitive tribes.
The first known practical application of the avalanche breakdown principle goes
back to the first century of our era. There is a fish in the Mediterranean, the
electric ray, or skate, which was called LLnurcueblly the ancient Greeks, a word which
means “paralyzing”. It is known nowadays that the voltage generated by this fish
can reach 200 Volts. The Roman physician Scribonius, in his famous writing “De
Compositiones Medicamentorum” , published in AD 40, described the using of this
narcue for the treatment of headaches, gout and some other diseases. The treatment
was rather painful. This may be the reason why the term “breakdown” is associated
very often with such unpleasant concepts as “failure” and “destruction”.
Electrical breakdown itself is not connected with any form of destriiction, however.
One widely used microwave device, the IMPATT diode, for example, has a
characteristic operation frequency of about 100 GHz (loll Hz), which means that
it goes into a mature avalanche breakdown regime 10l1 times a second. Since the
guaranteed lifetime of a commercial IMPATT diode is at least 5000 hours, each
diode will go into this regime safely no less than N 3 x 1OI8 times. Moreover,
impact ionization, avalanche and breakdown phenomena form the basis of many
very interesting and very important semiconductor devices, such as avalanche photodiodes,
avalanche transistors, suppressors, sharpening diodes (diodes with delayed
breakdown), and IMPATT and TRAPATT diodes.
We should note at the same time that avalanche phenomena are always associated
with high electric fields F, and that the optimal regimes of many devices can
be realised only at high current densities j. Thus the power density Po = j x F
can be extremely large. The value of the characteristic breakdown field Fi for a silicon
IMPATT diode with an operation frequency of about 100 GHz, for example, is
about 5 x lo5 V/cm, its characteristic current density j is approximately lo5 A/cm2,
and Po is about 5 x lolo W/cm3. As a result, the breakdown phenomena are often
accompanied by a high temperature. It is probable, of course, that if the temperature
is too high, the device may be destroyed due to melting or decomposition of
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viii Breakdown Phenomena in Semiconductors and Semiconductor Devices
the material of which it is constructed. This is not an electric breakdown as such,
but only “overheating”, ( (‘heat breakdown”) causes the device destruction.
It worth noting that operation in high electric fields is the backbone of modern
semiconductor electronics. Indeed, the mainstream of the modern electronics lies
in increasing the operation frequency and velocity of semiconductor device “switching”.
Both the operation frequency and the velocity of switching are inversely
proportional to the length of the ”active region” of the device, L. For the most important
devices used in semiconductor electronics, Field Effect Transistors (FETs)
and Bipolar Transistors (BJTs), the characteristic length of the active region (gate
or base) is about 0.1 pm. With a standard operation bias Vo of about 1 V, the
average value of the electric field Fo across the active region of the device is approximately
lo5 V/cm, which means that the maximal value of the electric field in
the active region can be as large as (2-3)x105 V/cm, i.e. practically equal to the
characteristic breakdown field Fi. Generally speaking, in order to provide maximal
speed and maximal power, many semiconductor devices must operate either under
breakdown conditions or very close to these. Consequently, an acquaintance with
breakdown phenomena is very important and useful for any scientist or engineer
dealing with semiconductor devices.
Many books contain chapters or sections devoted to the principal features of
the avalanche and breakdown phenomena, and there are many good books and outstanding
reviews concerning certain special aspects of these phenomena. The aim
of this book is to summarize the main experimental results on avalanche and breakdown
phenomena in semiconductors and semiconductor devices and to analyse them
from a unified point of view. This book has been written by experimentalists for
experimentalists. We will scarcely deal at all with fundamental theoretical aspects
such as the distribution function of hot electrons, nuances of the band structure at
high energy, etc., but instead we will focus our attention on the phenomenology of
avalanche multiplication and the various kinds of breakdown phenomena and their
qualitative analysis.
The book is organised as follows. In the introductory chapter (Chapter 1) we will
briefly discuss the main definitions and establish the main approaches to describing
breakdown phenomena.
Chapter 2 will be devoted to avalanche multiplication phenomena, and the main
parameters of avalanche photodiodes will be discussed and analysed on this basis.
In Chapter 3 we will consider the reverse current-voltage characteristic of semiconductor
diodes over an extremely wide range of current densities, including prebreakdown
leakage current, microplasma breakdown, mature (homogeneous) breakdown,
the part of the current-voltage characteristic with negative differential resistance
at very high current densities, and the second part with positive differential
resistance. The operation regimes and main characteristics of two important devices:
suppressor diodes and IMPATT diodes, will be also observed in this chapter.
The phenomenon of avalanche injection will be discussed in Chapter 4 for samPreface
ix
ples of the n+ - n - nf and p+ - p - p f types and for bipolar transistors. The
operation of Si avalanche transistors will be analysed for both a conventional regime
and a very effective, fast operation regime realised at extremely high current densities
(Section 4.4). In Section 4.5 we will discuss the recently discovered effect of
extremely fast switching of GaAs avalanche transistors at high current densities.
The phenomena of so called “dynamic breakdown” will be analysed in Chapter
5. This regime is realized under conditions in which the avalanche ionization front
moves along the samples with a velocity which is higher than the saturated velocity
of free carriers (the TRAPATT zone or streamer). The operation regimes of Silicon
Avalanche Sharpers (SAS) and Diodes with Delayed Breakdown (DDB) will be
considered in this chapter.
The main ideas of the book will be summarised in the Conclusion.
We are deeply indebted to Dr. Pave1 Rodin (The Ioffe Institute) for valuable
discussions. We would like to thank our wives and children for their understanding
and patience.
We will greatly appreciate any comments and suggestions which can be e-mailed
to
M . E. Levinshtein (melev@nimis.i offe .rssi.r u) ,
Juha Kostamovaara (juha.kostamovaara@ees2.oulu.fi),
and Sergey Vainshtein (vais@ee.oulu.fi).
The Authors

Contents
Preface vii
1 . Introductory Chapter 1
1.1 Elementary act of impact ionization . . . . . . . . . . . . . . . . . . 1
1.2 Auger recombination . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3 Energy of electrons and holes as a function of electric field . . . . . .
1.4 Main approaches for describing ionization phenomena . . . . . . . . 10
1.4.1 Approximation of the characteristic breakdown field Fi . . . 10
1.4.2 Monte-Carlo simulation . . . . . . . . . . . . . . . . . . . . . 13
1.4.3 Approximation of ionization rates . . . . . . . . . . . . . . . . 14
8
2 . Avalanche Multiplication 21
2.1 Fundamentals of avalanche multiplication . . . . . . . . . . . . . . . 21
2.2 Avalanche photodiodes . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.2.1 Spectral sensitivity . . . . . . . . . . . . . . . . . . . . . . . . 26
2.2.2 Dark current . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.2.3 Quantum efficiency . . . . . . . . . . . . . . . . . . . . . . . . 29
2.2.4 Time response . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.2.5 Multiplication factor . . . . . . . . . . . . . . . . . . . . . . . 32
2.2.6 Avalanche excess noise . . . . . . . . . . . . . . . . . . . . . . 36
3 . Static Avalanche Breakdown 39
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.2 General form of the static “breakdown” current-voltage characteristic 39
3.2.1 Microplasma breakdown . . . . . . . . . . . . . . . . . . . . . 41
3.2.2 Homogeneous (“mature”) breakdown . . . . . . . . . . . . . 44
3.2.2.1 Contact resistivity . . . . . . . . . . . . . . . . . . . 44
3.2.2.2 Thermal resistance . . . . . . . . . . . . . . . . . . . 45
3.2.2.3 Space-charge resistance . . . . . . . . . . . . . . . . . 47
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xii Breakdown Phenomena in Semiconductors and Semiconductor Devices
3.2.3 Negative differential resistance . . . . . . . . . . . . . . . . . .
3.2.3.1 Qualitative consideration . . . . . . . . . . . . . . . .
3.2.3.2 The zero doping ( p - i - n) structure . . . . . . . . .
3.2.3.3 Computer simulation . . . . . . . . . . . . . . . . . .
differential resistance at very high current densities
3.3 Avalanche suppressor diodes . . . . . . . . . . . . . . . . . . . . . . .
3.3.1 Principle of operation . . . . . . . . . . . . . . . . . . . . . . .
3.3.2 Main parameters . . . . . . . . . . . . . . . . . . . . . . . . .
3.4 IMPATT diodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.1 Principle of operation . . . . . . . . . . . . . . . . . . . . . . .
3.4.2 Some physical problems that arise at very high frequencies . .
3.2.4 Second part of the current-voltage characteristic, with positive
. . . . . .
50
50
50
55
58
60
60
62
65
66
75
4 . Avalanche Injection 81
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.2 Avalanche injection in n+ - n - n+ ( p f .p . p+ ) structures 81
4.3 Avalanche injection in bipolar transistors . . . . . . . . . . . . . . . 91
4.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.3.2 Avalanche transistor: conventional regime of operation . . . . 92
4.3.2.1 Difference in breakdown voltages of a BJT between
the common-base and common-emitter configurations 92
4.3.2.2 Dependence of the bipolar transistor gain coefficient
98
4.3.2.3 Main features of ABT operation in a conventional
regime . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.4 Operation regime of a Si avalanche transistor at very high current
densities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
4.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
4.4.2 Steady-state collector field distribution . Residual collector
voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
4.4.3 Transient properties of Si avalanche transistor at extreme current
densities . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
4.5 Operation regime of GaAs avalanche transistor at very high current
densities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
4.5.1 Experimental results . . . . . . . . . . . . . . . . . . . . . . . 122
4.5.2 Breakdown in moving Gunn domain in GaAs: qualitative
analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
4.5.3 Computer simulations of superfast switching in GaAs
avalanche transistor . . . . . . . . . . . . . . . . . . . . . . . . 133
. . . .
QO on current density . . . . . . . . . . . . . . . . . .
5 . Dynamic Breakdown 137
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
Contents xiii
5.2 Impact ionization front (TRAPATT zone) . . . . . . . . . . . . . . 140
5.3 Silicon Avalanche Sharpers (SAS) . . . . . . . . . . . . . . . . . . . . 142
5.3.1 Computer simulations and comparison with experimental results144
5.3.2 Stability of the plane ionization front . . . . . . . . . . . . . . 148
5.3.2.1 Short-wavelength instability of the plane ionization
front . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
5.3.2.2 Long-wave length instability of the plane ionization
front . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
5.3.3 The problem of the initial carriers . . . . . . . . . . . . . . . . 154
5.4 GaAs diodes with delayed breakdown . . . . . . . . . . . . . . . . . 157
5.5 Superfast switching of GaAs thyristors . . . . . . . . . . . . . . . . . 162
5.6 Main features of streamer breakdown . . . . . . . . . . . . . . . . . 168
5.6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
5.6.2 Analytical theory of a streamer discharge . . . . . . . . . . . 169
5.6.3 Computer simulation . . . . . . . . . . . . . . . . . . . . . . . 176
Conclusion 179
List of Symbols 181
Bibliography 185
Index 195

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