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Fundamentals of
SOLID STATE
JAMIESON ROWE
B.A. (Sydney), B.Sc. (Technology, N.S.W.), M.I.R.E.E. (Aust),
Editor, ‘Electronics Australia’
SECOND EDITION, COPYRIGHT 1979
Printed by Masterprint Pty. Ltd., of Dubbo, N.S.W., for the publisher, Sungravure Pty. Ltd., of 57/59 Regent Street, Sydney, N.S.W., Australia.
Preface
Se SaaS ae eR a TE Ia A Sa I SE TR SI EE IE
_ Much of the material in this book was first published in the monthly magazine ‘Electronics Australia’’, as a series of articles. In both the original articles and the present book I have attempted to provide a basic introduction to modern semicon- ductor devices and their operation. An introduction not just for the service techni- cian and the electronics hobbyist, who perhaps may never wish to delve into the sub- ject in greater depth, but also for the university or technical college student who may
need a broad introduction to semiconductor concepts before plunging into the mathematics.
There are many other introductory books on this subject, but most fall into two broad groups. In one group are the very elementary books, which are very easy to read and understand but generally don’t give you much more than a very superficial understanding. In the other group are books written for the college student, which tend to assume that the reader has a thorough grasp of solid state physics and ad- vanced calculus.
In this case I have tried to steer a middle course. The book starts at a very basic level, and doesn’t deal with the mathematics of solid state physics at all; yet at the same time it tries to present many of the concepts normally found only in the more advanced books. Concepts like the nature of a crystal lattice, energy bands, carrier . diffusion and drift, and so on.
To a certain extent the inclusion of these concepts may tend to make the book less easy to read. However I believe this is justified by the richer and more satisfying insight they give into device operation. In any case I have tried to present these con- cepts in particular as clearly as possible, to minimise the additional effort required by the reader.
For this second edition, chapter 17 has been completely rewritten to bring the book up to date. The discussion of recent advances in fabrication technology and current development trends represents the situation in January, 1979, as accurately as I have been able to determine it from current overseas journals and a recent trip to California’s “‘silicon valley”, the world heart of semiconductor manufacture. The glossary has also been revised and updated, to make it of greater potential value.
Needless to say, no book of this type is the work of one person, and I should like to thank a number of people who played important parts in making the present book possible. Many thanks are due to Neville Williams, Editor-in-Chief of ‘‘Electronics Australia’, Assistant Editor Phil Watson, and indeed the whole staff of the magazine, whose constructive criticism and friendly advice has surely helped to im- prove the quality of the text. And I would especially like to thank draftsman Bob Flynn, whose co-operation and involvement extended far beyond the preparation of diagrams. |
— Jamieson Rowe January 1979
The material in this book is copyright, and the contents may not be reproduced in whole or in part without written permission from the Editor in Chief or the Editor of ‘Electronics Australia”.
Fundamentals of Solid State
Contents
Chapter Chapter Chapter Chapter Chapter Chapter | Chapter Chapter Chapter Chapter Chapter Chapter Chapter Chapter Chapter Chapter Chapter
o ON OD oO FF WO DP =
a C= oe a ce « a FF @Wd pe —_— Oo
16: 17:
ATOMS AND ENERGY
: CRYSTALS AND CONDUCTION
> THE EFFECTS OF IMPURITIES
> THE P-N JUNCTION
> THE JUNCTION DIODE
: SPECIALISED DIODES
> THE UNIJUNCTION
: FIELD-EFFECT TRANSISTORS
> FET APPLICATIONS
> THE BIPOLAR TRANSISTOR
> PRACTICAL BIPOLAR TRANSISTORS : LINEAR BIPOLAR APPLICATIONS : THE BIPOLAR AS A SWITCH
> THYRISTOR DEVICES
: DEVICE FABRICATION
MICROCIRCUITS OR “IC’s” PRESENT AND FUTURE
Appendix — A GLOSSARY OF TERMS
Index
Fundamentals of Solid State
100 107
Chapter 1
ATOMS AND ENERGY
Introduction — modern concept of the atom — electrons
as both particles and waves — “allowed” orbits — electron
energy and energy levels—energy level capacities—valence
—excitation and energy ‘‘quanta’’—radiant energy as both waves and particles.
The concept of an atom as a micro- miniature “solar system” is a familiar One to most people in electronics. Ac- cording to this picture, atoms consist
of a central and relatively heavy nucleus having a_ positive electrical charge, around which orbit smaller,
lighter and negatively charged elec- trons whose number is such that in the “normal” state the atom carries zero nett charge. For each of the chemical elements, the atomic nucleus has particular values of mass and posi- tive charge, and is accompanied in the “normal” state by the appropriate num- ber of orbiting electrons.
Consistent with this picture is the idea that electrical conduction is a mechanism in which an applied elec- tric field causes outer orbiting ele- trons to be freed from their atoms, whereupon they can wander through the material to form the traditional “current * flow.” Conducting materials such as metals are thus understood as materials in which the outer electrons are “loosely bound’ to the atomic nuclei, while insulating materials are in contrast those in which the elec- trons are “tightly” bound, and unable to wander.
For many years, this simple and quite easily grasped concept of atomic structure and its relationship to elec- trical conduction proved quite satis- factory for most purposes. It was gen- erally adequate, for example, for an understanding of the operation of ther- miOnic valves and the circuits in which they were used. However as science, and consequently technology, progres- sed it was found increasingly that the simple picture could not adequately ex- plain many of the new discoveries. It became necessary, as with so many scientific concepts, to both revise and expand our conception of atomic structure, and with it our understand- ing of electrical conduction.
Hence it is that, in order to gain aclear knowledge not only of the mechanisms of electrical conduction as it is currently understood, but also and in particular of the operation of the many different semiconductor devices which are used in — and have vir- tually revolutionised —- modern elec- tronics, One must begin by becoming acquainted with the atom as it is now pictured.
Unfortunately, perhaps, a full un- derstanding of modern atomic theory and the physics of electrical conduc- tion requires a thorough grasp of the abstract and highly mathematical science of Quantum Mechanics; and this is beyond many professional en-
gineers. However a full understanding in this sense is really only necessary for the scientist, research student and device development engineer. A some-
what more limited understanding at a.
basically “qualitative” level is usually found both adequate and satisfying for most other purposes, including that of preparation for further detailed study. It is at this level that the following treatment is pitched.
Perhaps the first thing to be noted about the modern view of the atom is that it is somewhat more “fuzzy” than before, and in consequence it tends to be less satisfying. Although disconcerting, this must unfortunately be accepted as q fact of life. The fact is that the apparent clarity of the sim- ple “solar system” picture was an il- lusion, with no real justification on the basis of our actual knowledge.
We are unlikely to know for some considerable time, if indeed we will ever know, the “real” nature of elec- trons and other sub-atomic “particles,” or of such fundamental things as mass, energy, time, electric and magnetic fields, and electrical charge.
The modern picture of the atom and its behaviour tries to take this lack of knowledge into account. In producing a theory which “works,” in the sense that it can satisfactorily explain most of the little we do actually know, it aims at the same time at preventing us from kidding ourselves that we know more than this!
ALLOWED ELECTRON ORBITS (N= QUANTUM NUMBER)
Figure 1.1
At this stage the reader may well be wondering if the modern picture of the atom bears any resemblance at all to the simpler one. The truth is that there is a resemblance, although only a general one.
In broad terms, the atom may still be pictured as consisting of a central positively charged nucleus, surrounded by a number of negatively charged electrons, As the nucleus plays no
more than a nominal part in electrical behaviour, we need not concern our- selves here with its structure. Suffice to say that it is just as well that this is the case, because the closer physicists examine the nucleus, the more complex does it seem to become!
The electrons are still held to be the components of the atom which are responsible for its electrical and chemical behaviour. However, they can no longer be regarded simply as tiny physical particles orbiting around the nucleus, nor can the part which they play in electrical conduction be pic- tured as a straightforward one where- by an electric field “loosens” those in the outermost orbits and whisks them along to form a current flow. As with the nucleus, the closer the elec- tron and its behaviour are examined the more complex—-and in this case, the more elusive—does it become.
It has been found that, in some cir- cumstances, the behaviour of electrons can indeed only’ be explained by visualising them as small particles. Yet, equally, there are other situations in which their behaviour can only be ex- plained as consistent with that of small bursts of oscillations or ‘“waves” of a type similar to, but different from, those responsible for sound, heat and light. In other words, an electron must now be regarded as a somewhat vague thing which sometimes behaves as a physical particle, and at other times alternatively behaves as a “packet’’ of some sort of waves.
As it happens, it is the wave aspect of their “personality” which seems to play the major part in determining the behaviour of electrons as they sur- round the nucleus of an atom. So that in place of the simple picture of a number of electron “planets” orbiting around the nucleus, we must now try to visualise a system of spherical and and elliptical “surfaces” at various dis- tances from the nucleus, and each somewhat fuzzy and indistinct because
of wavelike variations over the perimeter.
Whereas it would appear that, at the more familiar macroscopic _ level,
planets may orbit around a sun at vir- tually any radius providing they have the appropriate orbital velocity, this does not occur in the’ microscopic level of the atom. Electrons are only able to “orbit” (the term is still used, for convenience) around the nucleus at certain definite radii. In terms of the wavelike aspect of the electron these radii can be interpreted broadly as those whose perimeter corresponds to an integral (or whole-number) mul- tiple of a compatible electron “wave-
length.” Although this concept may seem strange and rather hard to accept,
the full reasoning behind it is quite abstract and involves mathematical “gymnastics” which we cannot deal
Fundamentals of Solid State
with here. However, for the present it may help to compare the situation with the more familiar one involving the production of standing waves in a stretched string: waves can only occur at frequencies at which the string length corresponds to a single wave- length, two wavelengths, three wave- lengths, and so on.
The electrons of an individual atom, then, can only occupy orbits cor- responding to certain “allowed” effec- ive radii, This is illustrated by the diagram of figure 1.1. As may be seen, the various possible orbits are each assigned a so-called quantum number, commencing at “1” for the innermost. The effective radius of the orbits in- creases with the square of the quantum number, i.e., | unit, 4 units, 9 units, and so on.
Some idea of the size of the orbits may be gained from the fact that the innermost or N=1 orbit corresponds to an effective radius of approximately 5 <x 10° metre, or about 50 million- millionths of a metre.
Associated with each possible orbit is a corresponding energy level; ie., an electron occupying a particular orbit will have a particular amount of en- ergy. This will consist of both the kinetic or “motional” energy associated with its orbiting momentum, together with the potential or “latent” energy which it possesses by virtue of its posi- tion in the electric field surrounding the nucleus.
Because of the opposite charges of electrons and nuclei, an electron is attracted to the nucleus with a force which varies inversely with the square of its distance from the nucleus centre. In view of this, an electron at a par- ticular point in the electric field sur- rounding the nucleus has a positive potential energy with respect to that nucleus, and at the same time a nega- tive potential energy with respect to any point more distant from the latter.
If these polarities seem wrong, re- member that positive potential energy corresponds to the ability to perform work or release “internal” energy, while negative potential energy implies a need for energy to be externally sup- plied.
From the point of view of the elect- ron, therefore, the vicinity of the nucleus represents an area of lower or “more negative” potential energy than elsewhere. In fact the field around the nucleus forms what may be visualised as a potential energy “pocket” or well, with the nucleus at its centre and the “sides” sloping exponentially. Viewed in this light, a free electron wandering near ‘the nucleus and attracted to it effectively “falls into the well.” These ideas are illustrated in the diagrams of figure 1.2.
According to this view, an electron which is orbiting around the nucleus does so (rather than “fall”) by virtue of its orbital momentum — in effect, it “rolls around” the walls of the potential energy well at a sufficient speed to prevent itself from falling. An orbiting electron thus possesses a posi- tive kinetic energy, and because the required orbital momentum increases with decreasing effective orbit radius, the kinetic energy similarly increases. In fact it turns out that the positive kinetic energy follows the same ex- ponential curve as that of the negative potential energy, but with opposite _ sign and with an amplitude half as
Fundamentals of Solid State
(ELECTRIC 7 FIELD) ‘aa. NEGATIVE. / \ POTENTIAL 1° ENERGY
ELECTRON ATTRACTED TO NUCLEUS WITH A FORCE INVERSELY PROPORTIONAL TO THE SQUARE OF DISTANCE "d"
NEGATIVE ELECTRON ENERGY
NEGATIVE POTENTIAL ENERGY WITH RESPECT TO A DISTANT POINT
POSITIVE POTENTIAL ENERGY WITH RESPECT TO THE NUCLEUS
NUCLEUS
EFFECTIVE "POTENTIAL WELL" SURROUNDING
NUCLEUS, AS SEEN BY AN ELECTRON
Figure 1.2 DISTANCE FROM NUCLEUS 0 xX al ENERGY "LEVELS" CORRESPONDING TO ALLOWED ORBITS @ (NUCLEUS) Figure 1.3
great if spherical orbits are considered.
As the tota] energy of an orbiting electron consists of the algebraic sum of its potential energy (negative) and its kinetic energy (positive), and both these follow exponential laws with the former larger than the latter, the total energy will thus be negative and will also follow an exponential. In _ short, the vicinity of the nucleus represents for orbiting electrons a total energy well, similar to that for potential energy but “less deep.” A two-dimen- sional representation of this well is shown by the dashed curved lines in figure 1.3.
An example may help in clearing up any possible confusion at this point. An electron in an orbit of effective radius “r” is seen to occupy an energy level represented in figure 1.3 by the line C-C’, with a total negative energy of Wb. From the shape of the dashed outline of the energy well, it may be seen that the smaller the effective orbi- tal radius, the greater the negative energy possessed by an electron in that orbit.
It should be fairly evident at this stage that removal of a particular orbi- ting electron from the influence of the nucleus (i.e., taking it to an effectively distant place) will involve doing posi- tive work, to a degree which corres- ponds exactly to the negative energy level of the orbit concerned. Hence an electron occupying the energy level C-C’ in figure 1.3, in order to be “freed” from the nucleus altogether, must acquire a positive energy equal
and opposite in sign to Wb.
In short, the negative energy level of an orbit simply corresponds to the degree to which an electron in that orbit 1s “bound” to the nucleus.— the orbital binding energy.
AS we saw earlier, in an individual atom electrons can only occupy orbits having certain allowed effective radii. Hence, in terms of the energy level diagram of figure 1.3 an orbiting elec- tron must occupy one of the discrete energy levels represented by such lines as A-A’, B-B’, C-C’, and so on. Level A-A’ might correspond to the N=! orbit of figure 1.1, for example, and level B-B’ to the N=2 orbit.
Although only three of the permitted energy levels are shown in figure 1.3, there is in fact a very large number, corresponding to allowed orbits with effective radii increasing rapidly with the squares of successive quantum numbers. Because of the exponential Shape of the energy well around the nucleus the energy differences between. Successive Orbits actually decreases, however, so that if further levels were shown in figure 1.3. they would be seen to form a series of horizontal lines with decreasing vertical spacing, above level C-C’ and’ approaching the zero energy level represented by O-X.
One might perhaps imagine, from the foregoing, that in an_ individual atom of an element all of the electrons surrounding the nucleus would be _found occupying the lowest (most nega- tive) energy level, at least when the atom is in the ground state with no
5
additional energy or “excitation” re- ceived from external sources. However, this is not so.
In fact it is found that, in effect, each energy level has a definite elec- tron “capacity”; only two electrons can occupy the N=1 level, only eight can occupy N=2 level and so on.
The maximum number of electrons which may occupy the first five allowed energy levels are 2, 8, 18, 32 and 50 respectively.
Although quantum mechanical theory provides an adequate explana- tion of the electron capacities of the various energy levels, the detailed arguments involved are beyond the scope of the present treatment. For the present it should be sufficient to note that in addition to their energy level, electrons in orbit have other important characteristics such as degree of orbit ellipticity, magnetic moment, and spin polarity. It is be- lieved that only certain combinations of these characteristics are permitted at each energy level, and further that no two electrons at the same energy level can have the same combination. The latter “law” is held to apply to any unified system involving electrons, and is known as Pauli’s exclusion principle.
In an individual atom in the ground state, then, the electrons occupy the lowest permitted energy levels to a degree determined by the various energy level capacities.. For example in a boron atom, with five electrons, two occupy the N=1 level, which is thus “filled,” while the remaining three occupy but only partly fill the N=2 level; the remaining levels are empty. Similarly the fourteen electrons of the silicon atom are disposed with two
Number of
TABLE 1.1
Occupation of Orbits/Energy Levels
Element Cae. ai
Number) be Hydrogen | 1 | Helium 2 Lithium 3 Beryllium 4 Carbon 6 ONG BEn 8 Fluorine 9 Neon 10 Magnesium
Aluminium 2 Silicon 14 ~ Phosphorus 15 Sulphur 16 Chlorine Argon 18 es Potassium 19
ZL, N
filling the N=1 level, eight filling the N=2 level, and the remaining four partly filling the N=3 level.
Table 1.1 gives the electron disposi- tions of the first 20 elements of the “periodic table,” illustrating the way in which the various energy levels are progressively “filled.”
It is those electrons in the outer- most of the occupied energy levels of an atom which almost completely de- termine its external behaviour, both chemical and electrical, The electrons which may be present in any filled lower energy levels play little part in external behaviour, because they are relatively strongly bound to the nucleus. Accordingly the latter are usually called the “core” electrons, and can often be considered as “Jumped _to- gether” with the nucleus, whereas the former are called the valence electrons (from the Latin ‘“valere,” meaning strength; an allusion to the part played in chemical bonding), and are almost aes considered separately and in de- tall.
The energy level occupied by the valence electrons of an atom of a particular element is consequently known as the valence level for that element. Each of the allowed energy levels is the valence level for atoms of
certain elements; for example the N=2 level is the valence level for atoms of elements such as_ boron,
while the N=3 level is the valence level for elements such as silicon.
In the foregoing description of ‘the structure of the atom as it is currently pictured, we have considered the atom in the so-called ground state. Actually, this state is a purely hypothetical one; it would only occur if an atom could
be placed in a light-tight and radiation--
Z II
tod Z, [|
&
‘t
CA
(X-RAYS, GAMMA RAYS, ETC.)
ULTRA VIOLET
LA SNS A ANS NAKANO ANN SS NARS SS SAAN
"MICROWAVES" RADAR, NAVIGATION RADAR,
UHF RADIO, UHF TELEVISION
VHF RADIO, TELEVISION HF RADIO } ("SHORT WAVES") MF RADIO (BROADCAST BAND)
LF RADIO
FREQUENCY—HERTZ WAVELENGTH-——METRES
THE ELECTROMAGNETIC SPECTRUM Figure 1.4
proof container maintained at a tem- perature of absolute zero (-273°C). Let us therefore look briefly at the more usual situation, where an atom is at a somewhat more comfortable tempera- ture and is accessible to light and possibly other forms of radiation.
Most readers will probably be aware that light, heat and other forms of radiation such as X-rays are essentially energy, in the form of electromagnetic waves. As such, they are related to the familiar waves used for communi- cation and for sound and _ television broadcasting. They differ from the ‘latter almost solely in terms of fre- quency, or wavelength; in fact heat radiation corresponds’ virtually to “super-super-high frequency” radiation, or “ultra-ultra-short waves,” while light and X-rays correspond to even higher frequencies and shorter waves again. These relationships are illustrated in figure 1.4, which shows the relevant portion of the electromagnetic spec- trum.
In view of this, it should not be hard to understand that an atom which is in any practical situation involving light, heat and the other forms of radia- tion is virtually subjected to a constant bombardment of energy. And it should be no surprise that in such a situation the atom will tend to be found not in its ground state, but in one of many possible “excited’’ states which corres- pond to its having absorbed—at least temporarily —- additional energy.
As one might perhaps guess, the mechanism by which an atom “ab- sorbs” energy to become excited is a rather complex and obscure one; so too iS the converse mechanism whereby the atom “ejects” energy to return to
Fundamentals of Solid State
either the ground state or a_ lower excited state. For a full explanation, as before, one must delve quite deeply into quantum mechanics. However, there is a basic and important principle involved, and one which we can con- sider here briefly.
Stated simply, the principle is as follows: The absorption of energy by an atom corresponds to the transfer of electrons to higher energy levels. Bevause there are only certain allowed energy levels in an atom, as we have seen, this means that energy can only be absorbed in “lumps” or quanta of definite sizes. The sizes of the quanta correspond to the energy differences between the various allowed levels.
Hence an atom can absorb an amount of energy corresponding to the transfer of an electron from the N=! level to the N=3 level, for example, or to the transfer of perhaps three electrons at the N=2 level to the N=4 level. But, whatever the quantum of energy absorbed, it must correspond to the transfer of a whole number of electrons from one of the allowed energy levels to other, higher levels.
And the same principle holds for emission of energy. which as one would expect involves transfer of electrons from higher to lower allowed energy levels. An atom can only emit energy in quanta of fixed sizes, corresponding to the transfer of whole numbers of electrons from higher to lower allowed energy levels.
At this point the reader may well be asking how it is possible for atoms to be able to absorb and emit energy in discrete quanta. when the energy absorbed and emitted is in the form of supposedly continuous radiation such as light or heat.
The answer to this is that in fact electromagnetic energy, like the elect- ron, behaves in many ways as if it too has a “split personality.” In contrast with its continuous wavelike nature, it can equally readily behave as if it con- sists of small particles or quanta of energy. These particles have been named photons.
It happens that the amount of energy represented by a photon is independent of the intensity or “strength” of the radiation concerned; this only deter- mines the number of photons present. Rather, the energy of a photon is dir- ectly proportional to its frequency. This is a very important relationship which was discovered by the physicist Max Planck in 1900 and developed by Albert Einstein in 1905.
According to this relationship, pho- tons of “blue” visible light represent larger energy quanta than photons of lower frequency such as “red” light, and the latter in turn represent larger quanta than photons of heat radiation. Also. and very importantly for our present purposes. heat photons corres- ponding to higher temperatures repre- sent larger energy quanta than those corresponding to lower temperatures. This arises becauSe temperature is a direct function of frequency.
From the foregoing it may be seen that. because it is only capable of ab- sorbing energy quanta of certain fixed sizes corresponding to electron trans- fers between allowed energy levels. an atom can effectively only be excited by radiation of particular frequencies (wavelengths). Each frequency will correspond to an electron transfer be- tween a particular combination. of
Fundamentals of Solid State
N=5
N=4 SMALL ENERGY
-~ QUANTUM (LOW Nw 3 eg FREQUENCY PHOTON)
N =2
LARGER ENERGY QUANTUM (HIGH _ FREQUENCY PHOTON)
NEGATIVE ELECTRON ENERGY
EXCITATION (HORIZONTAL AXES HAVE
levels; hence a transfer from the N=1 level to the N=3 level might result from absorption of a photon of frequency fl, while a photon of an- other frequency f2 might produce a transfer of an electron from the N=3 to the N=4 level.
Similarly the ejection of energy by an atom dropping to the ground state or to a lower excitation state results in the emission of radiation only at particular frequencies. An_ electron transfer from the N=2 level to the N=! level might result in the emission of a photon of frequency f3, for example, while a transfer from the N=5 to the N=3 level would result in the emission of a photon at a different frequency.
These concepts are illustrated in the diagrams of figure 1.5.
In practical situations atoms can thus be found tending to continuously absorb and emit radiation at a number of specific frequencies, each of which corresponds to one of the possible energy level transitions. It is this be- haviour which accounts for the so- called “line spectra” obtained by ana- lysis of the wavelengths of light and heat absorbed and emitted by atoms of the various elements under suitable conditions.
As one might expect, the number of specific photon frequencies involved in atom energy absorption and emission tends to be quite large, as there are many possible energy leve] transitions, This is particularly so with elements having many electrons surrounding the nucleus. However due to. dif- ferences between levels concerning the allowed “secondary” electron charac- teristics of orbit ellipticity, magnetic moment and spin, some level transi- tions tend to be more prevalent than others, in a fashion which varies from element to element. As a result each element tends to have a characteristic
NO SIGNIFICANCE)
SMALL ENERGY N=5 sec‘ QUANTUM (LOW N= FREQUENCY PHOTON) N
LARGER ENERGY QUANTUM (HIGH FREQUENCY PHOTON}
NEGATIVE ELECTRON ENERGY EMISSION
Figure 1.5
pattern of “dominant” absorption and emission frequencies.
An atom in the excited state con- tains, as we have seen, electrons which are occupying higher energy levels than they would occupy in the ground State. It is interesting to consider whether we can make any inferences regarding which of the electrons will be more likely to be found at such higher levels.
As it happens, we can. Earlier, we saw that the energy differences between the allowed energy levels decrease with increasing orbit radius and quantum number. Hence somewhat _ preater energy would be required to transfer an electron from the innermost N=1 level to the mext or N=2 level for example, than to transfer an electron from the N=3 level to the adjacent N=4 level. Thus even for transfer be- tween adjacent levels, the electrons at the lower levels require larger energy quanta.
There is also the electron capacity of the various levels to be considered. i.e., Pauli’s exclusion principle. As the capacity of the various levels does not alter with excitation, this means that a transfer of an electron to a particular energy level can only take place if there is a “vacancy” at that level. From this it can be seen that transfer of electrons from the higher levels is more likely to occur than from the lower levels, both because the lower levels are more likely to be “full” and also because the capacity of the levels increases with increasing energy.
We can say, then, that for a given degree of excitation, the ‘excited level” electrons will tend to be those which already occupy the higher levels in the ground state, rather than those from the lower levels. In _ particular, there will tend to be a high proportion of the electrons from the valence level of the atom concerned.
PODGUCEOSOSUSOUOCDUDAOEOUUODOUOOPEOLDEODOGZUOTQOUEOSRREDERODEPOURROROSUSUSOEUSOCRQQOROSUQOSADDODSDOSTONRAGTRLDDELUSEUSCRUTUUODEOCRUODSCRAGORDERUOEOLOOUUORDISSODOREUSELGODUSOAEAAOGORRSUDOGODORAGRRSAGanES
SUGGESTED FURTHER READING
BURFORD, W. B.. and VERNER, H. G., Semiconductor Junctions and
Devices,
1965. McGraw-Hill Book Company, New York.
MORANT, M. J., Introduction to Semiconductor Devices, 1964. George
G. Harrap and Company, London. SCROGGIE, M. G., Fundamentals of Semiconductors,
Library Inc.. New York.
1960. Gernsback
SHIVE, J. N., Physics of Solid State Electronics, 1966. Charles E. Merrill
Books Inc., Columbus, Ohio.
SMITH, R. A., Semiconductors, 1959.
Cambridge University Press.
VODSHRDDODROOOUEDEDODDEGDDGDEDRSSOORNODSODOBDESDDAUBEDODEODEAPONOOOOEUSIDNUOEQDRISOODODUOS JINR DOOROUQCOUSUEODOLPLSIDDPSUQODBUSUGUSTODOUUQUEUOUIOCHILTSOOCQGUUUSUGUGUQLUOSHRUUUUEINUDOSDSDOODOSSURTOQGRORUD DED
7
Chapter 2
CRYSTALS AND CONDUCTION
Atoms in combination — energy interaction — crystalline
solids and energy bands—the valence band—conductors
and electrical conduction—insulators and semiconductors
—the effect of excitation—electrons and holes-——crystal conductivity and resistivity.
Having looked at the modern con- cept of atomic structure, and at what might be called the “internal” beha- viour of individual atoms, let us now examine what happens when atoms link together to form molecules and “solid” matter. It should become appar- ent as we progress that knowledge of this “external” behaviour is essential for a clear understanding of electrical conduction,
We have seen that in an individual atom, the electrons surrounding the central nucleus can only occupy cer- tain “allowed” orbits, each of which correspond to a_ particular value or level of total electron energy, and that in the unexcited or “ground” state the electrons of an atom are found occupy- ing the orbits. nearer the nucleus in numbers determined by the orbit capa- cities. We have also seen that in a practical situation involving light, heat and other forms of radiant energy, electrons are constantly transferred back and forth between allowed orbits as the atom absorbs and emits “lumps”’ or quanta of energy whose sizes corre- spond to the energy differences between the various levels,
Two individual and separate atoms of the same element will possess the same allowed orbit structure, or in other words the energy levels of their allowed orbits will be identical. Note that in saying this we make no refer- ence to the electrons occupying the levels, but refer only to the allowed levels themselves. Hence it js not im- plied that at every instant of time each atom will have exactly the same excita- tion energy. with identical numbers of electrons at each level, In fact this would not be so even if their situations were equivalent, because the random nature of energy absorption and emis- sion would produce instantaneous dif- ferences such that all we could say is that they had the same average excita- tion energy.
A most interesting thing happens if two such atoms are brought near to one another: the electric fields around the two nuclei interact in such a way that each of the allowed electron energy levels of both atoms progressively “splits” into a pair of levels (orbits), whose energy difference increases as the two atoms are brought closer to- gether. At first sight. this may seem quite inexplicable: however a moment’s
thought should show that it is no more so than many other similar effects with which the reader is likely to be familiar.
Recall, for example, that when two resonant circuits tuned separately to the same frequency are coupled to- gether, they interact such that in the coupled state neither is resonant at the original frequency. but both are effectively resonant at two new adja- cent frequencies whose separation de- pends upon the degree of coupling. It is this effect’ which produces the fami- liar “double humping” associated with large coupling factors.
Another example occurs in the case of loudspeakers fitted into tuned en- closures. Here a loudspeaker cone sys- tem and an enclosure, having the same
resonant frequency when separated, 0 D3 D2 DI : | | | | | | ee | ZL | | | ae | | | | I | | | , | | | | i NEGATIVE ELECTRON ENERGY
Figure 2.1
interact when together to produce the same sort of double resonance which in this case is used to smooth the low-frequency response.
In fact, it is found that this sort of interaction effect is quite universal where oscillatory systems are con- cerned. Therefore it should not be sur- prising that it occurs between the allowed electron energy levels. of “coupled” atoms, particularly as we have seen that each energy level corre- sponds to an orbit which represents a particular mode of “oscillation” associated with the wavelike aspect of electron behavpour.
—
As one might expect, it is the highest or least negative electron energy levels of two atoms which first split as they are brought nearer, because these cor- respond to the largest allowed orbits. For the same reason it wil] be the level pairs produced by these levels which will be found most widely separated for any given distance or spacing be- tween the two atomic nuclei. This is illustrated in figure 2.1, which shows
the splitting of the various energy levels as a function of the nucleus spacing,
Note particularly that this diagram applies equally to either atom, and that in the interests of clarity only the first four levels are shown. It may be seen that for large spacing, the levels are unaltered from their “individual atom” values, but as the spacing decreases they split progressively from the higher levels. At a spacing distance D1, for example, only the N=4 level has split, while at a smaller spacing D2 both the N=3 and N=2 levels have split also but by smaller amounts. At a still smaller spacing D3, the lower of the pair of levels corresponding to the N-4 level has moved below the higher of the N=3 pair. Such “overlapping”
INTER-NUCLEUS SPACING
N w 2
occurs more and more as the spacing Is reduced.
What does this mean? Simply that When two similar atoms are placed relatively near one another, their inter- action effectively alters and increases the number of “allowed” orbits for the electrons surrounding each. Hence when the atoms whose behaviour is represented by figure 2.1 are spaced at a distance D2 apart, each has two new allowed orbits in place of each of the orbits corresponding to its previous N~ 4, N~3 and N--2 energy levels. As splitting occurs progressively from the highest levels down, this will also mean
Fundamentals of Solid State
that all of the higher levels not shown will also have split into two, so that each atom will have very many more allowed orbits than it would have had alone. (In fact the number of allowed orbits will have almost doubled, as in this example only the N=I1 level has remained unaltered at a spacing of D2.)
It so happens that, in the same way that the energy levels of two atoms split into pairs when they are brought to- gether, the energy levels of larger num- bers of relatively close atoms are found to split into a corresponding number of new levels. With three atoms, the levels each tend to split into triplets; with four atoms, into quadruplets, and sO on,
Accordingly, if we have a lump of an element comprising a large number “M” of atoms regularly spaced at a particular distance, certain of the “in- dividual” energy levels will be found to have split into the same large number of M new energy levels, forming bands. The number of levels which will have split into such bands, and the energy width of the bands, will depend upon the atomic spacing, with the higher levels splitting before the lower and to a greater extent.
An example may help in picturing this situation. A cube of metal measur- ing One centimetre on each side typi- cally consists of something like 10” atoms one-hundred-thousand-mil- lion-million-million. This means that in place of certain of the higher energy levels of an individual isolated atom of the metal concerned, each of the atoms of the metal cube will have bands each containing no less than 10° extremely closely spaced indivi- dual levels. A cube one-hundred- thousand times smaller in volume will similarly have 10% levels in each of the atomic bands—still a very large number!
In both cases the number of bands present, and their “width” in terms of energy levels, will depend as before only upon the inter-atomic spacing. In fact the number of bands and their - width is exactly the same as the number of “paired” levels and the separation widths produced for the simple case of only two atoms, illustrated in figure 2.1. Hence, although the size of a lump of material determines the number of discrete levels making up each of the energy bands, it does not affect either the number or the width of the bands.
The type of atomic interaction which we have been considering occurs almost only in the “solid” state of matter, as opposed to the “liquid” and “gaseous” states, because it is only in the solid state that the spacing between atoms is sufficiently small and relatively fixed. And as one might expect, the solid materials whose behaviour most closely conforms to this picture are those in which the atoms are arranged in very regular 3-dimensional “lattice” patterns —the crystalline solids.
The electron energy relationsnips inside a typical crystal structure are illustrated in figure 2.2, which is a two-dimensional energy/distance rep- resentation of the same type as that for a single atom given previously in figure 1.3.
It may be noted that in this ex- ample the lattice spacing or distance between the atomic nuclei is such that the N=1 and N=2 energy levels have
Fundamentals of Solid State
remained unaltered, while the N=3 and higher levels have split into the expected bands each comptising M closely spaced new levels. In fact over- lapping of the N=5 and higher bands has produced virtually a single “higher band,” extending right up to the zero energy level. Such overlapping tends to occur with the higher levels in crys- talline solids, beth because the splitting is greater for these levels, and also be- cause aS We have seen previously the energy differences between the original atomic orbit levels decrease with in- creasing distance from the nucleus.
In this example the N=3 band is shown as the valence band, which cor- responds to the valence electron energy
"EDGE OF CRYSTAL"
Ste aT ares SS = > “ ————————— on — —== = _———
—ESESEoaoa—eeeEeaoaee_uqn@oqqn®aqmM0@mq0Qqmaee ee ———————————_—_— eoragemeneor
Ry a ee zi
——————— —————oaaess=S=$=S=ESaum eee f SSS Sr rn ————— =|
nnn — ————
—————EE————E E> ——
energy levels represented in figure 2.2 by the N=I and N=2 levels.
On the other hand, electrons having higher or less negative energy can oc- cupy any of the many levels compris- ing the valence and higher bands, in which they are no longer the “prop- erty” of individual atoms but belong only to the crystal as a whole. Those whose energy places tnem within the valence band are thus “shared” equally by all the atoms of the crystal, and it is in fact these electrons which effect- ively bind the crystal together. Any electrons in the higher bands are even less restrained than these, naving at the same time less negative potential energy and more kinetic energy, and
ATOMIC "LATTICE" SPACING
DISTANCE THROUGH CRYSTAL
SINGLE “BAND” FORMED BY OVERLAPPING CF N=5 AND HIGHER BANDS
Se B N= 4 BAND
N « 3 BAND {VALENCE BAND)
UNALTERED LEVELS
rd H Ly rN»! HL af Vw V Vt ( A ® ®@ ® ®@ @ NEGATIVE eZ ELECTRON ENERGY Figure 2.2
level of the individual atoms concern- ed. Although shown here as an isolated band, not overlapped by higher bands,
_ the valence band is not necessarily so
isolated, and is in fact overlapped in certain crystals.
As a result of the interactions be- tween the atoms of the crystal lattice, only the walls of the electron energy wells (dashed lines) surrounding the nuclei at the edge of the crystal rise fully to the zero energy level, as they do with an isolated atom. For the nuclei inside the crystal, the well “walls” fuse and cancel at a somewhat lower level, as shown, The level at which they fuse is in fact very close to the valence band, and this has con- siderable importance.
It may be noted that below the fus- ion level, the original electron energy levels are unaltered, and tnat they are shown as before separately for each nucleus. Conversely above the fusion level, all levels have become bands, and are shown extending continuously throughout the lattice. The significance of these distinctions is that electrons occupying energy levels below the fusion level are influenced almost solely by the individual atomic nuclei, whereas electrons occupying the energy bands above tne fusion level are vir- tually uninfluenced by single individ- ual nuclei, and are effectively ‘“com- mon _ property.”
In other words, this means firstly that electrons having low or more negative energy can exist in the cry- stal lattice only in orbits closely sur- rounding the individual nuclei, These are the highly bound “core electrons,” and they will be those occupying or- bits corresponding to the unaltered
these can accordingly move with in- creasing freedom anywhere inside the crystal,
It is those electrons in the “com- mon property” valence and higher en- ergy bands of a crystalline solid which are responsible for its electrical be- haviour, and the part played in this re- gard by such electrons is very largely determined both by the relative posi-- tions of these bands, and by the dis- tribution of electrons in them. Hence in order to gain an insight into elec- trical conduction in a crystal, we must look closely at both the bands them- selves and the ways in which electrons can occupy tnem.,
There are a number of different ways in which atoms can link or “biid” to- gether to form crystal structures. De- pending upon the type of atomic bond involved, and the size of the atoms, a particular crystal lattice will have a definite inter-atomic spacing, and thus an appropriate number of the atomic electron energy levels will be split into bands of appropriate width. The dis- position of electrons in the allowed levels and bands will depend, as_be- fore, upon both their disposition in the ground state of an individual atom, and on the excitation energy of the atom concerned.
From this is may be appreciated that each crystal structure .formed by the various elements will tend to have a different and unique overall energy pat- tern, with different energy band widths and spacing, and each different with respect to the number of electrons occupying the various levels and bands at a given temperature.
Despite this, it happens that most crystalline solids falt into only two
9
broad categories when one considers the electron energy situation associated with the valence and higher energy bands. One of these situations applies in the case of metal crystals which are excellent electrical conductors; the other applies in the case of crystalline solids which are basically either semi- conductors or insulators. —
The first type of situation is basic- ally that in which the valence electrons of the various atoms of the crystal do not completely fill the valence band in ne ground state, as illustrated in figure
iD,
This situation can arise if the elec- trons of an individual atom of the ele-
0
(FILLED LOWER "CORE" ENERGY LEVELS NOT SHOWN)
NEGATIVE ELECTRON
ENERGY Figure 2.3
ment concerned do not fill the original valence level; it can equally be caused by a crystal lattice spacing which re- sults in overlapping of the “true” valence band by a higher order band or bands, to produce a much wider effective valence band. For our pur- poses it does not matter which factor is responsible, the essential point being that the valence band is not completely filled.
In order to understand how this situation allows the crystal concerned to act as a good electrical conductor, consider for a moment what happens when an external source of EMF is connected across the crystal. the applied EMF, an electric field is set up through the crystal; as a result one end of the lattice has an effective potential energy with respect to the other, so that the various electron energy levels and bands no longer re- main horizontal but have a slope which corresponds to the electric field gradient. This is illustrated in figure 2.4, which shows the same valence and higher energy bands which were shown in equilibrium in figure 2.3.
Electrons are always in motion, and those in the valence band of a crystal are continually “sharing themselves around” among all the atoms of the lattice. The effect of the applied elec- tric field, as one might expect, is to produce a tendency for the electrons to be accelerated in the “downhill” direction of the field, and slowed down Or decelerated in the “uphill” direc- tion.
Now deceleration of electrons by the field is in fact difficult, because this
10
Due to |
implies loss in kinetic energy, and fall- ing of the electrons concerned to lower levels; yet the lower levels are filled. However, the converse process of elec- tron acceleration is quite easy, because this involves the transfer of electrons to higher energy levels, and such levels are in this case readily available in the form of the remaining empty upper levels of the partly filled valence band.
Acceleration of electrons thus occurs readily under the influence of the field, and there is the “nett flow of charge from one end of the crystal to the other” which we define as an electric current. In moving through the crystal the electrons exchange negative poten- tial energy for kinetic energy, jumping
EMPTY HIGHER BANDS
VALENCE BAND ONLY PARTLY FILLED
energy level which is completely filled with electrons, and in this case all the levels of the valence band are so filled.
The reason why a nett electron flow cannot occur ih a completely filled energy level is that, for a nett flow to occur, there must be set up either an electron density or an electron velocity unbalance between one “end” of the level and the other. In a completely filled level a density unbalance is fairly obviously impossible: but so too is.a velocity unbalance, because by defini- tion all electrons in a given level have the same kinetic energy.
It may help in understanding this point if one imagines a filled level as something like a highway capable of carrving only a single lane of cars in each direction. and on which all the
DISTANCE THROUGH CRYSTAL
——_
a ELECTRON ACCELERATED Se CRYSTAL BY FIELD = '-
g —LLSSS SSS VALENCE BAND LOPE ew SS PROPORTIONAL TO FIELD ELECTRIC ee eee enero FIELD bs NEGATIVE ELECTRON ENERGY Figure 2.4 from level to level and effectively cars must travel at a fixed speed (cor-
moving along the crystal energy dia- gram along paths such as that shown in figure 2.4,
A solid material can thus be defined as an electrical conductor if its energy band situation in the vicinity of the valence band corresponds to that shown in figure 2.3, In other words, it is one in which the valence band is only partly filled with electrons. This is the situa- tion which applies in the case of metal- lic conductors such as copper, gold.
“silver and aluminium.
The second type of energy band situation which can occur in the vicinity of the valence band of crys- tals in the ground state is that illus- trated in figure 2.5. It may. be seen that the only essential difference be- tween this situation and that for a good conductor shown in figure 2.3 is that the valence band jis here com- pletely filled. The only energy levels of the crystal unoccupied in the ground
state are thus those in the higher bands, separated from those of the valence band by a relatively wide
“forbidden energy gap.”
It may seem surprising, but qa crys- talline solid in which this energy band situation occurs is completely unable to conduct electricity when in the ground state. This jis because a nett electron flow from one region of. the crystal to another is impossible in any
responding to the particular energy level), If the highway is “filled” with both lanes carrying cars moving “bum- per to bumper,” there is no way in which more cars can travel in one direction than in the other; in other words. there can be no “nett car flow” in either direction.
The only ways in which a nett flow could occur would be either if the lanes of the highway were not filled. so that more cars could conceivably travel in one direction than in the other (a den- sity unbalance), or if cars could travel at different speeds (a velocity un- balance), the latter implying the availa- bility of additional “energy level” lanes.
From the foregoing it may be seen that if the valence band of a crystal- line solid is completely filled, the crys- tal concerned will be an electrical insulator. ALL crystals whose energy band situation in the vicinity of the valence band corresponds to that shown in figure 2.5 in the ground state are thus strictly insulators in that (hypo- thetical) state,
Into this category fall both those materials normally known as “insula- tors” and those which have relatively recently become known as “semicon- ductors,” ay noted earlier. In fact. there is no essential difference between these
Fundamentals of Solid State
two groups of materials, only a differ- ence in the degree to which their be- haviour change, with excitation level. To clarify this point, let us now look at the effect of excitation on the basic situation shown in figure 2.5.
We have seen previously that an indi- vidual atom would only be in its ground state if it could be maintained at a temperature of absolute zero (—273 deg. C), shielded against all forms of radiant energy such as heat and light; whereas in actual fact, an atom in a practical environment is taking part in a continual process of energy absorp- tion and emission, involving the trans- fer of electrons between its various allowed energy levels. As one might expect, the same argument applies to a crystal lattice composed of a large number of such atoms.
A crystalline solid in a practical en- involving heat, energy
light and is therefore
vironment
other radiant
“FORBIDDEN ENERGY GAP"
(FILLED LOWER "CORE" ENERGY LEVELS NOT SHOWN)
NEGATIVE ELECTRON
ENERGY Figure 2.5
similarly involved in a continuous pro- cess of absorption and emission, with electrons now transferring both be- tween levels within the crystalline energy bands, and also between the bands. The latter naturally involves absorption or emission of larger energy quanta than the former, as it involves transfer across the relatively large for- bidden energy gaps between bands.
Under such conditions the “insula- tor” energy band: situation shown in figure 2.5 will change. Absorption and emission of energy by the crystal lattice will reach a dynamic balance or equili- brium at an excitation level above the ground state, in which a small propor- tion of ever-changing electrons from the valence band have been transferred to higher energy bands. This is illus- trated in figure 2.6.
The extent to which this will occur depends both upon the energy level of the environment in which the crystal finds itself, and also upon the width of the forbidden energy gap between the valence and next higher energy band. Naturally enough, the higher the tem- perature of the heat energy present in the crystal, the “bluer”’ the light inci- dent on its surface, and so on, the greater will be the tendency of valence band electrons to acquire the energy necessary for them to be transferred to higher bands; but this granted, the proportion which do actually transfer
Fundamentals of Solid State
will depend upon the energy width of the forbidden gap.
The width of the forbidden energy gap varies widely among the crystalline solids whose valence band situation is represented by figures 2.5 and 2.6. Accordingly, such materials also vary widely in the degree to which electrons are transferred from the valence to higher bands under the influence of excitation. And as we shall see shortly, this behaviour determines directly their electrical characteristics. ;
In a crystal of diamond, the binding between the constituent carbon atoms is such that the forbidden energy gap is very wide. It amounts to some 6 electron-volts (eV), where an electron- volt is a convenient unit of energy used in atomic physics and other fields;
0
eee
EMPTY HIGHER BANDS
VALENCE BAND
ELECTRONS TRANSFERRED a
rn A A SR PC PR yee ren Ei EE et sit er apie ahSseNN SRO SS |
tion shown in figure 2.5, and both types of material behave as shown in figure 2.6 with excitation. The only difference is one of degree.
Hence by raising the temperature of an “insulator” crystal, for example, one could obtain a semiconductor, while conversely by cooling a “semiconduc- tor” one produces an insulator.
From our earlier look at conduction in metallic crystals, the reader may by now have deduced that a semiconductor crystal in the excited state shown in figure 2.6 will become quite a good conductor, by virtue of the electrons which have transferred from the origin- ally full valence band into the origin- ally empty higher bands. And this is quite so, although it is only half the story.
ee 2 ne oneal |
“CONDUCTION BANDS"
FROM VALENCE BAND
FORBIDDEN ENERGY GAP
VACANCIES LEFT IN — |
VALENCE BAND FILLED
NEGATIVE ELECTRON ENERGY
one electron volt is the potential energy acquired by an electron when it is moved through an electric field for a distance corresponding to an increase of one volt.
In comparison, the forbidden energy gap of pure germanium crystal is only 0.72eV, while that of pure silicon is only a little larger at 1.lleV. It may be seen from this that in such materials the proportion of electrons which have transferred from the valence band to higher bands will be much greater, at a given degree of excitation, than for a material such as diamond.
Because under “normal” practical conditions crystals of materials like germanium and silicon have significant numbers of electrons which have trans- ferred from the valence band to higher bands, whereas crystals of materials like diamond have not, and because this results in significant differences in the normal-conditions electrical be- haviour of the two groups of materials, it has become convenient to distinguish between them. Crystals of germanium and silicon are thus known as semi- conductors, while those of materials such as diamond are known as insula- tors.
It should perhaps be stressed again that there is no distinct division be- tween the two groups of materials; as we have seen, in the ground state both have the “insulator” energy band situa-
VALENCE BAND
(LOWER "CORE" ENERGY LEVELS NOT SHOWN)
Figure 2.6
The electrons which have transferred into the higher bands, because these bands are largely empty, are certainly capable of forming a nett carrier flow through the crystal under the influence of an applied electric field. In fact because of this, the higher bands are usually called the conduction bands, as shown in figure 2.6. However, as it happens, the “vacancies” which are left by transferred electrons in the valence band are also able to contribute to conduction.
In order to understand this, consider that when an electron is_ transferred from the valence band to a conduction band, this is actually equivalent to the weakening of a valence electron bond between two adjacent nuclei of the crystal lattice. Instead of the usual two-electron “covalent” bond which each nucleus shares with each of its four adjacent nuclei, there is left in the place concerned a weakened bond having only a single electron. This is illustrated in the two-dimensional picture of figure 2.7, where’ the weakened bond is shown consisting of the single remaining electron together
‘with a hole or vacancy in place of the
missing electron.
Because of the missing valence elec- tron, the electrical charge balance of the crystal lattice is upset in the vicinity of the weakened bond. The positive charges of the relatively fixed atomic nuclei are no longer exactly balanced by the negative charges of the surrounding electron population, so that a localised nett positive charge is produced.
1]
In fact this positive charge is local- ised right in the “hole” originally oc- cupied by the missing electron, and it has a value of charge equal and op- posite to the negative charge of an electron. Neither of these facts are really surprising in view of the way in which the charge is produced.
The interesting thing is that such a hole is capable of moving through the crystal lattice, and as a moving positive charge it can thus effectively make a contribution to a current flow which is almost equal (but opposite) to that of an electron,
A hole tends to move through the crystal lattice because electrons in neighbouring valence bonds are at- tracted by its positive charge; when such an adjacent electron jumps across to “fill? the hole, it in turn Jeaves a hole in its own original bond to be filled by another electron, and so on. This “leapfrog” effect results in the ef- fective movement of the hole through the lattice. Under the influence of an applied electric field, the hole move- ment will tend to take place in the direction opposite to that taken by a conduction band electron.
It may perhaps seem from this de- scription that the concept of a hole is a redundant one, for the reason that “hole movement” in a particular dir- ection through a crystal might seem to be “really nothing more” than a series of small jumps by electrons in the opposite direction; but this is not so. The fact is that the localised posi- tive charge present in a crystal lattice at a weakened valence bond is no more and no less qa reality than the “localised negative charge” which we are pleased to call an electron. It even has an effective mass, which is ap- proximately equal to that of an elec- tron.
To use an analogy, a hole in a crystal lattice valence band is rather like an air bubble in a test-tube almost filled with water, Both might be in- terpreted merely as “vacancies” whose effective movement takes place purely by means of movement in the oppos- ite direction Of something which super- ficially seems more ‘real’? — like elec- trons, or water. Yet like the air bub- ble, a hole makes its existence appar- ent by means of its behaviour, in this case its electrical behaviour,
In a semiconductor crystal of tne type whose valence band situation is shown in figures 2.5 and 2.6, then, for every electron which is transferred to the conduction bands and accordingly becomes available as a “negative cur- rent carrier,’ there is also produced a hole which remaing in the valence band but is equally available as a “positive current carrier.”
Because of this, it is usual to say that excitation of a semiconductor crystal lattice results in the production of electron-hole carrier pairs. Similar- ly the emission of energy by tne lattice is wisualised as a process whereby a wandering electron in the conduction band “accidentally” meets a hole wan- dering in the valence band, the two permanently cancelling or “annihilat- ing’ one another and_ producing a photon of appropriate energy. The latter process is usually termed recombination.
A pure or intrinsic semiconductor material such as we have been con- sidering thus contains, in the excited state, equal numbers of conduction
12 -
effect.
band electrons and valence band holes available for electrical conduction. However, the two types of carrier do not contribute to current flow in an exactly equal, manner, because holes are in the valence band and cannot move through the material at the same rate as conduction band electrons. In whereas the electrons in the conduction band can move speedily through the lattice without having to conform to any orbit requirements, tne holes in the valence band must “weave” their way through the crystal binding orbit system, and therefore travel] at a slower rate.
This means that while the numbers of free electrons and holes present in an excited intrinsic semiconductor at any one time are equal, any nett cur-
WANDERING » ELECTRON
(NUCLEI AND CORE ELECTRONS NOT SHOWN} Figure 2.7
rent flowing through the material is carried more by the faster-moving con- duction band electrons moving from negative to positive than by the slower- moving holes moving from positive to negative,
To use the analogy of a highway introduced earlier, but in a slightly different sense, the situation is now like a two-lane highway in which both lanes’ are packed with cars travelling in Opposite directions, bumper to bum- per but in this case at different speeds (corresponding to the two different energy bands). Although any given length of highway will contain equal numbers of cars in the two lanes, there will still be a greater car “flow” in the faster lane than in the slower lane.
Because the generation of electron- hole carrier pairs depends upon the excitation level of the crysta] lattice, the number of such carriers available for conduction varies directly with the excitation level. Hence the conductivity of an intrinsic semiconductor crystal similarly varies directly with excitation. In the ground state, as we have seen, it will be zero: in more practical cir- cumstances jt will rise to a value which will depend directly upon both the temperature and the frequency/
intensity characteristics of any light incident at its surface.
At this point it is perhaps worth- while to pause briefly and note the con- trast between the current picture of semiconductor - insulator conduction, which we have been examining, and earlier ones which held that these materials were merely those wherein the valence electrons: were “harder for the electric field to pull free.” It may be seen that the latter idea was quite wrong, because jn fact such materials cannot conduct at all under the in- fluence of an electric fleld alone; they become capable of conduction only when excited, Neither this fact nor the
TABLE 2.1
Material
Resistivity, Ohm-cM
Copper Bismuth Germanium
200,000 1 x 10°
Silicon
Diamond*
*Theoretical resistivity. In fact unmeasurable.
existence of holes as additional current carriers in these materials could be ex- plained by the earlier theories.
In talking about the electrical be- haviour of a semiconductor at a par- ticular excitation level, reference is often made to the resistivity, which is simply the reciprocal of the conduc- tivity. Resistivity is usually defined as the resistance in ohms between oppo- site faces of a. cube of material mea- suring One centimetre on each side; this gives units of ohms/cM/square cM, or ohm-cM.
As the conductivity of an instrinsic semiconductor rises from zero. with excitation, this means that the resis- tivity effectively falls from a value of infinity. Table 2.1 gives the approxi- mate resistivity figures for pure silicon and germanium under “normal” condi- tions, and also gives the equivalent figures for typical metallic conductors and insulators.
The fact that the resistivity of intrin- sic semiconductors falls sharply with excitation is exploited by using them in thermistors, or temperature-depen- dent resistors which have a negative coefficient. This is in fact the main use of intrinsic semiconductors as_ such, their resistivity being rather too high and too temperature-dependent for direct use in most other semiconductor devices.
SUGGESTED FURTHER READING BURFORD, W. B., and VERNER, H. G., Semiconductor Junctions and
Devices,
1965. McGraw-Hill Book Company, New York.
MORANT, M. J., Introduction to Semiconductor Devices, 1964. George
G. Harrap and Company. London.
SCROGGIE, M. G., Fundamentals of Semiconductors, 1960. Gernsback
Library Inc., New York.
SHIVE, J. N., Physics of Solid State Electronics, 1966. Charles E. Merrill
Books Inc., Columbus, Ohio.
SMITH, R. A., Semiconductors, 1959.
Cambridge University Press.
HUOUEAYDSOUOCSEASDEQONSUDDOOGOODUOUEANUDSOOAGUOOOOADENOUOVEAUNOOUODOLNUOUDEACECUULSOUILEDIOUESULDOUDSSDOLAOEOUDLOGELOSEOOROUDEEUDEEUEOANUEALEGLUDCOLIOEOOOOUEOROSDDSUOOUSODLODEODEDUAEOCODOREGODBCAODEREOAEE
Fundamentals of Solid State
Chapter 3
THE EFFECTS OF IMPURITIES.
Doping and impurity semiconductors—donor impurities and
N-type impurity semiconductor—majority and minority car-
riers—doping concentration and its effects—acceptor im-
purities and P-type impurity semiconductor—resistivity and
excitation—Fermi level and the Fermi-Dirac distribution— compensation.
As we have seen, electrical conduc- tion cannot take place in intrinsic semiconductor materials such as pure silicon and germanium when they are in the ground state, because of the completely filled valence band. How- ever excitation of the crystal lattice results in the production of electron- hole pairs, of which the _ electrons become available as negative current carriers moving in the conduction bands, and the holes become available as positive current carriers moving in the valence band,
Increasing the excitation of the lat- tice, by raising its temperature, for example, thus causes the conductivity of such materials to - increase. Or looked at in another way, their resis- tivity falls. At room temperature their resistivity has typically fallen to a value which, while quite high com- pared with metallic conductors, is still low compared with an insulator such as diamond.
Actually semiconductors such as sill- con and germanium only exhibit this so-called intrinsic behaviour when they are extremely pure—something like 99.9999999% pure, in fact, with any other elements present in the cry- stal lattice as “impurities” kept to less than one part in 10°. Even micro- scopic amounts of certain impurities can radically alter their electrical behaviour, and in different ways.
From this may be judged the degree of precision which has been evolved by modern semiconductor technology, which is not only concerned initially with the production of extremely pure materials such as silicon and ger- manium, but also and consequently with the controlled alteration of their electrical behaviour to an _ accurate extent. The latter technique, which is known as doping, involves the addi- tion of precise microscopic quantities of selected impurities, Typical concen- trations range from a few parts in 10° to a few parts in 10’.
As we Shall see, the presence of impurities in a semiconductor results in the availability, under normal con- ditions, of many more current carriers than are available in amr intrinsic semi- conductor. As a result the resistivity
Fundamentals of Solid .State
of such an impurity semiconductor is typically considerably lower than that of an intrinsic semiconductor, while the influence of temperature and other forms of excitation is less pronounced ——again under normal conditions. As figure 3.1 shows, the resistivity is still infinite for zero excitation (the ground State), and still drops proportional to excitation at very high levels; but at moderate excitation levels there is a “plateau” not present in the charac- teristic of an intrinsic semiconductor.
Although all impurities tend to alter
RESISTIVITY (OHM-CM)
IMPURITY SEMICONDUCTOR
Figure 3.1
the broad electrical behaviour of a semiconductor in this fashion, there are in fact two different and some- what complementary mechanisms by which ‘this can occur. Each mechan- ism is. associated with a_ particular group of impurity elements, so that when used for doping the elements of thé two groups produce two different “types” of impurity semiconductor material. The differences between these two types of impurity semiconductor are vital for the operation of virtually all semiconductor devices, so that we should now examine each in turn.
_We have seen that the atoms of a silicon or germanium crystal lattice are bound together by the valence
electrons, of which both silicon and germanium atoms have four. Each atom in the lattice is bound to its four neighbouring atoms by a so-called “covalent” bond, involving one valence electron of each atom in a common “shared pair” orbit. A simplified two dimensional representation of this was given previously in figure 2.7.
When atoms of elements such as phosphorus, arsenic, antimony or bis- muth are present as impurities in such a crystal lattice, they are for the most part incorporated into the lattice structure in a simple “replacement” or substitutional manner. Four of their valence electrons are engaged in cova- lent bonds with the neighbouring “host” atoms, so that in this respect an impurity atom is quite equivalent to a host atom.
Of course an impurity atom cannot be fully equivalent to a host atom, because it will have both a different nucleus mass and positive charge, and
a ~
EXCITATION (E.G. TEMPERATURE)
a correspondingly different number of surrounding electrons, The latter is of particular importance because in the case of phosphorus, arsenic, antimony and bismuth there are in fact five val- ence electrons, one more than is pre- Sent in silicon or germanium.
Because of this, when an atom of these elements is present as an impurity in a silicon or germanium crystal lattice there is one valence electron “left over” after the atom has engaged itself in covalent bonds with its neigh- bours. This is illustrated in figure 3.2, where the “left over” fifth electron is shown occupying an orbit surrounding its parent phosphorus nucleus in a silicon lattice.
13
Although the electron is shown in an orbit surrounding its parent im- purity nucleus, it may be remembered that electrons at the valence and high energy levels in a _ pure crystalline solid tend to be the “common property” of all the nuclei in the lattice. Thus while the additional positive charge on an impurity nucleus does produce a small local “dip” in the electron energy pattern of the lattice, with a con- sequent tendency for the fifth valence electron to remain, this effect is in fact quite slight. Very little energy is re- quired in order to free the electron, so that even when the lattice is only slightly excited such electrons are virtually al] freely wandering around the crystal and available as negative current’ carriers.
Because of this effective “donation” of electrons as additional negative current carriers to the basic simicon- ductor lattice, impurity elements such
(NUCLEI AND CORE ELECTRONS NO SHOWN)
Figure 3.2
as phosphorus, arsenic, antimony and bismuth are known as donor impuri- ties. And because with such donor impurities present there is an excess of negative current carriers, in contrast with the equal numbers of positive and negative carriers present in an excited intrinsic semiconductor lattice, a crystal lattice which has been doped with a donor impurity element is termed an N-type impurity semiconductor.
The energy band diagram of such an N-type impurity semiconductor is shown in figure 3.3. It may be seen that in the ground state the fifth valence electrons of the donor impurity atoms occupy localised and relatively isolated segments of a single energy level, which is only slightly below the bottom of the lowest con- duction band. The electrons occupy a single new level rather than a multi- level band because, being relatively isolated from one another, they are not subject to coupling interaction effects.
The small gap between this ‘donor level” and the bottom of the conduc- tion band represents the small energy increment required to free the electrons from their ground-state orbits. It may be seen that only a slight excitation of the crystal lattice will cause most of the donor level electrons to be ‘transferred to the conduction band levels, so that the resistivity of the material will fall rapidly with excita- tion to a value which is many times lower than an intrinsic semiconductor under normal conditions.
14
At this point the reader may perhaps be wondering whether the electrons which transfer from the donor level to the conduction band leave holes behind. The answer .to this is no, because the donor level simply corres- ponds to the isolated “fifth valence electron” orbits shown in figure 3.2, rather than to a complete binding orbit system, and the concept of a hole has little if any meaning except with reference to a complete binding system. To extend an earlier analogy, an empty
Figure 3.3
isolated orbit is somewhat like a test- tube emptied of water, in which an “air bubble” can scarcely have any meaningful existence.
When a fifth valence electron leaves its parent donor impurity atom to wander through the crystal lattice, then, it does not leave behind a hole. But this is not to say that the parent impurity atom then becomes _indist- inguishable from any of the host atoms; this can never occur, because it may be remembered that the nucleus and core electron system of the impurity atom will be always different from that
of the neighbouring — silicon or germanium atoms. In fact, a donor impurity atom
which has lost its fifth valence electron to the lattice will have a nett positive charge. This being the case it should Strictly no longer be called an ‘‘atom,” but given the name by _ convention applied to a charged particle — an ion, It will be a positive ion; naturally, and will be fixed rather than movable because of its covalent bonding with the neighbouring host semiconductor atoms.
Under moderately excited “normal” conditions, then, N-type impurity semi- conductor material contains two types of localised electric charge whose presence can be attributed to the addi- tion of impurity atoms to the crystal lattice. On the one hand are an appreciable number of electrons mov- ing through the crystal with an energy level which places them in the conduc- tion band, and which are therefore
STD ATS, Sa eeENAAAANNAR aan eyENEEEeneeere
available as negative current carriers; while there are also an equal number of positively charged donor impurity ions which are fixed and therefore not themselves available as current carriers. We will see later on that while the fixed impurity ions cannot act as current carriers themselves,. they can despite this play an important part in controlling the behaviour of the carriers.
Although the electrons “donated” by the donor impurity atoms are the main
DISTANCE THROUGH CRYSTAL
CONDUCTION BANDS (EMPTY IN GROUND STATE)
“DONOR LEVEL” CCCUPIED BY FIFIH VALENCE ELECTRONS OF IMPURITY ATOMS, IN GROUND STATE
VALENCE BAND (FILLED IN GROUND STATE}
Th ee
NEGATIVE ELECTRON POSITICNS OF DONOR ENERGY IMPURITY NUCLE}
Current carriers in N-type impurity semiconductor material, they are not the only available current carriers. The reason for this is that there will still be electron-hole carrier pairs produced by excitation of the lattice in the same fashion as in an intrinsic semi- conductor.
As one might expect, a particular degree of excitation of an impurity crystal tends to produce as many elec- tron-hole carrier pairs aS in an intrin- sic semiconductor crystal at the same degree of excitation. However in an impurity semiconductor the effective number of such carrier pairs present at any degree of excitation is con- siderably lower than in _ intrinsic material.
In the case of the N-type impurity semiconductor material which we have been considering, the reason for the reduction is that with a considerable number of donor-derived conduction electrons already wandering through the crystal lattice at the conduction band levels, there is an increased probability that wandering holes and electrons will meet to annihilate one another by re- combination. Naturally such recom- binations “remove” equal numbers of conduction-band electrons and valence- band holes from the crystal lattice, so that the mumbers of both types of carrier effectively available in addi- tion to the donor-derived conduction- band electrons will be somewhat smaller than the numbers of carrier pairs available in intrinsic material under the same conditions.
The total population of current car- riers available in N-type impurity semiconductor material under normal conditions thus consists mainly of conduction-band electrons, with a small minority of valence band holes.
Fundamentals of Solid State
“In this material electrons can thus be termed the majority carriers, and holes the minority carriers, Both these terms Serve to emphasise the contrast with the equal-numbers-of-electrons-and- holes situafion which applies with an intrinsic semiconductor.
As one might expect, increasing the ‘number of donor-derived conduction band electrons in the material further reduces the effective additional *pro- portions of “intrinsically produced” electron-hole pairs. And not surpris- imgly, the number of donor-derived electrons is in turn directly propor- tional to the number of donor impurity atoms originally added to the lattice — the doping concentration.
Hence We can say that in N-type impurity semiconductor material, the
NUMBER OF CARRIERS
TOTAL CARRIERS AVAILABLE FOR CONDUCTION
A eS
ELECTRONS
\
HOLES
(MAJORITY CARRIERS)
(MINORITY CARRIERS}
rg Ree Mat I enh ea | ppraees — > ee
may be remembered, are pentavalent. They have five valence electrons, in Other words, one more than the four
possessed’ by intrinsic. semiconductors
such as silicon and. germanium. As one might perhaps expect, there also exists a second group of important impurity elements which are in con- trast trivalent — possessing only three valence electrons, and hence in this case one less than silicon and _ ger- manium. Elements which fall into this group include boron, indium, alumin- ium and gallium.
When atoms of one of these elements are present as impurities in a semi- conductor crystal, they are for the most part incorporated into the lattice im much the same “substitutional” manner that applies in the case of
0
4 4 DONOR IMPURITY INTRINSIC LIGHTLY HEAVILY CONCENTRATION MATERIAL DOFED (N) DOPED (N+ +)
N-TYPE MATERIAL
Fiqure 3.4
proportion of total available current carriers represented by the majority carriers — in this case electrons — is directly proportional to the doping concentration. Highly or heavily doped material can thus be considered to be “more N-type” than lightly doped material, because it: will have a higher proportion of majority-carrier electrons and a lower proportion of miunority- carrier holes.
Figure 3.4 illustrates the foregoing by showing the effective numbers of electron and hole carriers which will normally be present in a crystal sample for various doping concentrations. It may be seen that for intrinsic material with zero donor impurity, there are present equal and modest numbers of electrons and holes — the “intrinsic” electron-hole pairs. With the progres- sive addition of donor impurity the number of electrons rises rapidly while the number of holes falls, so that while the total number of carriers available for conduction rises rapidly with donor impurity concentration, it progressively becomes composed more and more of electrons or majority car- riers, and less and less of holes or minority carriers.
Having looked fairly closely at one of the two types of impurity semi- conductor material, let us now examine the second type. We may well expect to find a similar but complementary set of situations involved, and this in fact turns out to be the case.
Those impurity elements which act as electron carrier donors to an intrin- sic semiconductor crystal lattice, it
Fundamentals of Solid State
N-TYPE MATERIAL
\
NEGATIVE i os ELECTRON pete tng eC ETIOR ENERGY Figure 3.6 donor impurities. However, having
only three valence electrons, they are able to enter into the required cova- lent bonds with only three of the
neighbouring host atoms. With the re- .
maining neighbour atom they can form only a weaker “non-contributory” bond involving a singlé electron.
As the illustration in figure 3.5 shows, the weakened fourth bond is .of exactly the same type which we saw to be present in an intrinsic semicon- ductor lattice bond when an electron has teen removed by excitation. In short, the impurity atom—in this case
aluminium—effectively brings with it into the crystal lattice nothing othez -
than a positively charged valence-band hole.
Although in the common-property valence electron binding system of the © crystal lattice, the hole has a weak tendency to remain in the vicirtity of its parent impurity nucleus. This is because of the lower positive charge or “relative negativity” of the impurity nucleus compared with the neighbour- ing host nuclei. However, as with the fifth valence electron of a donor im- purity, the hole binding is very weak, and very little energy is required for the hole to effectively move away through the crystal in the manner which we previously examined.
This means that even for quite low levels of excitation, the holes intro- duced into the lattice by the impurity
(NUCLEI AND CORE ELECTRONS NOT SHOWN)
Figure 3.5
DISTANCE THROUGH CRYSTAL
CONDUCTION BANOS
SS SS | a
“ACCEPTOR LEVEL"
OCCUPIED BY ACCEPTOR HOLES IN GROUND STATE
VALENCE BAND (FILLED IN GROUND STATE)
atoms will be found wandering through the crystal and available as positive current carriers. At the same time the impurity atoms themselves, having gained a valence electron, will have become fixed negatively charged ions.
It may be seen that in contrast with the behaviour of donor impurities, the impurity atoms have in this case effec- tively “accepted” valence electrons from the crystal lattice. To distinguish this behaviour from that of donor impuri- ties, elements such as boron, indium, aluminium and gallium are known as acceptor impurity elements. And _ be-
15
cause with an acceptor impurity pre- sent a semiconductor crystal has an excess of positive current carriers under normal conditions, compared with in- trinsic material, a crystal which has been doped with an acceptor impurity is termed a P-type impurity semicon- ductor.
The energy band diagram of a P- type impurity semiconductor is shown in figure 3.6, and the reader may care to compare it with that for N-type material shown in figure 3.3. It may be seen that the holes which “belong” to the acceptor impurity atoms in the ground state again occupy localised and isolated segments of a single energy level, but that in this case the impurity level is slightly above the top of the valence band.
The small gap between the “acceptor level” and the top of the valence band represents the small energy increment required for electrons in the valence band to transfer into this level, “fill- ing” a hole but leaving behind another in the valence band itself. Only slight excitation of the lattice is therefore required for most of the acceptor level holes to be filled, leaving many holes behind in the valence band to act as positive current carriers. The resis- tivity of P-type material thus falls rapidly’ with excitation in almost exactly the same fashion as with N- type material, and like the latter it has, under normal conditions, a resistivity many times lower than intrinsic semi- conductor.
ust aS the donated electrons are not the only carriers present in N-type impurity semiconductor, so the holes derived from acceptor atoms are simi-
concentration for a P-type impurity semiconductor may be represented as in figure 3.7, which is a similar dia- gram to that of figure 3.4 for an N- type semiconductor. Here the holes are the majority carriers and the electrons are the minority carriers, but other- wise the relationships are very similar. As before the total: number of carriers available for conduction. rises rapidly with impurity concentration, and pro- gressively becomes composed more and more of the majority carriers and less and less of the minority carriers.
It may be seen from the foregoing descriptions of the two types of im- purity semiconductor that both types have available under normal conditions
OCCUPATION OF LEVELS BY ELECTRONS
AREA REPRESENTS
CONDUCTION DISTRIBUTION OF BANCS — CONDUCTICN-BAND ELECTRONS (NEGATIVE CARRIERS) Ec By ee pete en eae ee ed tee, ee ee cp AVERAGE CARRIER ENERGY OR “FERMI LEVEL" Ev ~~+—— AREA REPRESENTS DISTRIBUTION OF etc VALENCE-BAND HOLES (POSITIVE CARRIERS) (FILLED CORE LEVELS NOT SHCWN) NEGATIVE NEGATIVE ELECTRON ELECTRON ENERGY ENERGY Figure 3.8
larly not the only carriers présent in P-type material. As before there will be “intrinsic” electron-hole pairs pro- duced by the normal excitation mecha- nism, although again the effective num- bers of these carriers is lower than in intrinsic material.
The reason for the reduction is again carrier loss by recombination, due in this case to the relatively large number of holes moving through the crystal lattice at valence band level. As before this means that the numbers of both types of “intrinsic” carrier effectively fall with increasing doping concentration.
Accordingly the effects of doping
16
of excitation considerably greater num- bers of current carriers than are avail- able in intrinsic semiconductor mate- rial. The numbers are of different composition in each case, to be sure, but the total numbers are in both cases greater—by an amount proportional to
=the concentration of the appropriate
doping impurity.
With applied excitation the resisti- vity of both types of impurity semi- conductor thus tends to fall much more rapidly than with intrinsic material, and this explains the steeper initial slope of the solid curve given earlier in figure 3.1. However, increasing ex- citation rapidly results in the situation
increased
where virtually all the electron or hole carriers derived from the impurity are available for conduction; at this point the resistivity tends to flatten out.
Further increase in excitation tends to produce little if any reduction in resistivity, because the tendency for numbers of electron-hole pairs to be produced is largely balanced by a corresponding increase in_ re- combination. In fact the resistivity of the material tends to increase slightly, because with increasing activity within the crystal lattice the motion of the carriers becomes impeded by an in- creasing number of “collisions.” This reduction in carrier mobility explains
NUMBER OF CARRIERS Ad tn a” “ os TOTAL CARRIERS Ss AVAILABLE FOR CONDUCTION a“ ee 7 a “ HOLES ee (MAJCRITY CARRIERS) 7 “” ~ ELECTRONS IMINORITY CARRIERS) ee, ene 0 7 ae ——— - ac ACCEPTOR IMPURITY INTRINSIC LIGHTLY HEAVILY CONCENTRATION MATERIAL DOPED (P) DOPED (P+ +} P-TYPE MATERIAL P-TYPE MATERIAL Figure 3.7 ‘ a as: the slight upward slope of the plateau
in figure 3.1.
If the increase in excitation is con- tmued still further, a point is even- tually reached where the production of “intrinsic” electron-hole carrier pairs simply swamps the recombination mechanism. When this happens the majority-minority carrier situation
gives way to the equal numbers situa-
tion, while resistivity again begins to fall. Thus in effect both N-type and P- type impurity semiconductor materials revert back to “intrinsic” semiconduc- tor at very high excitation levels.
From the foregoing it may be seen that both the total number of carriers available in a semiconductor, and the proportions of negative and positive carriers making up that number are determined by three factors. These are the presence and concentration of any impurities present, the type of impurity and the degree of excitation.
It has been found of considerable value to describe this rather complex situation using two very useful con- cepts: that of an ‘average carrier energy level,” and that of a statistical “spread” or distribution of the carriers above and below the average level. As with some of the concepts introduced earlier, a full understanding of these concepts requires considerable back- ground in quantum mechanics and is thus beyond the present discussion. However, the basic ideas involved are not unduly difficult, and can help con- siderably in understanding practical semiconductor device operation.
As we have seen, conducgion in semiconductor materials takes place by mcvement through the crystalline lat-
Fundamentals of Solid State
tice of two types of carrier—negative carriers which consists of electrons pos- sessing an energy which places them in in the conduction band, and _ positive carriers which consists of hole posses- sing an energy which places them in the valence band. Because of this, the most useful measure of the excitation level of the material from an electrical viewpoint is one which takes both types of carrier into account, in terms of both numbers and energy distribu- tion. We may thus talk meaningfully of an “average carrier energy level” of a semiconductor crystal, representing the average of the energy levels of all the carriers available in the crystal lattice.
In the case of an intrinsic semi- conductor it may be recalled that for any degree of excitation the number of conduction band electrons and valence band holes are equal. Hence the average carrier energy level for such material will be exactly midway between the valence and conduction bands. This is illustrated in figure 3.8, where the average carrier energy level is given its more usual name of Fermi level (in honour of the physicist Enrico Fermi), and labelled Ef.
It has been found that the distri- bution of carriers in the various energy
100%
0 50%
OCCUPATION OF LEVELS BY ELECTRONS
HIGH EXCITATION
_~ GROUND STATE Ao,
LOW EXCITATION
NEGATIVE ELECTRON ENERGY
Figure 3.9
bands above and below the Fermi level can be described quite accurately by the type of curve shown. The shape of the curve corresponds to what mathematicians call the Fermi-Dirac distribution.
As may be seen from figure 3.8— which, it should be remembered, cor- responds to an intrinsic semiconductor only —— the curve represents a plot of the relative occupation by electrons of any allowed energy level, expressed as a fraction or percentage of the level] capacity. Hence the curve has a value of 100 per cent for the lower filled levels, then slopes over to a value of 0 per cent for the uppermost empty levels.
Note that the continuous nature of the curve is not intended to imply that electrons are occupying levels other than the allowed levels of the various bands. Hence the portion of the curve between level Ec, marking the bottom of the conduction band, and Ev, marking the top of the
Fundamentals of Solid State
valence band, is essentially a theoretical interpolation or “fill in.” It is arranged so that the curve is sym- metrical above and below the Fermi level Ef, with the intersection at Ef corresponding to the theoretical point of 50 per cent level occupation.
In figure 3.8 the small cross-hatched area above the level Ec represents the distribution of electrons in the con-
duction band — i.e., the number and distribution of negative carriers. Similarly the lower = small cross-
hatched area below level Ev represents the distribution of electron vacancies or holes in the valence band levels —. j.e., the number and distribution of positive carriers. Note that the two areas are equal, and equal in shape.
The shape of the Fermi-Dirac curve changes to describe the way in which the number of carriers available in the material varies with excitation. Its Shape as shown in figure 3.8 cor- responds to a moderate degree of ex- citation, where the “tails” of the curve imdicate a modest number of each type of carrier.
In figure 3.9 is shown the way in
However although this is the case,. the new and changing distributions of Carrievs are still described by the Fermi-Dirac distribution curve, pro- viding its 5O per cent point is kept in alignment with the Fermi level.
Figure 3.10 shows the Fermi level positions and carrier distributions for N-type impurity semiconductor at three degrees of excitation. The energy band structure of the matemnial is not shown, but as before Ec and Ev repre- sent the bottom of the conduction band and the top of the valence band respectively. The donor level is repre- sented by Ed.
As may be seen, in the ground state the Fermi-Dirac curve is again a step curve with the “step” at the Fermi level. But the latter is now at a some- what higher level than in the case of intrinsic material. Its position will naturally vary with the donor impurity doping concentration, to take account of the changing carrier ratio illustrated in figure 3.4; thus the position be- tween Ed and Ec shown in figure 3.10 will correspond to a quite heavily doped N-type material. With lower
the shape of the curve’ varies doping concentrations Ef will be lower GROUND STATE MODERATE EXCITATION HIGH EXCITATION 0 50% 100% 0 50% 100% . 0 50% 100% 0 OCCUPATION 0 OCCUPATICN OF LEVELS OF LEVELS BY ELECTRONS BY ELECTRONS Ec —Et Ed = Ev = HOLES HCLES NEGATIVE NEGATIVE NEGATIVE ELFCTRON ELECTRON ELECTRON ENERGY ENERGY ENERGY Fiqure 3.10
with excitation. For the ground state or zero-excitation case, it is not a curve at all, but a sudden “step;” as excitation increases the “corners” of the step round off, producing longer and longer “tails.” It may be seen that this results in larger and larger areas above Ec and below Ev, correspond- ing to the increased numbers of carriers available with increasing ex- citation.
It should be noted that both figures 3.8 and 3.9 are drawn for ‘intrinsic material, in which as we have seen the Fermi level is fixed and exactly mid- way between Ec and Ev. Naturally this same situation carmot be true with either of the two types of impurity semiconductor, because in these cases there are not only unequal numbers of negative and positive carriers, but the ratio between the two varies with excitation.
Actually it turns out that the Fermi level of each of the two types of impurity semiconductor is_ different, and also that it varies both with the type of impurity and the excitation.
down than this, although it will always be higher than the fortudden-gap-mid- point position — which as we have seen corresponds to intrinsic material.
With moderate excitation, illustrated in the centre diagram of figure 3.10, two things have happened. Probably the most obvious thing is that the carrier distribution curve has develop- ed “tails,” as before, and that because the Fermi level is higher than the for- bidden gap midpoint, the curve tails indicate the expected majority/ minority carrier unbalance. But the more subtle thing that has occurred is that the Fermi level Ef has started to fall, slightly but perceptibly, to cor- respond to the effect of “intrinsic” (balanced) carrier generation.
The third diagram of figure 3.10 shows what happens at a very high degree of excitation. The Ferm:-Dirac curve has spread well out, as before, while at the same time the Fermi level itself has fallen almost to the forbidden gap midpojnt. Hence while there are large numbers of carriers, it can be seen that they are mow made up of
17
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18
almost equal numbers of electrons and holes —- showing that the material has almost completely reverted to an effective “intrinsic” semiconductor.
__In figure 3.11 are shown equivalent diagrams for a P-type impurity semi- conductor, and it may be seen that the situation is here very similar. The only difference is that the Fermi level in this caSe occupies in the ground State a position somewhat lower than the forbidden gap midpoint, and moves up with excitation. As _ before its ground-state position is determined by the doping concentration; the position shown between the acceptor level Ea
and the top of the valence band Ev
corresponds to a quite heavily doped P-type material.
GROUND STATE
0 50% 100% 0 50% OCCUPATION 0
OF LEVELS BY ELECTRONS
Thus far, in considering impurity semiconductor materials we have assumed that only one type of impurity is present. Although modern semi- conductor technology can approxi- mate this situation, this is all that can be done. In practice, a number of dif- ferent impurity elements are almost always present, in electrically signifi- cant amounts. The reader may there- fore well wonder what effect such “spurious” impurities have on_ the concepts which we have looked at in the foregoing.
The answer to this is that there occurs an effect called compensation Whereby opposite types of impurity element tend to “cancel out” one
MODERATE EXCITATION
ELECTRONS
another when they are present in small quantities. Due to the compensation effect, the effective type and impurity concentration of a practical semi- conductor material is really the resul- tant or net effect of whatever types of impurity are present in the lattice.
Hence in practice an N-type im- purity semiconductor is one in which a donor impurity is present in greater proportion than any other impurities, and a “heavily doped” N-type mater- ial is one in which this dominance is even greater, Similarly P-type mater- ial is material in which an acceptor impurity is dominant, again to a degree which determines the effective doping concentration.
HIGH EXCITATION
100% 0 50% 100%
OCCUPATION OF LEVELS BY ELECTRONS
OCCUPATION 0 CF LEVELS BY ELECTRONS
NEGATIVE ELECTRON ENERGY
NEGATIVE NEGATIVE ELECTRON ELECTRON ENERGY ENERGY Fiqure 3.11
The same argument applies in the CaSe of “intrinsic” semiconductor mate- rial. If a material has equal and minute amounts of opposite types of impurity, mutual compensation can- cels out their effect so that in practice the behaviour of the material is indis- tinguishable from a_ perfect intrinsic semiconductor. The success of modern semiconductor technology in producing “pure” samples of intrinsic semicon- ductors such as silicon and germanium is therefore not due solely to reduction of impurity levels, but also to the development of ways of ensuring that the inevitable residuals of impurities compensate one another to a _ highly accurate degree.
DUODOOUADUGUAUADUUCQUDOUERUAUUUCUOCODUNUDEOUDYUOUUSUSOCOTTCUCUCCOUCCDORDCUEOUPOQISV TUCO CC CO CCC CEE EEE ee
SUGGESTED FURTHER READING BURFORD, W. B., and VERNER, H. G., Semiconductor Junctions and Devices, 1965. McGraw-Hill Book Company, New York.
MORANT, M. J., Introduction to Semiconductor Devices, 1964. George G. Harrap and Company, London. |
SCROGGIE, M. G., Fundamentals of Semiconductors, 1960. Gernsback
Library, Inc., New York.
SHIVE, J.-N., Physics of Solid State Electronics, 1966. Charles E. Merrill
Books, Inc., Columbus, Ohio.
SMITH, R. A., Semiconductors, 1950. Cambridge University Press.
Me LOOP LEP CUPP OP LOOSE OL CLOGS POPPOTPePRPTPOTOS TPO IIL RIITITH ttt Thiel crlirtii Ti iitlirtiiitiiririiiHiiliriti rier iii
Fundamentals of Solid State
Chapter 4
THE P-N JUNCTION
Non-homogeneous
semiconductors—carrier
diffusion—
“inbuilt” electric fields—drift currents—equilibrium and the Fermi level—the P-N junction—equilibrium, forward
and reverse bias
conditions—depletion
layer width—
junction ‘‘breakdown’’— the semiconductor diode.
In our examination of semicon- ductor materials in the foregoing chap- ters, we have, for simplicity, looked only at the properties and behaviour of what might be called “homogeneous” samples—lumps of crystalline material in which the composition is uniform throughout. Thus we have considered, separately, uniform lumps of intrinsic semiconductor and of both N-type and P-type impurity semiconductor. In each case, by considering only a simple homogeneous sample of the material concerned, we have been able to isolate and examine its “basic” pro- perties. |
As the reader might suspect, how- ever, such homogeneous samples of semiconductor materials are in fact mainly of academic interest. A large majority of practical solid-state devices depend for their operation upon fur- ther interesting properties and aspects of behaviour which arise in the more complex type of situation wherein the semiconductor crystal concerned is not homogeneous, but effectively composed of regions of different types of semi- conductor material.
In order that the reader might gain a clear understanding of the operation of practical solid-state devices, it is therefore necessary that the basic con- cepts of semiconductor properties and behaviour developed earlier are ex- panded to cover the additional pro- perties and behaviour of non-homo- geneous samples.
With this aim in view, the present chapter will introduce and _ discuss some of the further basic concepts which apply to non-homogeneous semi- conductor samples in general, and will then deal at some length with the extremely important “special case” of the P-N junction. Later chapters will show and explain how such P-N junc- tions, singly or in combination, and in one or another of a variety of _ physical forms and configurations, form the basis for almost every type of practical solid-state device.
To begin, then. Probably the most basic situation involving a non-homo- geneous semiconductor sample, from the theoretical point of view, is a lump of impurity semiconductor crys- tal in which the impurity doping has not been made uniformly, but rather in a gradually increasing manner from
Fundamentals of Solid State
one end of the specimen to the other. This situation is represented in sim- plified form in the upper diagram of figure 4.1, which shows a crystal of N-type material, whose donor impurity cencentration has been arranged to in- crease from a low value at one end to a considerably higher value at the other.
We have seen in the preceding chap- ter that each donor impurity atom in a semiconductor crystal lattice effect-
0 N-TYPE ee0 (LIGHTLY Go DOPED)
0° @°0 @eo0 eoe 0 @-@ © = HOST NUCLEI ® Nd DONOR "CONCENTRATION IMPURITY GRADIENT Sa CONCENTRATION
td
in a heavily doped region there will
tend to be a considerably larger num- ber of both.
Hence the donor impurity ‘concen- tration gradient” of the sample in figure 4.1 tends to result in identical gradients for both donor-derived elec- tron carriers and fixed positive ions. This is shown in the lower diagram of the figure. —
As a result of the impurity concen- tration gradient, one might therefore expect to find in such a sample, when it is excited, a gradual increase in the number of fixed positive ions from
' one end to the other, matched by an
exactly equal gradual increase in the number of negatively charged donor- derived electron charges. The charges of the two types of particie would therefore cancel in -every part of the crystal sample, and, as the only other
(HEAVILY DOPED)
= DONOR NUCLEI
‘ANd*
CONCENTRATION OF FIXED POSITIVE IONS, ALSO OF DONOR-DERIVED ELECTRON CARRIERS PRIOR TO DIFFUSION
DISTANCE THROUGH CRYSTAI.
Figure 4.1
ively “splits,” with excitation, into two parts—each of which plays a different part in determining the electrical be- haviour of the crystal. The fifth or “excess” valence electron constitutes one part, leaving to wander through the lattice as a potential current car- rier; the remainder of the donor atom is naturally fixed in the lattice, but having lost one of its original com- plement of electrons, it becomes a fixed positively charged ion.
Just as the donor impurity concen- tration therefore quite naturally deter- mines the number of donor-derived electron carriers and fixed positive ions in an excited homogeneous sample of N-type semiconductor, it similarly also tends to determine the number of these particles present at any point in an excited non-homogeneous sample. Thus, in a lightly doped region of such a sample, there will tend to be relatively few donor-derived electron carriers and fixed positive ions, while
effective charges present would be “in- trinsic” electron-hole carrier: pairs, the sample would be electrically neutral thoughout its length.
If the distribution of donor-derived electron carriers in such a sample was determined only by the impurity con- centration, as it is for a uniformly excited homogeneous sample, this satis- fying picture would indeed represent the situation. However, the impurity ° concentration is not the only factor which applies for non-homogeneous material, so that in actual fact the situation is a litthe more complex.
It may be remembered that in an excited semiconductor crystal lattice, electron and hole carriers do not re- main fixed, but move around “at random” as a result of acquired excita- tion energy. In so doing, they act in a very similar fashion to gas molecules in a container at room temperature. And it happens that, just as this type of motion tends to result: in the uniform
19
diffusion or “spreading out” of gas molecules throughout a container, a similar diffusion of both electron and hole carriers tends to occur in any excited semiconductor sample.
This diffusion effect occurs in all excited crystalline lattices, although in the case of a homogeneous semicon- ductor it cannot be detected if the material is uniformly excited. The reason for this is that in such a case the excitation itself produces both carriers and fixed ions which are uniformly distributed throughout the sample, The effect of diffusion can be made apparent in a homogeneous semi- conductor only if the excitation js applied in a non-uniform manner.
For example: if one end of a_ bar of uniformly heavily doped P-type impurity semiconductor is heated, while the remainder of the bar is kept at a low temperature, it will be found that the heated end acquires a_ negative electric charge with respect to the rest of the bar. This occurs because, while the localised excitation at the heated end produces equal numbers of positive hole carriers and_ fixed negative acceptor impurity ions, the positive hole carriers tend to diffuse throughout the bar while the acceptor ions remain fixed at the heated end. The heated region thus acquires a net negative charge due to excess ions, while the remainder acquires a positive charge due to excess holes.
In an excited semiconductor lattice, then, both electron and hole carriers tend to diffuse themselves throughout a sample. Hence if, for one reason or another, a-localised concentration of carriers tends to be produced in some part of a sample, there will accordingly be a tendency for such a concentration to diffuse away. This will occur irres- pective of whether the localised carrier concentration is due to localised excita- tion, as in the case of our heated bar example, or due to a localised impurity concentration as in the non-homo- geneous sample of figure 4.1, or due to any other possible cause.
Further, and most importantly, the tendency for a concentration of carriers to diffuse away and spread evenly through a sample is in itself quite in- dependent of any electric field or fields which may be acting through the material, being dependent only upon the*excitation leve] and the degree of carrier concentration. The presence of electric fields can only influence diffus- ion indirectly, by modifying energy levels in the material in a way which determines the energy necessary for carriers to participate in diffusion in any particular direction.
Because electron and hole carriers are electrically charged, their motion through the crystal lattice constitutes a current regardless of its cause, Hence the motion of carriers due to _ the diffusion effect may be quite accurately described as diffusion currents.
In a uniformly excited homogeneous semiconductor sample, there will fairly obviously be no net diffusion current as all carrier movements will on the average cancel. However, in the previ- ous example of a P-type rod heated at one end there is, in contrast, a net diffusion current of holes from thé heated end.
From the foregoing, it may be expected that in our graded-doped specimen of figure 4.1 any tendency for a concentration of electron carriers
20
to be produced at the heavily doped end as a result of the larger numbers of donor impurities will be opposed by an electron diffusion current toward the lightly doped end. And this is, in fact, exactly what happens.
However, as in the case of the heated bar, the effect of the diffusion current is to upset the electrical neu- trality of the specimen. In this case, the diffusion of electrons away from the heavily doped end leaves an excess of positively charged donor ions, while at the same time producing an excess of negatively charged electron carriers at the lightly doped end. The heavily doped end of the specimen thus tecomes positively charged, while the lightly doped end becomes negatively charged. A potential difference is thus set up between the ends of the speci- men and an electric field appears.
It should perhaps be noted that the potential difference set up in the speci- men has exactly the oppodsite polarity of that which one might intuitively predict from the fact that the heavily
LIGHTLY DOPED END
nificant, it always remains quite small relative to the acceleration due _ to excitation energy. It is because of this that the motion of carriers through a crystal lattice due to an electric field is usually described as a drift current,
From the foregoing, it may be seen that when the specimen of figure 4.1 is excited, the electron carriers present in the material are subjected to two cpposing tendencies. Firstly, there is the tendency to diffuse uniformly throughout the specimen, which in this case means to diffuse away from the heavily doped end. And, secondly, there is the opposing tendency to drift back in the direction of the heavily doped end as a result of the charge unbalance and electric field set up by the diffusion.
What does this mean? Simply that the specimen Will reach an equilibrium, in Which an electron diffusion current from the heavily doped end to the lightly doped end is balanced by an equal electron drift current in the oppo- site direction. And as part of this
HEAVILY DOPED END DISTANCE THROUGH CRYSTAL
4
: ———— fee —-———
NEGATIVE
ELECTRON
ENERGY Figure 4.2 doped end has been given a _ larger
proportion of electron DONOR _ im- purity. Surprisingly, perhaps, it is this end which acquires the positive charge!
In an example of graded doping such as that of figure 4.1, therefore, the combined effect of the impurity concentration gradient and the carrier diffusion current is to set up in the material an “inbuilt” electric field, act- ing in the same direction as the con- centration gradient.
We have seen in an earlier chapter that the effect of an electric field act- ing through a semiconductor lattice is to cause any available current carriers to be accelerated in the appro- priate direction, Naturally, this will! be the effect of the “inbuilt” field set up 10 OUr specimen.
Hence, there will be a tendency for the very electrons which diffused away from the heavily doped end of the material, setting up the electric field, to drift back again under its influence.
‘Note that the term “drift” has been used here to describe the effect of the electric field on the carriers, suggest- ing a relatively modest influence. This is quite intentional, because, in fact, although the acceleration produced by practical electric fields acting through semiconductor crystals at normal levels of excitation may be quite sig-
tween the ends of the
SLOPE REPRESENTS | ELECTRIC OR DRIFT FIELD
equilibrium there will be a_ potentiai difference between the ends of the material and, accordingly, an electric field through it.
In saying that the specimen reaches equilibrium, it is not implied that when this occurs all current in the specimen ceases. This cannot occur, for the simple reason that the very conditions which would result in cessation of the diffusion current are those which would result in maximum drift current, and vice-versa. For zero diffusion current the carrier concentration would have to be constant throughout, giving a maximum charge unbaiance and hence maximum drift current: conversely, for zero drift current the carrier-fixed ion charges would have to be balanced throughout, giving a maximum carrier concentration gradient and_ therefore maximum diffusion current.
By its very nature, then. the equili- brium must be and is a dynamic one. Both the diffusion and drift currents centinue to flow indefinitely in the specimen, although as their magnitudes are equal and their directions opposite, they have no measurable net resultant. Their continued presence in the speci- men can only be inferred by the mea- surable potential difference set up be- specimen as part of the equilibrium process. The
Fundamentais of Solid State
magnitude of the potential difference wilf naturally depend upon the semi-
conductor involved and = the doping ‘gradient present; for P-type or N-type silicon it could amount to as much as 500 millivolts.
Perhaps it should be noted in pass- ing that while the potential difference generated “inside” such a semiconduc- tor specimen is measurable, it can only be measured using extremely sen- sitive equipment such as an electro- meter. The reason for this is that the equilibrium mechanism involved can- not supply significant power to any “external” circuitry without itself be- ing disturbed.
The example of figure 4.1 illustrates what has been found to be a most im- portant general principle, one which applies to all cases involving non- homogeneous’ semiconductors. This is that wherever there exists a gradient of doping concentration, an inbuilt electric or “drift” field is set up along that gradient.
Further important aspects of the principle may be appreciated by refer- ring to the energy band picture for such a non-homogeneous semiconduc- tor. The relevant part of the energy band diagram for the graded-doped specimen of figure 4.1 is shown in figure 4.2, and it may be seen to reveal a number of interesting points.
Perhaps the most obvious point is that the energy bands are tilted, in exactly the same way which We saw in an earlier chapter to apply when an electric field is set up through a semiconductor specimen by the appli- cation of an external potential! differ- ence. And, as in such a case, the slope of the tilting is directly propor- tional to the intensity of the field and the effective potential difference between the ends of the specimen.
What may not be quite so obvious is that here the slope of the bands is precisely such that the average car- rier energy level—the Fermi level— remains constant throughout the material, despite the large number of conduction band electrons at the heavily doped end. This may be seen from the fact that the line Ef, rep- resenting the Fermi level, has ‘zero slope.
Although this may seem somewhat
fortuitous, it is really nothing more than the natural outcome of the dynamic equilibrium which we have just seen to be set up in the material due to a balancing of the opposing effects of diffusion and drift. As we have noted, the equilibrium occurs when diffusion current of electron carriers in one direction is balanced by an exactly equal and opposite drift current in the other direction; this 1m- plies that there is then no net carrier flow in either direction, and conse- quently that the average carrier energy is constant throughout.
It is found that all non-homogeneous semiconductors, in equilibrium, con- form to this pattern. In other words, the electric or drift fields which are set up inside such materials as a result of impurity concentration gradients are always such that the Fermi level—the average carrier energy level—remains constant throughout the material.
Looked at conversely, this fact pro- vides a most important general prin- ciple, and one which we will find most useful in understanding the operation of the various solid-state devices which
Fundamentals of Solid State
P-TYPE
N (LIGHTLY DOPE NS
ACCEPTOR CONCENTRATION
DONOR CONCENTRATION
SPACE CHARGE
as | NEGATIVE CHARGE DUE TO "UNCOVERED" ACCEPTOR IONS
CARRIER CONCENTRATION
REGION + | ,
ELECTROSTATIC POTENTIAL
ELECTRIC ("DRIFT") FIELD STRENGTH
Figure 4.3
we will meet in later chapters. This is simply that, for all semiconductors— whether homogeneous or non-homo- geneous—we can describe a specimen of material as being in electrical equili- brium if, and only if, the Fermi level is constant throughout the specimen. In actual fact this principle is quite
_ fundamental and applies not just to
semiconductors, but to all materials.
Before leaving this general discussion concerning non-homogeneous semi- conductors, we should perhaps note that a very usefu] conclusion may be drawn regarding the intensity of the electric drift fields set up in such materials as a result of impurity con- centration gradients. This is simply that, because a high concentration gradient will tend to produce a corres- pondingly high diffusion current, it will naturally also tend to result in the set- ting up of an appropriately strong internal drift field, in order to produce the high reverse drift current necessary for equilibrium.
In other words, the intensity of any electric fields set up in non-homo- geneous semiconductors, in equilibrium, is directly. proportional to the impurity concentration gradients with which they are associated. Thus high gradi- ents, produced by _ relatively large changes in doping concentration over short distances through the material, set up quite high. electric field inten-— sities. Conversely low gradients, pro- duced by either smal] changes in doping level, or changes spread over relatively
ON
N-TYPE
y
t
JUNCTION
(b)
POSITIVE CHARGE DUE TO “UNCOVERED” DONOR IONS
TOTAL POSITIVE CHARGE EQUAL TO TOTAL NEGATIVE CHARGE
ELECTRONS (MAJORITY)
(d) (MINORITY)
TOTAL DRIFT
POTENTIAL (e)
(f)
long distances, or both, set up relatively low field intensities, We wil] find in later chapters that this fact has many implications for solid state device design and operation.
For the present, however, let us turn to consider what is probably the most important basic “special case” of a non- homogeneous semiconductor, know- ledge of which is virtually essential for an understanding of the operation of almost any solid state device. This is the P-N junction.
In its most basic form a P-N junct- ion, as the name suggests, is a place in an impurity semiconductor crystal at which there is a relatively abrupt trans- ition between qa uniform P-type region and a_ similarly uniform (but not necessarily equa] in resistivity) N-type region. Such a situation is illustrated in figure 4.3(a), which shows a junction between a lightly doped P-type region and a relatively heavily doped N-type region.
There are quite a variety of methods by which this type of situation may be produced in a semiconductor crystal, and a number of the appropriate tech- niques will be described in a_ later chapter. However, for our present pur- poses the method used to produce such a junction is not important. The essen- tial requirement is that we have a crystal specimen in whch one region has been uniformly doped with an acceptor impurity to produce P-type material, while closely adjacent to this: region is another which has_ been
21
uniformly doped with a donor impurity to produce N-type material.
Although both regions of the speci- men of figure 4.3(a) are uniformly doped, they are of opposite “type,” so that the specimen is therefore not homogeneous. This much the reader may have deduced already; however, a fact which may be less obvious is that the specimen also has a steep impurity concentration gradient, despite the uniform doping on either side of the junction. —
The fact is that the concentration gradient occurs right at the junction itself, because here the impurity con- centration changes rapidly and effect- ively “reverses polarity” over a very short distance. This is shown clearly by the impurity concentration curve of figure 4.3(b),
From the foregoing ‘discussion of impurity concentration gradients and their effects, one might predict that the steep concentration gradient rep- resented by a P-N junction would re- sult in a high carrier diffusion current, and consequently an equally high re- verse drift current and an associated high-intensity electric field. And _ this is, in fact, exactly what happens.
Because of. the large number of conduction band electrons in_ the N-type materia] relative to the num- ber of such carriers in the P-type material, there will tend to be a dif- fusion current of electrons across the junction in the N-P direction. Simi- larly, because of the greater number of valence band holes in the P-type material relative to the N-type material, there will tend to be a hole diffusion current across the junction in the P-N direction.
As before, the effect of these dif- fusion currents is to upset the electrical neutrality of the specimen. The elec- tron diffusion current in the N-P direc- tion leaves an excess of positively charged donor ions in the N-type material, while also tending to create an excess of conduction band elec- trons in the P-type material. Con- versely, the hole diffusion current in the P-N direction leaves an excess of negatively charged acceptor ions in the P-type material, while also tending to ereate an excess of valence band holes in the N-type material.
The P-type material thus tends to gain an excess of both conduction band electrons and fixed acceptor ions, both of which are negatively charged, while
at the same time the N-type material
tends to gain ‘an excess of both val- ence band holes and fixed donor ions —both of which are positively charged. A potential difference is thus set up between the two types of material, with the P-type material negatively charged with respect to the N-type, and hence an intense inbuilt electric “drift” field is set up across the junction. From the fact that the only im- purity concentration gradient present in such a semiconductor sample is confined to the narrow junction region itself, it: might be expected that the drift field set up would similarly be confined to this region. However, this is not the case: in fact, the field “spreads” slightly to either side of the actual junction region, to an _ extent depending upon the doping concentra- tion of the materia] concerned, What happens is that, in diffusing across the junction. both holes and electrons effectively leave regions in
22
which they are the majority carriers, to enter regions in which they are minority carriers. There is thus a very high incidence of carrier recom- bination on either side of the junction —so high, in fact, that few, if any, free carriers of either type are found near the Junction on either side.
As a result of this effective deple- tion of carriers from the regions im- mediately adjacent to the junction, there are no electric charges available in these regions to compensate for the fixed charges of ionised impurity atoms. Hence a negative space charge is set up in the region on the P-type side, due to ionised acceptor atoms, while conversely a positive space charge is set up im the region on the N-type side due to ionised donor atoms. It is these space charges which are, in fact, responsible for the drift field set up across the junction.
The total] charge unbalance produced by the two space charge regions js just sufficient to produce a drift field such that carrier -drift back across the junction balances the diffusion currents. And because the space charge regions are effectively only the result of re- distribution of charge within the semi- conductor specimen, and not the result of a gain or loss of charge by the specimen as a whole. the net charges
~ regions
charge region in the lightly doped P-type material is seen to have extend- ed further than the positive region in the heavily doped N-type material, in order to “uncover” an equal number of 1onised impurity atoms.
The curves of figure 4.3(d) show the carrier concentrations which coires- pond to this type of situation. It may be seen that the two space charge together constitute a region, extending from either side of the junctton, which is nearly exhausted of carriers and thus virtually “intrinsic” comiconductor. From this it should not be surprising to learn that it is usual to call this region the depletion layer.
In figure 4.3(e) is shown the curve of electrostatic potentia] for the P-N junction of figure 4.3(a), illustrating that the potential difference which appears in the specimen as part of the equilibrium is set up entirely within the depletion layer region. In other words, under equilibrium conditzons there is virtually no change in electro- static potential] throughout the re- mainder of the specimen. Hence, as shown in figure 4.3(f), the electric drift ficld is confined to the depletion layer region, and reaches its maximum jnten- sity at the junction proper.
Further insight into the P-N junction in equilibrium may be provided by the
JUNCTION
P-TYPE (HEAVILY DOPED) \t
ra a, ae 4 404 7%
’ s . § ¢ 4 A
4 os <Jvv v7 + cory ,
a ae
i N-TYPE 7 {LIGHTLY DOPED)
va
—»| DEPLETION | LAYER ELECTRON DRIFT CURRENT ee Narre es Eo ae Be S | | \ | t= ELECTRON DIFFUSION CURRENT
Ec We eee
Figure 4.4
contained in the two regions must be equal and opposite.
Because of this, each region § is found to extend into the material con- cerned to a distance just sufficient to “uncover” ionised impurity atoms equal to half the necessary total charge un- balance. If the P-type and N-type materials have equivalent doping con- centrations, this will mean that the space charge regions will extend equally on either side of the junction, to a distance inversely proportional to the value of the doping concentration. A high doping level wil] thus result in narrow space charge regions, and a low doping level in relatively wider regions for the same degree of excitation.
If the doping concentrations of the P-type and N-type materials are dis- similar, .as in the example of figure 4.3(a), the space charge regions will naturally extend by differing amounts. This is illustrated by the curve of figure 4.3(c), where the negative space
SS \ N\
~t—————_ HOLE DRIFT CURRENT
energy level diagram of figure 4.4. Here the particular junction represent- ed for the purpose of illustration again has an asymmetric doping concentra- tion profile, but the ratio has been reversed from that of the specimen of figure 4.3, In other words the junction is here visualised as between heavily doped P-type materia] and_ lightly doped N-type material.
As may be seen, the equilibrium set up between diffusion and drift currents cf both conduction band electrons and valence band holes has set up in the specimen the expected potential differ- ence between the P-type and N-type materials, with a value just sufficient to make the Fermi level Ef constant throughout the specimen. The electric field associated with this potential difference is confined to the deplet’on layer region, as expected, this being Shown by the fact that the energy levels slope appreciably only in this region,
Fundamentals of Solid State
At this stage it is hoped that the reader has gained a reasonably clear and satisfying picture of the P-N junction “in equilibrium” — which is, naturally enough, the situation which applies when such a_ semiconductor specimen is “left to itself’ and not dis- turbed by the application of external electric fields.
Understandably this situation, while basic for an understanding of P-N junction operation, is of little direct interest where solid state device is concerned. Hence we should now turn to consider what happens when the junction is disturbed by external, po- tential differences. However, before doing so it may be worthwhile to con- clude the foregoing section with a brief summary which draws attention to the important points.
As we have seen, the steep doping concentration gradient present at a P- N junction results in carrier diffusion currents across the junction, with majority carriers from either side diffusing across to the other side and becoming minority carriers. A high incidence of carrier recom- bination thus tends to occur in the vicinity of the junction, which leaves a region of low overall carrier concen- tration and resultant “uncovered” im- purity ions extending from the junc-
tion on either side. This region is the depletion layer, and corresponds to a layer of effectively “intrinsic”
semiconductor material.
The “uncovered” impurity ions in the depletion layer result in a charge unbalance, and an electric “drift” field is set up across the junction. This re- sults in drift currents of carriers across the junction in the reverse directions to the diffusion currents, and an equili- brium is set up when the two types of currents balance.
The higher the doping concentra- tions of the materials from which the junction is formed, the greater tends to be the concentration gradient at the junction, and the larger the dif- fusion currents. However the densi- ties of impunity ions in the materials are directly proportional to the doping concentrations, with the result that the overall width of the depletion layer actually decreases with increasing dop- ing concentration. Thus a junction be- tween heavily doped materials tends to be relatively narrow, while a junction between lightly doped materials tends to be wide. The same factors result in unequal depletion layer widths on either side of a junction formed be- tween materials of differing doping concentration, as we have seen.
It may be noted that the diffusion currents are effectively composed of majority carriers, because the carriers concerned are drawn from the majority catrier populations on each side of the junction, In contrast with this, the re- verse drift currents are effectively com- posed of minoritv carriers, being drawn from the minority carrier populations of each material.
Let us now turn to consider what happens when a P-N junction ts disturb- ed bv the application of external potential differences. We shall find that its behaviour will depend quite markedly upon the polarity of the applied potential difference.
In figure 4.5 is shown the effect of connecting to a P-N junction specimen an external “bias” voltage, supplied by
Fundamentals of Solid State
a battery whose positive pole is con- nected to the P-type material, and whose negative pole is connected to the N-type material. This situation is normally called forward bias.
We have seen earlier that the effect of a potential difference applied to a semiconductor specimen is to set up an electric field along its length, and effectively raise the energy levels of the end of the specimen connected to the positive polarity relative to those of the end connected to the negative polarity. And this is what happens here, although the. situation is com- plicated by the fact that the effective
doping concentration — and hence the electrical resistivity — varies along the specimen.
Whether or not the P-type and N-type materials at either end of the specimen have differing resistivity will depend upon their doping concentra- tions, of course, and this will vary from specimen to specimen. However,
BATTERY
P-TYPE (HEAVILY DOPED)
semiconductor
tion to the “inbuilt” field set up in equilibrium.
It may be seen that the polarity o7 this new field is opposite to that of the inbuilt field; that is, the two fields oppose. The effect of the forward bias is therefore to reduce the strength of the inbuilt field acting across the de- pletion layer, by partial cancellation. And, as shown by the electrostatic potential curve of figure 4.5(b), this has the result of effectively reducing the “potential barrier” opposing major- ity carrier diffusion across the junction. The majority carrier diffusion currents are therefore allowed to increase beyond their equilibrium values.
The minority carrier reverse drift currents in opposition to the diffusion currents cannot increase proportionally to maintain a balance, because they in contrast are almost completely limit- ed by the numbers of minority carriers generated in the bulk of the material by the familiar “intrinsic” excitation mechanism. In short, the drift currents
AMMETER
N-TYPE : : (LIGHTLY DOPED) //J (a)
| DEPLETION LAYER
{NARROWED)
ELECTROSTATIC POTENTIAL
|
ELECTRON DRIFT CURRENT (UNALTERED)
| UD eta et es ___ (EQUILIBRIUM} FORWARD BIAS
t+ (b|
REDUCED POTENTIAL BARRIER
Vi ELECTRON DIFFUSION CURRENT . (INCREASED)
——— Cotes semen ete
SS Ne
a ~ (c)
| 9 l
0 02 92 { | ——O = RR ; 2 NWS 0 é ¥
ASS
Ch X HOLE DIFFUSION CURRENT S— 7 (INCREASED) SS oO
&m——————— HOLE DRIFT CURRENT
Fiqure 4.5
regardless of the doping concentrations of these regions, the effective doping concentration of the depletion layer region is, aS we have seen from the equilibrium case, very low. In effect, it behaves as “intrinsic” material, and has a relatively high resistivity. Because of the high resistivity of the depletion layer region relative to the end regions, a major proportion of the applied potential difference is
applied across the former, Hence the
main effect of the applied forward bias 's to tend to set up across the depletion layer a second electric field, in addi-
(UNALTERED}
are “saturated,” and virtually indepen- dent of the actual value of the poten- tial difference across the depletion layer. (For this reason they are often called the saturation currents of the junction.)
When forward bias is applied to a P-N junction, then, the majonity dift fusion currents increase beyond their equilibrium values while their oppos- ing minority drsft currents remain sub- stantially unaltered. A net current flow therefore takes place across the junction, with conduction band _ elec- trons moving from the N-type material
23
to the P-type, and valence band holes moving from the P-type material to the N-type. As the applied forward bias voltage is increased, the predo- minance of majority diffusion currents increases rapidly as the “inbuilt” po- tential barrier of the junction is pro- gressively eliminated.
The current passed by a forward biased P-N junction thus increases quite rapidly with applied voltage, its resistivity falling rapidly to a very low value. This is illustrated by the right- hand half of the diagram shown in figure 4.7. a
The energy level diagram for such a forward biased junction is shown in figure 4.5(c). Note that the Fermi level Ef is not constant throughout the material, an immediate sign that equili- brium conditions have been upset. The relatively steep slope of Ef in the de- pletion layer region indicates the degree to which the “inbuilt” field has been attenuated, while the correspond- ing slope in the energy bands them- selves indicates the extent to which this field remains.
_ The composition of the current pass- ing across a forward biased junction
will naturally depend upon the im- purity doping concentrations of the P-type and N-type materials. If the
doping concentrations are equal, the current will be composed of equal numbers of conduction band electrons and valence band holes; however, if one material has a higher doping concen- tration than the other, the correspond- ing majority carriers will predominate.
Hence the forward biased junction current of a heavy-P/light-N junction such as that of figure 4.4 will consist mainly of holes, while that of a light- P/heavy-N junction such as __ that shown in. figure 4.3 will consist mainly of electrons. But it should be remem- bered that conduction band electrons have a greater mobility than valence band holes, and this fact will also influence the exact ratio of currents flowing across the junction.
In should perhaps be noted, in con- nection with the foregoing discussion of the composition of forward biased junction current, that the composition of the junction current in no way deter- mimes the composition of the current current entering and leaving the semi- conductor specimen from the external circuit, As we have seen, conduction in metallic conductors is effectively com- posed entirely of conduction band elec- trons; hence all current entering and leaving the P-N junction as a whole is of this form. What happens is that the “composition” of the current changes in the bulk of the material, due to the complementary mechanisms of “in- strinsic” carrier generation and carrier recombination,
A further point to note regarding the forward biased P-N junction is that the width of the depletion layer region of a junction is narrower under forward bias conditions than for the equilibrium situation. This occurs be- cause as we have seen the _ space charge of “uncovered” impurity ions in the depletion layer is intimately asso- ciated with the electric field and po- tential barrier. Hence when the latter are reduced in value, the space charge also reduces to correspond, The de- pletion layer thus contracts, leaving a smaller number of ions “uncovered.”
24
If the external bias voltage connect- ed to a P-N junction specimen is con- nected with the polarities reversed from the situation which we have just considered, its behaviour is somewhat different. This alternative arrangement is known as reverse bias and_ is illustrated in the diagrams of figure 4.6.
From figure 4.6(a) it may be seen that reverse bias involves the connec- tion of the negative polarity o: the external voltage to the P-type end of the specimen, and the positive polarity to the N-type end.
As before, a major proportion of such an applied potential difference is applied directly across the depletion
BATTERY
effectively extinguishes the diffusion currents altogether.
As before, the minority carrier drift — currents are virtually unaltered by the new situation, because they are “satu- rated” or limited by the numbers of minoritv carriers generated in the ma- terial by excitation. However, the mag- nitudes of the minority drift currents are actually very small—with silicon P-N junctions of modern manufacture, they tcgether usually amount to but a small fraction of a microamp.
In the equilibrium condition, of course, the majority carrer diffusion currents are of equally small and opposite magnitude. However as we have seen, the diffusion currents fall
AMMETER
¢
7 7 4 6 / 7“, LIGHTLY DOPED]
7 Oe DO LOG
7
7
N-TYPE
| DEPLETION | LAYER
ELECTROSTATIC POTENTIAL
ELECTRON DRIFT CURRENT ————dm
(UNALTERED) |
Ef
HOLE DIFFUSION CURRENT — — — (EXTINGUISHED}
(WIDENED)
REVERSE BIAS (EQUILIBRIUM)
(b)
INCREASED POTENTIAL BARRIER
ELECTRON DIFFUSION CURRENT (EXTINGUISHED}
ad (|
—t-————_ HOLE DRIFT CURRENT
Fiqure 4.6
layer region, because of its high re- sistivity, and a second electric field tends to be set up across the depletion layer in addition to the “inbuilt” field. But in contrast with the forward bias case, in which the two fields opposed, here the two fields are acting in the Same direction. The field across the de- pletion layer is therefore increased in intensity from its equilibrium value, rather than decreased.
The effect of this increase in field Strength is to effectively increase the height of the potential barrier which majority carriers must surmount in order to diffuse across the junction. This is illustrated in figure 4.6(b). As a result, few if any majority carriers of either type are able to cross the junction, and the diffusion currents fall consideratly from their equili- brium values. Increasing the reverse bias voltage beyond about 0.5V
imcrease only very slightly with
(UNALTERED)
away very rapidly with reverse biasing, virtually extinguishing for applied vol- tages greater than about 0.5V. For reverse bjas voltages above this level the only currents drawn by a P-N junction are therefore the unopposed but very small minority carrier drift currents—the saturation currents.
The current drawn by a_ reverse biased P-N junction thus tends to in- creasing voltage, rapidly reaching a constant and very low value _ corres- ponding to the sum of the saturation currents. This is illustrated by the left-hand portion of figure 4.7.
The energy level diagram for such a reverse biased junction is shown in figure 4.6(c). Again it may be seen that the Fermi level Ff is not con- stant throughout the material, indicat- Ing non-equilibrium conditions. The steep slope of Ef again occurs in the
Fundamentals of Solid State
depletion layer region, here signifying the extent to which the “inbuilt” field and the potential barrier of the junc- tion ‘have been increased. The full extent of the field present at the junc- tion is indicated by the energy bands themselves.
In contrast with the situation under forward bias conditions, it may be noted that the depletion layer of a reverse biased junction § is actually wider than for the equilibrium case. As before this occurs because of the intimate association between the space charge of “uncovered” impurity ions and the potential barrier. When the potential barrier is increased due to external reverse bias, the depletion layer therefore widens in order to “uncover” a correspondingly greater number of ions,
Because of this widening of the depletion layer the electric field inten- sity in the region does not imcreaSe as rapidly as it would if the layer width remained constant. However, it does steadily increase with increasing reverse bias, and inevitably a point is reached where one or another of a number of “breakdown” mechanisms occurs. When this occurs the effective resistivity of the junction again falls
rapidly, and the current increases sharply from. its basic “saturation” value.
The various mechanisms which may be involved when a_ reverse biased junction “breaks down” are each rather complex, and in fact not entirely understood: hence it will not be appro- priate to examine them here in any detail, However. in broad terms the two main mechanisms involved are so- called field emission or Zener break- down, and avalanche breakdown.
The field emission or Zener break- down mechanism is usually that res- ponsible for the breakdown of very heavily doped P-N junctions, which generally enter breakdown at reverse bias levels below about 6V. Due to the heavy doping concentrations in such junctions the depletion layer in very narrow, even under reverse bias conditions, and as a result of this the peak electric field intensity at the junction can be extremely high — in the order of 10° volts per cM, even at the low reverse voltages concerned.
When the electric field intensity reaches this order of: magnitude, val- ence electrons may be effectively ripped from their orbit system, pro- ducing both a conduction band elec- tron and a valence band hole. In short, the field itself produces electron- hole carrier pairs, and this explains the term “field emission.” The carrier pairs thus produced in the depletion
layer region are immediately swept away in opposite directions by the field, and as a result the junction current increases sharply from _ its saturation or “leakage’’ level. Avalanche breakdown, the other main breakdown mechanism, is_ that
usually responsible for breakdown in lightly doped junctions — _ generally those breaking down at reverse. vol- tages above about 10V. As the name Suggests, it is a mechanism whereby the minority carrier drift or saturation current itself effectively increases, due to an avalanching or “snowball” action.
In this type of breakdown the deple- tion layer is wide, both because of the light doping concentrations and as a result of the appreciable reverse
Fundamentals of Solid State
bias voltage. Because of this the minority carriers drifting across the junciion are ultimately able to de-
velop sufficient momentum that, when each collides with a fixed atom, it is effectively able to ionise that atom by “knocking out” one or more new Carrier pairs.
Such “ionisation by collision” in- volves a net gain in the number of carriers crossing the junction, because each carrier upon collision with a fix- ed atom can effectively produce two or more carriers. Hence as a result the junction current again rises from its saturation value.
It should be noted that neither of the “breakdown” mechanisms just des-
cribed involves inherent damage to the
P-N junction: in themselves, they are
FORWARD CURRENT
ALMOST CONSTANT AND VERY SMALL CURRENT REVERSE CURRENT
Figure 4.7
merely mechanisms whereby the cur- rent drawn by the junction under re- verse bias conditions increases marked- ly from its low saturation value when a particular voltage level is reached. It may be seen that they are thus rather different from the type of “breakdown” which occurs when _ ex- cessive voltage is applied to dielectric materials such as paper or plastic.
Whether or not a junction sustains damage when it enters “breakdown” is primarily determined by the very same factor which determines whether Or not it sustains damage in the for- ward bias mode: the pOwer dissipation. If the power dissipated in the semi- conductor material — most of which is dissipated in the depletion layer region, because of its greater voltage drop + is sufficient to cause overheating and disturbance to the crystal lattice struc- ture, then damage generally results. But if this level is not reached, then the junction will sustain no damage. Some junctions in practical semicon-
sharply
ductor devices are in fact designed to Operate continuously in the “break- down” condition, as we shall see in later chapters.
We have seen in the present chapter that the P-N _— junction behaves in rather different ways when external bias voltage is applied, depending up- on the polarity of that applied bias. In one direction it tends to con- duct readily, whereas in the other direction it tends to conduct only very slightly. No doubt the thoughtful reader will have already realised that this behaviour is virtually identical to that of the familiar thermionic diode valve, and will have noted the resem- blance between the curve of figure 4.7 and the voltage-current characteristic. of a diode valve.
RESULTANT HOLE DIFFUSION CURRENT
/ / ELECTRON DIFFUSION La CURRENT
STEEPLY RISING CURRENT
FORWARD BIAS
ELECTRON DRIET CURRENT
HOLE DRIFT CURRENT
It should therefore come as no sur- prise to learn that the P-N junction is in fact the heart of the modern semi- conductor or “crystal”? diode, a device used in large’ numbers in almost every branch of modern electronics. At the same time, P-N junctions either singly or in combination also form the basis of almost every other modern semi- conductor device, so that in the fore- going discussion of the P-N junction we have not only been describing the theory of crystal diode operation, but also laying the theoretical groundwork for many of the later chapters.
In the next chapter we take a look at the practical aspects of semiconduc- tor diodes, examining’ both _ their various physical forms and their applhi- cations. However, before passing to this material the reader might perhaps be well advised to glance back over the material which has been present- ed in the present chapter, to ensure that he has fully grasped the im- portant concepts involved.
SORUDCADODUQDOADELUEUCUOOCSOCEDUSOPUOGTUSORUOUDUTOLCOOUUDESOPRCRPODCPEDOPDUSAPOSEROSROOSESOO ONCE EDERRPEEO RET EDED EEC COC EOS T CEO ECO
SUGGESTED FURTHER READING
BURFORD, W. B., and VERNER, H. G., Semiconductor Junctions and Devices, 1965. McGraw-Hill Book Company, New York.
MORANT, M. J., Introduction to Semiconductor Devices, 1964. George G. Harrap and Company, London.
SHIVE, J. N., Physics of Solid State Electronics, 1966. Charles E. Merrill
Books, Inc., Columbus, Ohio.
SMITH, R. A., Semiconductors, 1950. Cambridge University Press.
CORPO DADOGSPASERDADESDERODELGQSDQUUEUDRECUDER DRCOG QULORTEUDOCOODGREDASGOURGPAUSPON ADIN DPOERSDOPDPRRA DA RSTTLEN AT PP OES PDIP PREC REDUU ERTS GRADE RCDTUO DADE UGRRDELUSUUN STUD OSTPRUTAPOLE PSUS PGUUPSOTPEDOP DUT EUTCQUEEE
25
Chapter 5
THE JUNCTION DIODE
Diodes and semiconductor materials — reverse bias current — temperature effects — forward bias characteristics — high temperature operation —— power rating — surge cur- rent rating —- reverse breakdown — peak inverse voltage rating — switching speed — package capacitance — junc- tion capacitance — charge storage — diode applications.
The basic P-N_ junction, whose behaviour was described in the pre- ceding chapter, effectively forms the
functional “heart” of almost every type -
of semiconductor diode. However, as the reader may already be aware, practical semiconductor diodes are encountered with widely differing electrical ratings. They are also found in circuits performing a variety of rather different tasks, and seen in an almost bewildering array of different physical forms.
In order to provide the reader with a satisfying explanation of these wide divergences between practical semi- conductor diodes, it is necessary to ex- pand the concepts of basic P-N junc- tion Operation already developed, and this will be attempted in the present chapter and in that which follows it. The present chapter will deal with what may be called “orthodox” diodes — that is, those devices which are de- signed to take advantage mainly of the unidirectional conduction properties of the P-N junction. Such diodes include those commonly encountered in circuits performing rectification, signal detec- tion, mixing, switching, gating and clipping.
Chapter six will deal in turn with those diode devices which are designed to take advantage of aspects of P-N junction behaviour other than that of unidirectional conduction. Examples of this type of device are diodes used as voltage regulators and coupling ele- ments, variable capacitors, oscillators and amplifiers, light detectors and energy converters.
Perhaps the first thing to be noted regarding practical semiconductor diodes is that, as one might perhaps expect, they are made from a number of different semiconductors. A very large majority of diodes in use at the present time are made from either germanium or silicon; the latter having been used to a lesser extent in the early days of semiconductor _ tech- nology because of manufacturing diffi- culties, but now used very extensively and possibly to a greater extent than germanium. Other semiconductor materials which are becoming used for diodes include gallium arsenide, gallium phosphide and gallium anti- monide.
26
The electrical behaviour and _ the ratings of a diode are both influenced significantly by the semiconductor material from which it is made. As we shall see, the semiconductor’ con- cerned plays a Significant part, along with the doping level, in determining the voltage-current characteristics of a diode for both forward and_ reverse bias. It also determines the extent to which this behaviour varies with temperature, and the power which the
if
0.72eV_ (electron-volts), while silicon has a somewhat larger gap width of 1.1leV. The compound semiconductor gallium arsenide has a gap width which is even larger again at 1.39eV.
The width of the forbidden energy gap was shown earlier to control the conductivity of intrinsic semicon- ductor material, by determining the excitation energy required for elec- trons to be transferred to the conduc- tion band. From this, and knowing that the generation of minority carriers in an impurity semiconductor material takes place by the same “intrinsic” mechanism, it should be fairly clear that the gap width also determines the number of minority carriers generated in an impurity semiconductor at any given excitation and doping level.
However, it is also true that the
width of the energy gap controls, in a minor, but inverse manner, the rela-
60°C, 25°C
U / U
{ 60°C! 25°C
'
10mA | ( | NOTE: DIFFERENT SCALES vl : USED FOR FORWARD AND GERMANIUM —_/ be > SILICON [REVERSE BIAS CONDITIONS ! ! 5mA ‘ / / / / / / / SILICON Bs / 7 ” " 25°C - 500mV IV Mie SS Se By A 25°C / GERMANIUM a —10pA -?’ Coe es Figure 5.1
device is capable of dissipating before this behaviour is permanently altered.
AS we saw in chapter 2, all crystal- line semiconductors are alike in the sense that, in the ground state, they behave as electrical insulators. The valence electron energy band is com- pletely filled, while the empty conduc- tion band is isolated from it by the “forbidden energy” gap. From = an electrical viewpoint the — essential differences between the various semi- conductors arise mainly because this forbidden energy gap has a different width in each case.
Germanium, it may be remembered, has a forbidden energy gap width of
tionship between minority carrier level and excitation level. Thus, although material with a wide energy gap tends initially to have a smaller number of minority carriers than material with a narrower gap, for the same excitation, its minority carrier population tends to multiply slightly more rapidly with increasing excitation.
Hence, while silicon impurity semi- conductor material tends to have a con- siderably smaller minority carrier population than germanium material, at room temperatures, it also exhibits a slightly increased tendency for this population to grow as the temperature is increased. Despite this the minority carrier population of typical silicon
Fundamentals of Solid State
material does not even approach that of germanium until very high tempera- tures are reached, both because. per- manium has a larger initial population, and because this population itself in- creases significantly with temperature.
What effect do these differences have on the behaviour of practical P-N diodes? They have a significant effect upon the reverse-bias saturation cur- rents, because it may be recalled that these currents are directly proportional to the minority carrier populations on either side of the junction.
In short, diodes made from a semi- conductor material having a relatively
ANODE LEAD {CONNECTS TO P-TYPE}
ANODE COS NECTION SPRING P-N JUNCTION DIE : PS ade
CATHODE LEAD (CONNECTS TO N-TYPE)
CATHODE LEAD
bias currents of something like 100 times this figure, i.e, a few tens of uA (microamps), Because of the influ- ence of excitation upon minority carrier generation these figures both increase as the temperature is raised, the silicon device current increasing slightly more rapidly.
Typically the reverse bias current of a germanium diode approximately doubles for every 8°C rise in tem- Perature, while that of a silicon diode approximately doubles _ for every 5°C rise.
An illustration of the reverse-bias aspect of diode performance is pro- ANODE LEAD ANODE LEAD
GLASS OR EPOXY SEAL
CATHODE LEAD
“DOUBLE HEATSINK" PACKAGE
USED FOR MEDIUM POWER
MINIATURE GLASS PACKAGE USED FOR LOW PCWER DIOCES
wide forbidden energy gap, such as silicon or gallium arsenide, tend to have a very low reverse bias satura- tion current at normal temperatures. In comparison diodes made from a semiconductor material such as ger- manium, which has a relatively narrow energy gap, tend to have a somewhat larger saturation current at the same temperature. This despite the fact that in the former case the saturation cur- rent will tend to increase slightly more rapidly with temperature.
It is true that the total reverse bias current drawn by a practical semi- conductor diode is not composed of the minority carrier saturation currents alone. It is very difficult, during the manufacture of practical diodes, to ensure that the surface of the semi- conductor crystal element or “die” does not become contaminated in some -way, and such contamination tends to result in additional reverse bias currents, which are commonly referred to as leakage currents.
Early in the history of semicon- ductor device development, these leakage currents were typically of the same order of magnitude as the satura- tlon currents, However, in recent years, manufacturing techniques have been considerably improved, and_ leakage currents can typically be held to a very small fraction of the saturation § cur- rents, Hence, with modern’ semi- conductor diodes and other devices, the reverse bias current drawn by an independent P-N junction is almost entirely composed of the minority carrier saturation currents.
In quantitative terms, the _ total reverse bias current of a typical modern silicon diode is of the order of a few hundred nA (nanoamps), at room temperature. Comparable §ger- manium diodes typically have reverse
Fundamentals of Solid State
DIODES (STOUT LEAD ENDS CONDUCT HEAT AWAY FROM CIE}
“TOP HAT" PACKAGE
Figure 5.2
vided by the left-hand portion of figure 5.1, which shows the reverse-bias cur- rents of typical silicon and germanium diodes compared at room temperature (25°C) and at 60°C. It may be seen that at both temperatures the silicon diode has a considerably lower satura- tion current, even though the propor- tional increase may be larger over the temperature range concerned.
From the foregoing one might be tempted to infer that, because silicon diodes have lower reverse bias currents than germanium diodes under similar conditions, they would consequently be preferable for any application requir- ing a device whose performance should approach that of an “ideal” unidirec- tional conducting element. However, while this is true where reverse bias is concerned, unfortunately the reverse is the case under forward bias condi- tions. Here it is found that germanium diodes are somewhat closer to the ideal.
The reason for this is that, in addi- tion to its influence upon minority Carrier generation, and consequently upon saturation currents, the forbidden energy gap width of a semiconductor also plays an important part in deter- mining the magnitude of the “inbuilt” drift field and potentia] barrier set up across a P-N junction in equilibrium. As a result the gap width also has a controlling influence upon the forward bias characteristic of such a junction, because it may be remembered that the forward bias current consists of excess majority carrier diffusion currents, which develop as the inbuilt potential barrier is surmounted.
For a semiconductor with a_ rela- tively wide forbidden energy gap, there will be a large energy difference be- tween the Fermi levels of P-type and N-type material. Because of this, the potential barrier set up across a P-N
USED FOR MEDIUM POWER DIODES
‘ideal
junction made from the material will be relatively large under equilibrium conditions, compared with that across a junction made from a semiconductor having a relatively narrow energy gap. In turn this will mean that a relatively high external forward bias will be. re- quired before the internal barrier is surmounted,
Hence, because of the wider energy gap of silicon, a diode made from this material tends to require a_ higher applied forward bias than a compar- able germanium diode for the same total forward conduction current. This is illustrated by the right-hand portion
GLASS OR EPQXY SEAL
PN JUNCTION ANODE IE CONNECTION earns SPRING / HEXAGON HEADER SHAPED HEADER
CATHODE
“STUD TYPE" PACKAGE USED FOR HIGH POWER DIODES (NORMALLY BOLTED TO HEAT RADIATOR)
of figure 5.1, which shows the forward conduction characteristics of typical silicon and germanium diodes com- pared as before at 25°C and 60°C. It may be seen that the silicon diode is “harder to turn on” than the ger- manium device, and also that it has a higher voltage drop when in forward conduction.
It should be noted that both types of device “turn On” at a lower voltage, and have a lower conducting voltage drop, at the elevated temperature. The reason for this should become clear if it is recalled that the Ferm; level of an impurity semiconductor moves to- ward the forbidden energy gap mid- point with increasing excitation, due to the increase in minority carriers. This means that the energy difference between the Fermi levels of the P- type and N-type materials becomes less as the temperature is_ raised, and accordingly the junction barrier poten- tial also decreases. Forward conduc- tion thus takes place at a lower applied voltage.
At this stage it should be fairly clear that when both forward and _ reverse characteristics are considered, neither silicon nor germanium diodes have a clear advantage. The silicon diode tends to have a somewhat lower reverse bias current, and therefore, more closely approximates the “ideal”? diode in the reverse bias condition, but the ger- manium diode has a lower forward bias voltage requirement and thus rep- resents the closer approximation to the in the forward bias condition.
In terms of characteristics, then, the choice of the semiconductor material from which a diode is made depends largely upon the ultimate application and its requirements. If the application is one in Which low reverse bias current is necessary or desirable, then a diode
27
made from a wide energy-gap material such as silicon or gallium = arsenide would be most appropriate.
Conversely if the prime requirement of the application concerned is for turn-on at a low voltage and minimum forward voltage drop in conduction, then the choice would favour a diode made from a narrow energy-gap semi- conductor such as germanium. It is true that if either both forward and reverse bias behaviour were critical, or both were not unduly critical, the choice would be less straightforward. In such cases the decision might well be made on the basis of other factors, One of which would probably be oper- ating temperature capability.
Generally a diode made from a semi- conductor having a wide energy gap is more suitable for high temperature Operation than a diode made from a semiconductor having a narrow energy gap. This is partly because of the somewhat lower reverse bias cur- rent at higher temperatures. However, a further reason is that the energy gap of a semiconductor plays a part in determining both the temperature at which the electrical structure of the device begins to alter permanently, due
to thermal diffusion of the actual im- purity atoms and ions, and also the crystal melting point. The wider the energy gap, the higher these tempera- tures tend to occur,
In practice the manufacturer of a semiconductor diode or other device usually rates his product in terms of the maximum allowable junction temperature. This is done in order to take into account the fact that both the ambient temperature and_ the power dissipated by the device con- tribute to its internal operating tem- perature.
Typically, germanium devices are given a maximum junction tempera-
ture rating of around 80-90°C, while silicon devices are usually given a somewhat higher rating of between 150-180°C. A silicon device would, therefore, be the logical choice for most applications involv- ing high temperatures and/or very high power dissipation.
In order to allow the user to ensure that a device is operated within its maximum junction temperature rating at all ambient temperatures, the manu- facturer must also normally provide information regarding the typical tem- perature rise of the device junction(s) with power dissipation. This informa- ton is usually given in terms of the thermal resistance of the device, ex- pressed in unjts of (degrees C/watt dis- sipation),
Naturally the thermal resistance of a particular device depends upon both the size of the semiconductor crystal die itself, and the physical “package” in which it is mounted. Hence a de- vice intended for very low power ap- plications may have a very small die and be mounted in a small glass or plastic package having a fairly high thermal resistance, while a device for high power use will normally have a relatively large die and will be mount- ed in a large metal package of low thermal resistance.
In addition to thermal resistance, a crystal die and its package also possess thermal “capacitance” or inertia. Be- cause of this, heating and cooling of the device involve definite thermal time- constants. Hence the heating of the
28
the device.
die tends to be proportional not to the instantaneous power dissipation, but to the average dissipation taken over a short time interval — the interval length depending upon the crystal die itself, and on the package and its thermal time-constant.
As a result of this averaging effect, a diode is typically able to withstand short bursts or “surges” of power dis- sipation which may be considerably higher than its continuous or “steady- state” dissipation rating. This short- term capability is often expressed in terms of the forward conduction surge current rating of the device, which may be given a number of values for different time periods.
Depending upon the device itself and also upon the time period for which a surge rating is given, it may represent
4. swt crate iionncinstatin Myasthenia
ae Hien s aa i, ha erate ae i af wie ayant fa atbystrestion™
Figure 5.3. Typical semiconductor diodes. “signal” diodes, compared in size with a common
tous low-power or
con type are made available are further subdivided into many individual device types differing from one another mainly in terms of two other important para- meters, These are the reverse break- down characteristic, and the switching speed, each of which will now be brief- ly discussed.
It may be remembered that if the reverse bias voltage applied to a P-N junction ts increased, a point is eventually reached where the junction current rises rapidly from its low saturation value, and the junction 18 then said to have entered “breakdown.” One of two main mechanisms js usually responsible for this behaviour. one being called field emission” or fener breakdown, and the - other avalanche breakdown.
As was explained in the preceding
At upper left are var-
paper clip. At upper right are four medium-power diodes as used in
many receiver and amplifier power supplies, together with a power
diode used in the rectifier within an automotive alternator. At lower
left is an assembly centaining four high-power silicon diodes, con-
nected for bridge rectification. At lower right is a single stud-mount-
ing high power silicon diode capable of handling an average current of 40 amps. All devices are shown approximately normal size.
from about five times to more than 50 times the forward current correspond- ing to the continuous power rating of The shorter the time in- volved, naturally enough, the higher tends to be the figure: however devices may be produced with the ability to withstand quite long surges of high amplitude, by appropriate thermal de- sign.
Further discussion of thermal con- siderations will be given in a_ later chapter. However, from the foregoing it should be apparent that power dis- sipation requirements provide at least a partial explanation for the variety of packages in which semiconductor de- vices are found. Figures 5.2 and 5.3 show the basic construction of some of the diode packages in common use.
In general each of the various sizes and packages in which “orthodox” diodes of both the germanium and sili-
chapter, the phenomenon of junction reverse breakdown does not involve inherent damage. However, it does con- stitute a potentially high-dissipation mode of operation, because under breakdown conditions a junction tends to maintain a relatively large voltage drop while at the same time being capable of heavy conduction.
It is also true that with practical P-N junctions, in diodes and other semiconductor devices, breakdown tends to occur unevenly and in a
localised manner at some specific point on the crystal die. As a result, the increased current which flows is con- centrated in a small area, and localised Overheating and damage can occur with great rapidity at power levels considerably lower than the forward conduction cOnUAUOUS. power raling of the device.
By exercising extreme control over
Fundamentals of Solid State
cleanliness and such factors as doping uniformity during the various fabrica- lion processes, device manufacturers have recently been able to effect a considerable reduction in this tendency for localised breakdown. However, the “transient protected” devices which have resulted from this effort are necessarily more costly than devices fabricated under less stringent condi- tions: and, of course, such devices still enter breakdown eventually, albeit in a uniform and evenly distributed man- ner.
Junction breakdown thus represents a condition which at the very least involves potential device damage. It should also be evident that quite apart from this, the rise in reverse current, which tends to occur at breakdown, represents in itself a significant de- parture from the ideal diode character- ISUIC,
For a practical diode, therefore, the reverse breakdown characteristic is of considerable importance. It must be considered not only with relevance to the protection of the device itself, but also because of its possible conse-
Germanium diodes are typically available with PIV ratings ranging from less than a volt to about 150V. Silicon dicdes are available with PIV ratings ranging from about 3V_ to more than 1500V. Still higher PIV ratings can be produced by connect- ing a number of individual silicon dice im series; devices with PIV ratings in excess of 50KV have been produced using this technique.
As noted earlier, a further import- ant general parameter of practical semi- conductor diode behaviour is switching speed. This basically describes the abil- ity, or otherwise, of a device to rapidly follow any changes in external circuit conditions. As diodes are often found in circuits involving rapid reversal of the bias voltages applied to the device,
FORWARD BIAS
aie: cen
DEPLETION LAYER
“oe
| § Nh oe We een eed
EFFECTIVE DIELECTRIC OF CAPACITOR
REVERSE BIAS
FORWARD CURRENT
JUNCTION CAPACITANCE
REVERSE ¥ CURRENT
REVERSE ae ae FORWARD
BIAS Figure 5.4
quences im the circuitry into which the device is connected,
Usually the reverse breakdown characteristic of a semiconductor diode is specified in terms of a peak inverse voltage or “PIV” rating, which in effect represents a specific value of reverse bias voltage at or below which no device of the type concerned should enter breakdown. Some types of de- vice may be given a number of different PIV ratings, to cover both steady-state and various reverse transient conditions. The “transient protected”’ diodes mentioned earlier are examples of devices normally given such multiple ratings.
Both silicon and germanium diodes may be manufactured to exhibit a wide range of breakdown voltages. How- ever, devices required to have a very high breakdown voltage rating are usually made from silicon or some other semiconductor having a similarly Wide energy gap. This is because the relatively high reverse saturation cur- rent of a narrow-gap semi-conductor such as germanium tends to make it very difficult to delay the onset of avalanche breakdown.
Fundamentals of Solid State
BIAS
this parameter can be of considerable importance.
One of the main factors determining the switching speed of a diode is its shunt capacitance, which is simply the total effective capacitance present be- tween. the two device electrodes. Be- cause it is effectively in parallel with the actual diode element, this capaci- tance can have a considerable influence upon the overall high-speed perform- ance. For example, it tends to draw a current component which is purely pro- portional to the rate of change of ap- plied voltage, regardless of polarity; behaviour which fairly obviously re- presents a significant departure from that of an ideal diode.
Naturally enough the diode package alone will contribute to the total shunt Capacitance, as some finite package capacitance is unavoidable with prac- tical devices. However, by careful de- sign manufacturers have been able to produce packages with very low shunt capacitance, and these are normally employed for those devices intended for extremely high speed operation.
Quite apart from the package cap- acitance, however, an important com-
ponent of the total shunt capacitance is provided by the inherent capaci- tance of the diode P-N junction it- self. This capacitance is known as the “depletion layer capacitance,” “barrier capacitance,” “space charge capacitance,” “junction capacitance,” or “transition capacitance.”
Although it may seem Surprising at first that the P-N junction itself acts as a capacitor, the reason for this should become evident after a moment’s consideration. Essentially, a capacitor consists of two conductors separated by a dielectric, and in the P-N junction we have, after all, two quite high con- | ductivity semiconductor regions separ- ated by a low conductivity depletion layer region. The latter is largely devoid of carriers, yet provided with the facil- |
TIME
“IDEAL DIODE"
TIME
NORMAL REVERSE (SATURATION) CURRENT
Fiqure 5.5
ity for charge storage in the form of ionised impurity atoms; small wonder, therefore, that it acts as a very effec- tive dielectric,
Of course the width of the depletion layer varies with applied voltage, as we have seen. Under equilibrium con- ditions, with zero applied bias, it has a width determined by the semiconduc- tor concerned and by the doping tevels. If reverse bias is applied, the depletion layer widens to uncover more impurity ions, and conversely if forward bias is applied it.narrows to reduce the num- ber of uncovered ions.
Because of this width variation, the junction capacitance jis not static but also varies with applied voltage. This is illustrated in figure 5.4, where it may be seen that the junction capacitance of a typical diode varies inversely with reverse bias voltage, and directly with forward bias voltage.
The junction capacitance of a de- vice may be minimised by using the smallest crystal die capable of handling the required power, and by using low doping levels to result in a relatively wide depletion layer. Naturally the lat- ter technique involves a compromise, as low doping levels also increase the resistivity of the material and hence tend to increase the forward voltage drop and consequently lower efficiency.
As will be discussed in the next chap- ter, some semiconductor diodes are ex- pressly designed to exhibit a very high junction capacitance. Such diodes are intended not for use as unidirectional
29
circuit elements, but rather as voltage- controlled variable capacitors.
Yet another important factor which
influences the switching speed of a semi- conductor diode is the phenomenon known as charge storage or minority carrier storage, This is particularly re- levant where a diode is required to switch rapidly between the forward conducting or “on” state and the re- verse-biased “off” state. When a P-N junction is conducting due to forward bias, it may be remem- bered, excess majority carrier diffusion currents are flowing in both directions across the junction. At the same time the depletion layer has a width some- what less than that for equilibrium conditions, and the potential barrier a somewhat lower value.
If the voltage applied to the device is changed, these conditions must also change to achieve a new dynamic bal- ance. Thus if the forward bias is in creased, additional carriers must be swept across the junction to set up higher diffusion current levels, while at the same time some of the previous- ly ionised impurity atoms must be neu- tralised to reduce the depletion layer width and reduce the potential barrier.
Conversely, if the bias is reduced or reversed in polarity, the number of carriers crossing the junction must fall, while additional impurity atoms must be ionised to widen the depletion layer and increase the potential barrier.
In both cases, significant time must elapse before the new _ conditions stabilise. The depletion layer changes involve movement of carriers through a finite volume of material, and this necessarily takes time. Hence there is an inevitable delay involved before the new balance conditions are reached, and during the delay period the be- haviour of the device may differ con- siderably from that of an ideal diode.
For example, figure 5.5 shows what tends to happen if the polarity of the applied voltage is suddenly switched from a forward bias value to a reverse bias value. Ideally when this occurs the diode current would drop immedi- ately to its very low reverse satura- tion current value; however, it can be seen that what in fact happens is that the current swings rapidly to a high reverse value, and only subsequently falls back exponentially to its satura- tion value,
The reason for this is that at the instant of bias reversal, a considerable number of carriers of both types are stored or “trapped,” in the depletion layer region and also in the adjacent P-type and N-type material as injected minority carriers. Before normal reverse-bias operation can be achieved, these carriers must all be removed, generally by being swept back across the junction in both directions. It is the removal of these stored carriers which results in the temporary high reverse current.
The charge-storage mechanism can.
be controlled to a considerable extent’
by special techniques involving non- uniform doping and careful choice of impurities. The rather — specialised diodes produced by such _ techniques include those called “step-recovery diodes,” ‘“‘snap-off diodes,” “avalanche switching diodes” and “PIN diodes.” To conclude this’ discussion of “orthodox” semiconductor — diodes, brief descriptions will be given of a small, but representative selection of the great many applications of these
30
devices. Before the applications are discussed, however, brief mention will be made regarding diode symbols used in circuit diagrams, for the possible tenefit of those readers as yet un- familiar with the devices.
The circuit symbols most commonly used for semiconductor diodes are shown in figure 5.6, together with a simplified representation of the basic P-N junction shown for reference. Note that the symbols are all similar in that they use an arrow-head_ to represent the P-type material, and a bar or line to represent the N-type material. The arrow-head is actually
intended to indicate the direction of forward or “easy” current flow according to the classical “positive
charge” current convention. For orthodox diodes the electrode connecting to the P-type material is
ANODE CATHODE DIODE SYMBOLS Figure 5.6
D of. AC ca Dc AC INPUT al OUTPUT INPL
(a) HALF-WAVE RECTIFIER
AC INPUT
(c) BRIDGE RECTIFIER
simplest circuit in common use. As the name suggests, this configuration employs a single diode element which is arranged to allow only alternate half-cycles of the AC input to reach the load circuit, while simply rejecting the half-cycles of Opposite polarity.
The use of a reservoir capacitor “C” helps to smooth out the appreciable ripple which tends to be present in the output as aresult of the “gaps” between the half-cycle pulses delivered by the diode. However, even with a relatively large reservoir capacitor the ripple tends to be high, and the output rather poorly regulated, as a result of the fact that the reservoir capacitor may be discharged continuously by the load, but can only be recharged by the diode on every alternate half-cycle. The half- wave rectifier circuit accordingly finds uSe mainly in very low current appli- cations.
The limitations of the half-wave cir- cuit are obviated in the “full-wave” circuit shown in figure 5.7(b). Here two diode elements are connected to a transformer effectively having two identical secondary windings connect- ed in series. Each diode conducts only on alternate half-cycles, as before, but the two elements are arranged so that one conducts for the positive half- cycles and the- other for the negative
DI
iC OUTPUT
D2
(b) FULL-WAVE RECTIFIER
(d} VOLTAGE-DOUBLING RECTIFIER
Figure 5.7
normally labelled the “anode,” as shown, while the N-type electrode is latelled the “cathode.” However, these terms really depend upon the polarity of the applied voltage, and may be reversed in certain cases.
Probably the most familiar applica- tion of semiconductor diodes jis in circuits used for the rectification of alternating current into unidirectional current. In fact they are particularly well suited for this task, because, despite the limitations discussed in this chapter, they still represent the closest available approximation to an_ ideal diode element.
There are numerous different recti- fier circuit configurations, each of which has certain distinct advantages in specific situations. Four of the most cOmmon configurations are illustrated in figure 5.7,
The first of these is the “half-wave’” rectifier, figure 5.7(a), which is the
half-cycles, and both charge the reser- voir capacitor in the same direction.
Because it effectively “uses” both the positive and negative half-cycles of the AC input, the full-wave rectifier tends to deliver Jess output ripple and possess better load regulation than the _half- Wave circuit. The ripple is also easier to filter out, having a fundamental fre- quency component of twice the AC supply frequency, whereas the ripple of the half-wave circuit has a funda- mental component equal to the AC supply frequency.
‘The full-wave circuit is therefore better suited for high culrent applica- tions; however it has the disadvantage that it normally requires a transformer having a double secondary winding. This requirement can be obviated by the use of the so-called “bridge” cir- cuit, shown in figure 5.7(c).
Here a single transformer secondary winding is used, with two additional
Fundamentals of Solid State
diode elements used to. effectively reverse both connections between the load and the AC supply on successive half-cycles. The circuit still performs full-wave rectification, and therefore tends to have low ripple and good load regulation. It differs from the ‘“full- wave” configuration mainly in_ that transformer complexity has been reduc- ed at the cost of two additional diodes.
The fourth configuration shown is the “full-wave voltage doubler” recti- fier, figure 5.7(d), one of many con- figurations used to deliver an output voltage higher than the peak value of the input A.C. In this case the two diodes used are arranged to charge sep- arate reservoir capacitors during their respective half-cycles, the capacitors
being effectively connected in series + DI Di A G A D2 D2 B B
(c) LOGIC GATING
(c) AC SIGNAL CLIPPING
handling capacity, to ensure that they share the current properly.
The PLLYV, rating of the diodes used in rectifier circuits depends upon the configuration used. For the half-wave and full-wave circuits, for example, the diode P.LV. than twice the peak no-load output voltage, whereas for the bridge and doubler circuits it need only be greater than the peak no-load output voltage itself.
Individual diodes may be connected in series to achieve a suitably high P.L.V. rating. However, unless “tran-
sient protected”’ devices are used, paral- lel R-C networks must be connected across each device to ensure that they and
Share both _ repetitive reverse voltages equally.
surge
+V
OUTPUT
(b) SIGNAL SWITCHING
(d) METER MOVEMENT “PROTECTION
Figure 5.8
with circult.
In a half-wave rectifier circuit, the diode used should normally have a cur- ‘ent rating sufficient to allow it to carry the full value of the average load current. In contrast, the diodes used in full-wave, bridge or full-wave doubler circuits need only have a rating sufficient to allow them to carry ap- proximately 50% of the average load current because in these circuits the average current is shared between ele- ments. In other circuits a different sharing factor may apply, depending upon the number of diodes involved.
In each type of rectifier circuit the diodes used should also be capable of handling both the initial surge current which flows when power is applied with the reservoir capacitor(s) fully dis- charged, and also the repetitive current pulses involved because of the con- tinuous discharge/ periodic charge situation. The‘\peak currents due to the latter effect tend to be higher with the half-wave circuit because of larger “gaps” between charging pulses.
The amplitude of switch-on current surges is limited by the effective impe- dance in series with the diodes, and typically this is mainly composed of the effective secondary impedance of of the transformer. If this impedance is too low, external low-value high wattage resistors may be added in series with each diode, Such resistors must also be used if devices are con- nected in parallel for increased current
respect to the output and load
Fundamentals of Solid State
Many “rectifier” circuit configura- tions are in basic form suitable not only for power rectification, but also for detection—the process of extract- ing modulation information from a high frequency carrier signal. Hence signal detection circuits form another important application of semiconduc- tor diodes, and account for many of the diodes found in radio and televi- sion receivers and test equipment.
A rapidly growing application for semiconductor diades is in circuitry involved in logic gating and_ signal switching. Here the unidirectional pro- perties of the device are used. to effec-
rating should be greater:
tively connect or disconnect circuit paints in response to their relative voltage polarities.
Simple circuit configurations of this type are shown in figure 5.8(a) and (b). In the first circuit of (a), it may be seen that the diodes perform the “AND” operation, because point “C”- will rise to a positive potential if, and only if, both points “A” and “B” ar also raised to a positive potential.
Contrasted with this behaviour is that of the second circuit, which because of the changed diode connections performs the “OR” operation. In this case point “C” will go positive if either, or both, points “A” or “B” go positive.
The circuit in figure 5.8(b) illustrates the use of diodes for remote switching of AC signals. Here the circuitry 1s arranged so that when D1 is conduct- ing and providing a signal path for input “A,” diode D2 is reverse biased and held “off.” Operating the switch reverses the situation, with diode D2 conducting and D1 held off.
Another important class of appli- cations for semiconductor diodes in- cludes circuits which take advantage of the fact that the forward charac- teristic of such devices is non-linear, representing a high initial resistance and subsequently a low _ resistance when the device reaches full conduc- tion. Figure 5.8 also illustrates two of the many types of circuit which ex- ploit this behaviour.
In the circuit of figure 5.8(c) it may be seen that two diodes are connected in inverse parallel across. a source of sinewave Signals, a resistor being used to limit diode current. During each half-cycle, one of the two diodes con- ducts; however, because of the forward bias characteristic, this conduction is effectively confined to that part of the half-cycle during which the signal ex- ceeds the turn-on “knee.” Hence the effect of the diodes is to effectively “clip” the signal to a known peak-to- peak amplitude.
The circuit of figure 5.8(d) shows how a similar diode configuration may be used to protect a delicate meter movement from damage due to over- load. Here the non-linearity of the diodes effectively prevents the voltage applied to the movement from rising above the turn-on knee voltage, .in either direction. Silicon diodes are normally used in this type of applica- tion, because their higher turn-on volt- age and lower saturation current both ensure that normal meter operation is not disturbed.
CRUORUED ADEM ACUDGREASSPACQUCQCCUMEOCTSEODESOUDSOUETODECETOQOUEAGUCDCTO TEP OCTOUATEODTECPEDODDEOGQUGLUTORGTOUCUAECEDECTTOGUUUCTEEUUATASET TOLL UUUSTORCORTODOCCUTOTRCUDRUECECOUEUOCUDEUD OR CCTROOLOGTURODEUEGL
SUGGESTED FURTHER READING
BRAZEE. J. G., Semiconductor and Tube Electronics, New York.
Introduction to Semiconductor Devices, G. Harrap and Company, London.
PHILLIPS, A.'B., Transistor Engineering, 1962.
hart and Winston, Inc., MORANT, M. J.,
pany, Inc., New York.
ROWE, J., An Introduction to Digital Electronics, Ltd., Sydney. , —Transient Protected Rectifiers,” No. 10, January, 1969.
1968, Holt, Rine-
1964. George McGraw-Hill Book Com- 1967. Sungravure Pty.
in Electronics Australia, V.30.
SMITH, R. A., Semiconductors, 1950. Cambridge Uniersity Press.
SURINA, T.,
and HERRICK, C., Semiconductor Electronics, 1964. Holt,
Rinehart and Winston, Inc., New York.
Also “Solid-State Diodes,” No. 1, July, 1969.
a special section
in Electronics World, V.82,
VECUKUSOGEURUOROOROLOAONGOUASROCCEOTCODTACUROUAUROGUCEOAUOROOUSOGOTDGOTUCUORCACOSURGSOUOUOLECSTEODEROUODUOULEOTCURCEUEUERUCORSEOCUCLERCQOTEDEETUECECOTECUU TOLEDO UU CUUS ERECTED TREES ESE
31
Chapter 6
SPECIALISED DIODES
Zener diodes —- breakdown voltage —— power dissipation —~ temperature coefficient -—— reference diodes — com- pensation — zener applications — varicaps —- capacitance range — Q-factor — varicap applications —— varactors — frequency multiplication — parametric amplification — tunnel diodes —back diodes —applications ——photo- diodes — light-emitting diodes —— injection lasers.
Increasing the reverse bias voltage applied to a P-N junction diode even- tually results in a phenomenon known as “breakdown,” as we have seen in previous chapters. When breakdown occurs the normally very small and almost constant reverse bias current of the device suddenly and rapidly increases. It may be remembered that One Of a number of mechanisms may be responsible for this rise in current, depending upon the doping levels and the construction of the device.
The mechanisms of breakdown do not involve inherent damage to the device, aS we have noted. However, a diode which has entered this region of operation is capable of heavy con- duction, while at the same time tend- ing to maintaim an appreciable voltage drop. The region therefore tends to be one of high power dissipation, and consequently of potential device dam- age.
In addition to the risk of device damage, there is the further considera- tion that in the breakdown region the behaviour of a device represents a significant departure from that of an “ideal” diode. It should therefore not be surprising that in a great many diode applications, considerable care is taken to ensure that device breakdown cannot occur.
Despite this there are certain appli- cations in which diode breakdown is not avoided, but in fact intentionally planned. The reason for this is that, provided the device dissipation is kept below damage level, the voltage drop of a P-N junction in the breakdown region tends to be substantially con- stant, and independent of current level. A diode which is operating in the breakdown region may thus be used as a voltage regulating or limit- ing element, with applications similar to those of gas-discharge regulator tubes.
Although many “orthodox” semi- conductor diodes may be used in this fashion, their usefulness as voltage regulators or limiters is generally rather limited. This is because with many devices there is a_ tendency, noted earlier, for breakdown to occur unevenly and in a localised manner at
32
some specific point on the crystal die. Breakdown current thus tends to be concentrated in a. small area, causing localised overheating and damage, even at relatively low power levels. Some years ago, device manufac- turers found it possible to obviate this problem by careful control of doping level, doping gradients and the cleanli- ness levels maintained during the various fabrication processes. This en- abled them to produce devices de- signed specifically to be capable of
BREAKDOWN "KNEE"
REVERSE BIAS VOLTAGE
FOLLOWING BREAKDOWN, VOLTAGE DROP IS ALMOST CONSTANT FOR VARYING CURRENTS.
continuous operation in the break- down region. At first these devices were capable of only modest power dissipation but, in recent years, the techniques have been further develop- ed and power capability has risen significantly. (The same development in techniques has resulted in the ap- pearance of the “transient protected” rectifier diodes mentioned in the pre- vious chapter.)
The names given to devices speci- fically intended for breakdown region Operation are “breakdown” diodes, “regulator diodes,” “reference” diodes, and “zener” diodes (often contracted to “zeners”. The last of these terms should strictly only be applied to devices whose breakdown is due to the field-effect of Zener mechanism: how-
NORMAL SMALL REVERSE CURRENT PRIOR TO BREAKDOWN.
{SLOPE = DYNAMIC RESISTANCE)
Figure 6.1
ever, it is widely used to describe all devices designed for breakdown opera- tion,
Zener diodes are fabricated almost exclusively from silicon, because of the higher temperature/dissipation cap- ability of this material compared with the other commonly used semiconduc- tors. They are made in many of the physical packages used for “orthodox” diodes, including most of those shown in the previous chapter. The break- down characteristic of a typical device is shown In figure 6.1.
By varying doping’ levels and gradients, device manufacturers are able to provide circuit designers with zener diodes having breakdown voltage figures ranging from about 3V to above 200V. For convenience, device types are usually given a nominal breakdown voltage designation according to the familiar logarithmic “preferred value” series used for resistors, capacitors and other components, and a similar toler-
FORWARD CONDUCTION
REVERSE CURRENT
ance system is used. Hence a particular device might have a rated breakdown voltage. of (4.7V + 5%).
The nominal breakdown voltage of a zener diode is actually a somewhat arbitrary figure, because the voltage drop of a practical device in the reverse breakdown region is not entire- ly independent of current level. It also tends to be temperature dependent. With devices having a very low break- down voltage there is also the problem that breakdown is not characterised by a Sharp “knee” in the reverse bias be- haviour, but by a rather gradual cur- rent increase.
Because of these factors, it is usual for the nominal voltage of a zener diode to be quoted for a _ particular current level, and for a specific am-
Fundamentals of Solid State
bient temperature. The behaviour of the device at other current levels and temperatures may then be described in terms of a current-voltage character- istic and/or a dynamic resistance figure, together with a temperature co- efficient. The dynamic resistance of a device is the slope of the characteristic following breakdown, as indicated in figure 6.1; the temperature coefficient will be discussed shortly.
For most zener diode applications, a parameter of importance almost equal to that of nominal breakdown voltage is the device power dissipation rating. As with “orthodox” diodes, this rating determines the operating current levels at which the device may be operated for a given ambient temperature.
Currently available devices