14.1 INTRODUCTION
Devices in which a controlled flow of electrons can be obtained are the
basic building blocks of all the electronic circuits. Before the discovery of
transistor in 1948, such devices were mostly vacuum tubes (also called
valves) like the vacuum diode which has two electrodes, viz., anode (often
called plate) and cathode; triode which has three electrodes – cathode,
plate and grid; tetrode and pentode (respectively with 4 and 5 electrodes).
In a vacuum tube, the electrons are supplied by a heated cathode and
the controlled flow of these electrons in vacuum is obtained by varying
the voltage between its different electrodes. Vacuum is required in the
inter-electrode space; otherwise the moving electrons may lose their
energy on collision with the air molecules in their path. In these devices
the electrons can flow only from the cathode to the anode (i.e., only in one
direction). Therefore, such devices are generally referred to as valves.
These vacuum tube devices are bulky, consume high power, operate
generally at high voltages (~100 V) and have limited life and low reliability.
The seed of the development of modern solid-state semiconductor
electronics goes back to 1930’s when it was realised that some solid-
state semiconductors and their junctions offer the possibility of controlling
the number and the direction of flow of charge carriers through them.
Simple excitations like light, heat or small applied voltage can change
the number of mobile charges in a semiconductor. Note that the supply
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SEMICONDUCTOR
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and flow of charge carriers in the semiconductor devices are within the
solid itself, while in the earlier vacuum tubes/valves, the mobile electrons
were obtained from a heated cathode and they were made to flow in an
evacuated space or vacuum. No external heating or large evacuated space
is required by the semiconductor devices. They are small in size, consume
low power, operate at low voltages and have long life and high reliability.
Even the Cathode Ray Tubes (CRT) used in television and computer
monitors which work on the principle of vacuum tubes are being replaced
by Liquid Crystal Display (LCD) monitors with supporting solid state
electronics. Much before the full implications of the semiconductor devices
was formally understood, a naturally occurring crystal of galena (Lead
sulphide, PbS) with a metal point contact attached to it was used as
detector of radio waves.
In the following sections, we will introduce the basic concepts of
semiconductor physics and discuss some semiconductor devices like
junction diodes (a 2-electrode device) and bipolar junction transistor (a
3-electrode device). A few circuits illustrating their applications will also
be described.
14.2 CLASSIFICATION OF METALS, CONDUCTORS AND
SEMICONDUCTORS
On the basis of conductivity
On the basis of the relative values of electrical conductivity (
σ
) or resistivity
(
ρ
= 1/
σ
), the solids are broadly classified as:
(i) Metals: They possess very low resistivity (or high conductivity).
ρ
~ 10
–2
– 10
–8
Ω m
σ
~ 10
2
– 10
8
S m
–1
(ii) Semiconductors: They have resistivity or conductivity intermediate
to metals and insulators.
ρ
~ 10
–5
– 10
6
Ω m
σ
~ 10
5
– 10
–6
S m
–1
(iii)Insulators: They have high resistivity (or low conductivity).
ρ
~ 10
11
– 10
19
Ω m
σ
~ 10
–11
– 10
–19
S m
–1
The values of
ρ
and
σ
given above are indicative of magnitude and
could well go outside the ranges as well. Relative values of the resistivity
are not the only criteria for distinguishing metals, insulators and
semiconductors from each other. There are some other differences, which
will become clear as we go along in this chapter.
Our interest in this chapter is in the study of semiconductors which
could be:
(i) Elemental semiconductors: Si and Ge
(ii) Compound semiconductors: Examples are:
• Inorganic: CdS, GaAs, CdSe, InP, etc.
• Organic: anthracene, doped pthalocyanines, etc.
• Organic polymers: polypyrrole, polyaniline, polythiophene, etc.
Most of the currently available semiconductor devices are based on
elemental semiconductors Si or Ge and compound inorganic
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semiconductors. However, after 1990, a few semiconductor devices using
organic semiconductors and semiconducting polymers have been
developed signalling the birth of a futuristic technology of polymer-
electronics and molecular-electronics. In this chapter, we will restrict
ourselves to the study of inorganic semiconductors, particularly
elemental semiconductors Si and Ge. The general concepts introduced
here for discussing the elemental semiconductors, by-and-large, apply
to most of the compound semiconductors as well.
On the basis of energy bands
According to the Bohr atomic model, in an isolated atom the energy of
any of its electrons is decided by the orbit in which it revolves. But when
the atoms come together to form a solid they are close to each other. So
the outer orbits of electrons from neighbouring atoms would come very
close or could even overlap. This would make the nature of electron motion
in a solid very different from that in an isolated atom.
Inside the crystal each electron has a unique position and no two
electrons see exactly the same pattern of surrounding charges. Because
of this, each electron will have a different energy level. These different
energy levels with continuous energy variation form what are called
energy bands. The energy band which includes the energy levels of the
valence electrons is called the valence band
. The energy band above the
valence band is called the conduction band. With no external energy, all
the valence electrons will reside in the valence band. If the lowest level in
the conduction band happens to be lower than the highest level of the
valence band, the electrons from the valence band can easily move into
the conduction band. Normally the conduction band is empty. But when
it overlaps on the valence band electrons can move freely into it. This is
the case with metallic conductors.
If there is some gap between the conduction band and the valence
band, electrons in the valence band all remain bound and no free electrons
are available in the conduction band. This makes the material an
insulator. But some of the electrons from the valence band may gain
external energy to cross the gap between the conduction band and the
valence band. Then these electrons will move into the conduction band.
At the same time they will create vacant energy levels in the valence band
where other valence electrons can move. Thus the process creates the
possibility of conduction due to electrons in conduction band as well as
due to vacancies in the valence band.
Let us consider what happens in the case of Si or Ge crystal containing
N atoms. For Si, the outermost orbit is the third orbit (n = 3), while for Ge
it is the fourth orbit (n = 4). The number of electrons in the outermost
orbit is 4 (2s
and 2p electrons). Hence, the total number of outer electrons
in the crystal is 4N. The maximum possible number of electrons in the
outer orbit is 8 (2s + 6p electrons). So, for the 4N valence electrons there
are 8N available energy states. These 8N discrete energy levels can either
form a continuous band or they may be grouped in different bands
depending upon the distance between the atoms in the crystal (see box
on Band Theory of Solids).
At the distance between the atoms in the crystal lattices of Si and Ge,
the energy band of these 8N states is split apart into two which are
separated by an energy gap E
g
(Fig. 14.1). The lower band which is
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completely occupied by the 4N valence electrons at temperature of absolute
zero is the valence band. The other band consisting of 4N energy states,
called the conduction band, is completely empty at absolute zero.
BAND THEORY OF SOLIDS
Consider that the Si or Ge crystal
contains N atoms. Electrons of each
atom will have discrete energies in
different orbits. The electron energy
will be same if all the atoms are
isolated, i.e., separated from each
other by a large distance. However,
in a crystal, the atoms are close to
each other (2 to 3 Å) and therefore
the electrons interact with each
other and also with the
neighbouring atomic cores. The
overlap (or interaction) will be more
felt by the electrons in the
outermost orbit while the inner
orbit or core electron energies may
remain unaffected. Therefore, for understanding electron energies in Si or Ge crystal, we
need to consider the changes in the energies of the electrons in the outermost orbit only.
For Si, the outermost orbit is the third orbit (n = 3), while for Ge it is the fourth orbit
(n = 4). The number of electrons in the outermost orbit is 4 (2s and 2p electrons). Hence,
the total number of outer electrons in the crystal is 4N. The maximum possible number of
outer electrons in the orbit is 8 (2s + 6p electrons). So, out of the 4N electrons, 2N electrons
are in the 2N s-states (orbital quantum number l = 0) and 2N electrons are in the available
6N p-states. Obviously, some p-electron states are empty as shown in the extreme right of
Figure. This is the case of well separated or isolated atoms [region A of Figure].
Suppose these atoms start coming nearer to each other to form a solid. The energies
of these electrons in the outermost orbit may change (both increase and decrease) due to
the interaction between the electrons of different atoms. The 6N states for l = 1, which
originally had identical energies in the isolated atoms, spread out and form an energy
band [region B in Figure]. Similarly, the 2N states for l = 0, having identical energies in
the isolated atoms, split into a second band (carefully see the region B of Figure) separated
from the first one by an energy gap.
At still smaller spacing, however, there comes a region in which the bands merge with
each other. The lowest energy state that is a split from the upper atomic level appears to
drop below the upper state that has come from the lower atomic level. In this region (region
C in Figure), no energy gap exists where the upper and lower energy states get mixed.
Finally, if the distance between the atoms further decreases, the energy bands again
split apart and are separated by an energy gap E
g
(region D in Figure). The total number
of available energy states 8N has been re-apportioned between the two bands (4N states
each in the lower and upper energy bands). Here the significant point is that there are
exactly as many states in the lower band (4N) as there are available valence electrons
from the atoms (4N).
Therefore, this band (called the valence band) is completely filled while the upper
band is completely empty. The upper band is called the conduction band.
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The lowest energy level in the
conduction band is shown as E
C
and
highest energy level in the valence band
is shown as E
V
. Above E
C
and below E
V
there are a large number of closely spaced
energy levels, as shown in Fig. 14.1.
The gap between the top of the valence
band and bottom of the conduction band
is called the energy band gap (Energy gap
E
g
). It may be large, small, or zero,
depending upon the material. These
different situations, are depicted in Fig.
14.2 and discussed below:
Case I: This refers to a situation, as
shown in Fig. 14.2(a). One can have a
metal either when the conduction band
is partially filled and the balanced band
is partially empty or when the conduction
and valance bands overlap. When there
is overlap electrons from valence band can
easily move into the conduction band.
This situation makes a large number of
electrons available for electrical conduction. When the valence band is
partially empty, electrons from its lower level can move to higher level
making conduction possible. Therefore, the resistance of such materials
is low or the conductivity is high.
FIGURE 14.2 Difference between energy bands of (a) metals,
(b) insulators and (c) semiconductors.
FIGURE 14.1 The energy band positions in a
semiconductor at 0 K. The upper band, called the
conduction band, consists of infinitely large number
of closely spaced energy states. The lower band,
called the valence band, consists of closely spaced
completely filled energy states.
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Case II: In this case, as shown in Fig. 14.2(b), a large band gap
E
g
exists
(E
g
> 3 eV). There are no electrons in the conduction band, and therefore
no electrical conduction is possible. Note that the energy gap is so large
that electrons cannot be excited from the valence band to the conduction
band by thermal excitation. This is the case of insulators.
Case III: This situation is shown in Fig. 14.2(c). Here a finite but small
band gap (E
g
< 3 eV) exists. Because of the small band gap, at room
temperature some electrons from valence band can acquire enough
energy to cross the energy gap and enter the conduction band. These
electrons (though small in numbers) can move in the conduction band.
Hence, the resistance of semiconductors is not as high as that of the
insulators.
In this section we have made a broad classification of metals,
conductors and semiconductors. In the section which follows you will
learn the conduction process in semiconductors.
14.3 INTRINSIC SEMICONDUCTOR
We shall take the most common case of Ge and Si whose lattice structure
is shown in Fig. 14.3. These structures are called the diamond-like
structures. Each atom is surr
ounded by four near
est neighbours. We
know that Si and Ge have four valence electrons. In its crystalline
structure, every Si or Ge atom tends to share one of its four valence
electrons with each of its four nearest neighbour atoms, and also to take
share of one electron from each such neighbour. These shar
ed electron
pairs are referred to as forming a covalent bond or simply a valence
bond
. The two shared electrons can be assumed to shuttle back-and-
forth between the associated atoms holding them together strongly.
Figure 14.4 schematically shows the 2-dimensional representation of Si
or Ge structure shown in Fig. 14.3 which overemphasises the covalent
bond. It shows an idealised picture in which no bonds are broken (all
bonds are intact). Such a situation arises at low
temperatures. As the temperature increases, more
thermal energy becomes available to these electrons
and some of these electrons may break–away
(becoming free electrons contributing to conduction).
The thermal energy effectively ionises only a few atoms
in the crystalline lattice and creates a
vacancy in the
bond as shown in Fig. 14.5(a). The neighbourhood,
from which the free electron (with charge –q) has come
out leaves a vacancy with an effective charge (+q). This
vacancy with the effective positive electronic charge is
called a hole. The hole behaves as an apparent free
particle with effective positive charge.
In intrinsic semiconductors, the number of free
electrons, n
e
is equal to the number of holes, n
h
. That is
n
e
= n
h
= n
i
(14.1)
where n
i
is called intrinsic carrier concentration.
Semiconductors posses the unique property in
which, apart from electrons, the holes also move.
FIGURE 14.3 Three-dimensional dia-
mond-like crystal structure for Carbon,
Silicon or Germanium with
respective lattice spacing a equal
to 3.56, 5.43 and 5.66 Å.
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Suppose there is a hole at site 1 as shown in
Fig. 14.5(a). The movement of holes can be
visualised as shown in Fig. 14.5(b). An electron
from the covalent bond at site 2 may jump to
the vacant site 1 (hole). Thus, after such a jump,
the hole is at site 2 and the site 1 has now an
electron. Therefore, apparently, the hole has
moved from site 1 to site 2. Note that the electron
originally set free [Fig. 14.5(a)] is not
involved
in this process of hole motion. The free electron
moves completely independently as conduction
electron and gives rise to an electron current, I
e
under an applied electric field. Remember that
the motion of hole is only a convenient way of
describing the actual motion of bound electrons,
whenever there is an empty bond anywhere in
the crystal. Under the action of an electric field,
these holes move towards negative potential
giving the hole current, I
h
. The total current, I is
thus the sum of the electron current I
e
and the
hole current I
h
:
I = I
e
+ I
h
(14.2)
It may be noted that apart from the process of generation of conduction
electrons and holes, a simultaneous process of recombination occurs in
which the electrons recombine with the holes. At equilibrium, the rate of
generation is equal to the rate of recombination of charge carriers. The
recombination occurs due to an electron colliding with a hole.
FIGURE 14.4 Schematic two-dimensional
representation of Si or Ge structure showing
covalent bonds at low temperature
(all bonds intact). +4 symbol
indicates inner cores of Si or Ge.
FIGURE 14.5 (a) Schematic model of generation of hole at site 1 and conduction electron
due to thermal energy at moderate temperatures. (b) Simplified representation of
possible thermal motion of a hole. The electron from the lower left hand covalent bond
(site 2) goes to the earlier hole site1, leaving a hole at its site indicating an
apparent movement of the hole from site 1 to site 2.
(a) (b)
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EXAMPLE 14.1
An intrinsic semiconductor
will behave like an insulator at
T = 0 K as shown in Fig. 14.6(a).
It is the thermal energy at
higher temperatures (T > 0K),
which excites some electrons
from the valence band to the
conduction band. These
thermally excited electrons at
T > 0 K, partially occupy the
conduction band. Therefore,
the energy-band diagram of an
intrinsic semiconductor will be
as shown in Fig. 14.6(b). Here,
some electrons are shown in
the conduction band. These
have come from the valence
band leaving equal number of
holes there.
Example 14.1 C, Si and Ge have same lattice structure. Why is C
insulator while Si and Ge intrinsic semiconductors?
Solution The 4 bonding electrons of C, Si or Ge lie, respectively, in
the second, third and fourth orbit. Hence, energy required to take
out an electron from these atoms (i.e., ionisation energy E
g
) will be
least for Ge, followed by Si and highest for C. Hence, number of free
electrons for conduction in Ge and Si are significant but negligibly
small for C.
14.4 EXTRINSIC SEMICONDUCTOR
The conductivity of an intrinsic semiconductor depends on its
temperature, but at room temperature its conductivity is very low. As
such, no important electronic devices can be developed using these
semiconductors. Hence there is a necessity of improving their
conductivity. This can be done by making use of impurities.
When a small amount, say, a few parts per million (ppm), of a suitable
impurity is added to the pure semiconductor, the conductivity of the
semiconductor is increased manifold. Such materials are known as
extrinsic semiconductors or impurity semiconductors. The deliberate
addition of a desirable impurity is called doping and the impurity atoms
are called dopants. Such a material is also called a doped semiconductor.
The dopant has to be such that it does not distort the original pure
semiconductor lattice. It occupies only a very few of the original
semiconductor atom sites in the crystal. A necessary condition to attain
this is that the sizes of the dopant and the semiconductor atoms should
be nearly the same.
There are two types of dopants used in doping the tetravalent Si
or Ge:
(i) Pentavalent (valency 5); like Arsenic (As), Antimony (Sb), Phosphorous
(P), etc.
FIGURE 14.6 (a) An intrinsic semiconductor at T = 0 K
behaves like insulator. (b) At T > 0 K, four thermally generated
electron-hole pairs. The filled circles ( ) represent electrons
and empty circles ( ) represent holes.
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(ii) Trivalent (valency 3); like Indium (In),
Boron (B), Aluminium (Al), etc.
We shall now discuss how the doping
changes the number of charge carriers (and
hence the conductivity) of semiconductors.
Si or Ge belongs to the fourth group in the
Periodic table and, therefore, we choose the
dopant element from nearby fifth or third
group, expecting and taking care that the
size of the dopant atom is nearly the same as
that of Si or Ge. Interestingly, the pentavalent
and trivalent dopants in Si or Ge give two
entirely different types of semiconductors as
discussed below.
(i) n-type semiconductor
Suppose we dope Si or Ge with a pentavalent
element as shown in Fig. 14.7. When an atom
of +5 valency element occupies the position
of an atom in the crystal lattice of Si, four of
its electrons bond with the four silicon
neighbours while the fifth remains very
weakly bound to its parent atom. This is
because the four electrons participating in
bonding are seen as part of the effective core
of the atom by the fifth electron. As a result
the ionisation energy required to set this
electron free is very small and even at room
temperature it will be free to move in the
lattice of the semiconductor. For example, the
energy required is ~ 0.01 eV for germanium,
and 0.05 eV for silicon, to separate this
electron from its atom. This is in contrast to the energy required to jump
the forbidden band (about 0.72 eV for germanium and about 1.1 eV for
silicon) at room temperature in the intrinsic semiconductor. Thus, the
pentavalent dopant is donating one extra electron for conduction and
hence is known as donor impurity. The number of electrons made
available for conduction by dopant atoms depends strongly upon the
doping level and is independent of any increase in ambient temperature.
On the other hand, the number of free electrons (with an equal number
of holes) generated by Si atoms, increases weakly with temperature.
In a doped semiconductor the total number of conduction electrons
n
e
is due to the electrons contributed by donors and those generated
intrinsically, while the total number of holes n
h
is only due to the holes
from the intrinsic source. But the rate of recombination of holes would
increase due to the increase in the number of electrons. As a result, the
number of holes would get reduced further.
Thus, with proper level of doping the number of conduction electrons
can be made much larger than the number of holes. Hence in an extrinsic
FIGURE 14.7 (a) Pentavalent donor atom (As, Sb,
P, etc.) doped for tetravalent Si or Ge giving n-
type semiconductor, and (b) Commonly used
schematic representation of n-type material
which shows only the fixed cores of the
substituent donors with one additional effective
positive charge and its associated extra electron.
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semiconductor doped with pentavalent impurity, electrons
become the majority carriers and holes the minority carriers.
These semiconductors are, therefore, known as n-type
semiconductors. For n-type semiconductors, we have,
n
e
>> n
h
(14.3)
(ii) p-type semiconductor
This is obtained when Si or Ge is doped with a trivalent impurity
like Al, B, In, etc. The dopant has one valence electron less than
Si or Ge and, therefore, this atom can form covalent bonds with
neighbouring three Si atoms but does not have any electron to
offer to the fourth Si atom. So the bond between the fourth
neighbour and the trivalent atom has a vacancy or hole as shown
in Fig. 14.8. Since the neighbouring Si atom in the lattice wants
an electron in place of a hole, an electron in the outer orbit of
an atom in the neighbourhood may jump to fill this vacancy,
leaving a vacancy or hole at its own site. Thus the hole is
available for conduction. Note that the trivalent foreign atom
becomes effectively negatively charged when it shares fourth
electron with neighbouring Si atom. Therefore, the dopant atom
of p-type material can be treated as core of one negative charge
along with its associated hole as shown in Fig. 14.8(b). It is
obvious that one acceptor atom gives one hole. These holes are
in addition to the intrinsically generated holes while the source
of conduction electrons is only intrinsic generation. Thus, for
such a material, the holes are the majority carriers and electrons
are minority carriers. Therefore, extrinsic semiconductors doped
with trivalent impurity are called p-type semiconductors. For
p-type semiconductors, the recombination process will reduce
the number (n
i
)of intrinsically generated electrons to n
e
. We
have, for p-type semiconductors
n
h
>> n
e
(14.4)
Note that the crystal maintains an overall charge neutrality
as the charge of additional charge carriers is just equal and
opposite to that of the ionised cores in the lattice.
In extrinsic semiconductors, because of the abundance of
majority current carriers, the minority carriers produced
thermally have more chance of meeting majority carriers and
thus getting destroyed. Hence, the dopant, by adding a large number of
current carriers of one type, which become the majority carriers, indirectly
helps to reduce the intrinsic concentration of minority carriers.
The semiconductor’s energy band structure is affected by doping. In
the case of extrinsic semiconductors, additional energy states due to donor
impurities (E
D
) and acceptor impurities (E
A
) also exist. In the energy band
diagram of n-type Si semiconductor, the donor energy level E
D
is slightly
below the bottom E
C
of the conduction band and electrons from this level
move into the conduction band with very small supply of energy. At room
temperature, most of the donor atoms get ionised but very few (~10
12
)
atoms of Si get ionised. So the conduction band will have most electrons
coming from the donor impurities, as shown in Fig. 14.9(a). Similarly,
FIGURE 14.8 (a) Trivalent
acceptor atom (In, Al, B etc.)
doped in tetravalent Si or Ge
lattice giving p-type semicon-
ductor. (b) Commonly used
schematic representation of
p-type material which shows
only the fixed core of the
substituent acceptor with
one effective additional
negative charge and its
associated hole.
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EXAMPLE 14.2
for p-type semiconductor, the acceptor energy level E
A
is slightly above
the top E
V
of the valence band as shown in Fig. 14.9(b). With very small
supply of energy an electron from the valence band can jump to the level
E
A
and ionise the acceptor negatively. (Alternately, we can also say that
with very small supply of energy the hole from level E
A
sinks down into
the valence band. Electrons rise up and holes fall down when they gain
external energy.) At room temperature, most of the acceptor atoms get
ionised leaving holes in the valence band. Thus at room temperature the
density of holes in the valence band is predominantly due to impurity in
the extrinsic semiconductor. The electron and hole concentration in a
semiconductor in thermal equilibrium is given by
n
e
n
h
= n
i
2
(14.5)
Though the above description is grossly approximate and
hypothetical, it helps in understanding the difference between metals,
insulators and semiconductors (extrinsic and intrinsic) in a simple
manner. The difference in the resistivity of C, Si and Ge depends upon
the energy gap between their conduction and valence bands. For C
(diamond), Si and Ge, the energy gaps are 5.4 eV, 1.1 eV and 0.7 eV,
respectively. Sn also is a group IV element but it is a metal because the
energy gap in its case is 0 eV.
FIGURE 14.9 Energy bands of (a) n-type semiconductor at T > 0K, (b) p-type
semiconductor at T > 0K.
Example 14.2 Suppose a pure Si crystal has 5 × 10
28
atoms m
–3
. It is
doped by 1 ppm concentration of pentavalent As. Calculate the
number of electrons and holes. Given that n
i
=1.5 × 10
16
m
–3
.
Solution Note that thermally generated electrons (n
i
~10
16
m
–3
) are
negligibly small as compared to those produced by doping.
Therefore, n
e
≈≈
≈≈
≈
N
D
.
Since n
e
n
h
= n
i
2
, The number of holes
n
h
= (2.25 × 10
32
)/(5 ×10
22
)
~ 4.5 × 10
9
m
–3
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14.5 p-n JUNCTION
A p-n junction is the basic building block of many semiconductor devices
like diodes, transistor, etc. A clear understanding of the junction behaviour
is important to analyse the working of other semiconductor devices.
We will now try to understand how a junction is formed and how the
junction behaves under the influence of external applied voltage (also
called bias).
14.5.1 p-n junction formation
Consider a thin p-type silicon (p-Si) semiconductor wafer. By adding
precisely a small quantity of pentavelent impurity, part of the p-Si wafer
can be converted into n-Si. There are several processes by which a
semiconductor can be formed. The wafer now contains p-region and
n-region and a metallurgical junction between p-, and n- region.
Two important processes occur during the formation of a p-n junction:
diffusion and drift. We know that in an n-type semiconductor, the
concentration of electrons (number of electrons per unit volume) is more
compared to the concentration of holes. Similarly, in a p-type
semiconductor, the concentration of holes is more than the concentration
of electrons. During the formation of p-n junction, and due to the
concentration gradient across p-, and n- sides, holes diffuse from p-side
to n-side (p → n) and electrons diffuse from n-side to p-side (n → p). This
motion of charge carries gives rise to diffusion current across the junction.
When an electron diffuses from n → p, it leaves behind an ionised
donor on n-side. This ionised donor (positive charge) is immobile as it is
bonded to the surrounding atoms. As the electrons continue to diffuse
from n → p, a layer of positive charge (or positive space-charge region) on
n-side of the junction is developed.
Similarly, when a hole diffuses from p → n due to the concentration
gradient, it leaves behind an ionised acceptor (negative charge) which is
immobile. As the holes continue to diffuse, a layer of negative charge (or
negative space-charge region) on the p-side of the junction is developed.
This space-charge region on either side of the junction together is known
as depletion region as the electrons and holes taking part in the initial
movement across the junction depleted the region of its
free charges (Fig. 14.10). The thickness of depletion region
is of the order of one-tenth of a micrometre. Due to the
positive space-charge region on n-side of the junction and
negative space charge region on p-side of the junction,
an electric field directed from positive charge towards
negative charge develops. Due to this field, an electron on
p-side of the junction moves to n-side and a hole on n-
side of the junction moves to p-side. The motion of charge
carriers due to the electric field is called drift. Thus a
drift current, which is opposite in direction to the diffusion
current (Fig. 14.10) starts.
FIGURE 14.10 p-n junction
formation process.
Formation and working of p-n junction diode
http://hyperphysics.phy-astr.gsu.edu/hbase/solids/pnjun.html
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EXAMPLE 14.3
Initially, diffusion current is large and drift current is small.
As the diffusion process continues, the space-charge regions
on either side of the junction extend, thus increasing the electric
field strength and hence drift current. This process continues
until the diffusion current equals the drift current. Thus a p-n
junction is formed. In a p-n junction under equilibrium there
is no net current.
The loss of electrons from the n-region and the gain of
electron by the p-region causes a difference of potential across
the junction of the two regions. The polarity of this potential is
such as to oppose further flow of carriers so that a condition of
equilibrium exists. Figure 14.11 shows the p-n junction at
equilibrium and the potential across the junction. The
n-material has lost electrons, and p material has acquired
electrons. The n material is thus positive relative to the p
material. Since this potential tends to prevent the movement of
electron from the n region into the p region, it is often called a
barrier potential.
Example 14.3 Can we take one slab of p-type semiconductor and
physically join it to another n-type semiconductor to get p-n junction?
Solution No! Any slab, howsoever flat, will have roughness much
larger than the inter-atomic crystal spacing (~2 to 3 Å) and hence
continuous contact at the atomic level will not be possible. The junction
will behave as a discontinuity for the flowing charge carriers.
14.6 SEMICONDUCTOR DIODE
A semiconductor diode [Fig. 14.12(a)] is basically a
p-n junction with metallic contacts provided at the
ends for the application of an external voltage. It is a
two terminal device. A p-n junction diode is
symbolically represented as shown in Fig. 14.12(b).
The direction of arrow indicates the conventional
direction of current (when the diode is under forward
bias). The equilibrium barrier potential can be altered
by applying an external voltage V across the diode.
The situation of p-n junction diode under equilibrium
(without bias) is shown in Fig. 14.11(a) and (b).
14.6.1 p-n junction diode under forward bias
When an external voltage V is applied across a semiconductor diode such
that p-side is connected to the positive terminal of the battery and n-side
to the negative terminal [Fig. 14.13(a)], it is said to be forward biased.
The applied voltage mostly drops across the depletion region and the
voltage drop across the p-side and n-side of the junction is negligible.
(This is because the resistance of the depletion region – a region where
there are no charges – is very high compared to the resistance of n-side
and p-side.) The direction of the applied voltage (V) is opposite to the
FIGURE 14.11 (a) Diode under
equilibrium (V = 0), (b) Barrier
potential under no bias.
FIGURE 14.12 (a) Semiconductor diode,
(b) Symbol for p-n junction diode.
np
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built-in potential V
0
. As a result, the depletion layer width
decreases and the barrier height is reduced [Fig. 14.13(b)]. The
effective barrier height under forward bias is (V
0
– V).
If the applied voltage is small, the barrier potential will be
reduced only slightly below the equilibrium value, and only a
small number of carriers in the material—those that happen to
be in the uppermost energy levels—will possess enough energy
to cross the junction. So the current will be small. If we increase
the applied voltage significantly, the barrier height will be reduced
and more number of carriers will have the required energy. Thus
the current increases.
Due to the applied voltage, electrons from n-side cross the
depletion region and reach p-side (where they are minority
carries). Similarly, holes from p-side cross the junction and reach
the n-side (where they are minority carries). This process under
forward bias is known as minority carrier injection. At the
junction boundary, on each side, the minority carrier
concentration increases significantly compared to the locations
far from the junction.
Due to this concentration gradient, the injected electrons on
p-side diffuse from the junction edge of p-side to the other end
of p-side. Likewise, the injected holes on n-side diffuse from the
junction edge of n-side to the other end of n-side
(Fig. 14.14). This motion of charged carriers on either side
gives rise to current. The total diode forward current is sum
of hole diffusion current and conventional current due to
electron diffusion. The magnitude of this current is usually
in mA.
14.6.2 p-n junction diode under reverse bias
When an external voltage (V) is applied across the diode such
that n-side is positive and p-side is negative, it is said to be
reverse biased [Fig.14.15(a)]. The applied voltage mostly
drops across the depletion region. The direction of applied voltage is same
as the direction of barrier potential. As a result, the barrier height increases
and the depletion region widens due to the change in the electric field.
The effective barrier height under reverse bias is (V
0
+ V), [Fig. 14.15(b)].
This suppresses the flow of electrons from n → p and holes from p → n.
Thus, diffusion current, decreases enormously compared to the diode
under forward bias.
The electric field direction of the junction is such that if electrons on
p-side or holes on n-side in their random motion come close to the
junction, they will be swept to its majority zone. This drift of carriers
gives rise to current. The drift current is of the order of a few µA. This is
quite low because it is due to the motion of carriers from their minority
side to their majority side across the junction. The drift current is also
there under forward bias but it is negligible (µA) when compared with
current due to injected carriers which is usually in mA.
The diode reverse current is not very much dependent on the applied
voltage. Even a small voltage is sufficient to sweep the minority carriers
from one side of the junction to the other side of the junction. The current
FIGURE 14.13 (a) p-n
junction diode under forward
bias, (b) Barrier potential
(1) without battery, (2) Low
battery voltage, and (3) High
voltage battery.
FIGURE 14.14 Forward bias
minority carrier injection.
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is not limited by the magnitude of the applied voltage but is
limited due to the concentration of the minority carrier on either
side of the junction.
The current under reverse bias is essentially voltage
independent upto a critical reverse bias voltage, known as
breakdown voltage (V
br
). When V = V
br
, the diode reverse current
increases sharply. Even a slight increase in the bias voltage causes
large change in the current. If the reverse current is not limited by
an external circuit below the rated value (specified by the
manufacturer) the p-n junction will get destroyed. Once it exceeds
the rated value, the diode gets destroyed due to overheating. This
can happen even for the diode under forward bias, if the forward
current exceeds the rated value.
The circuit arrangement for studying the V-I characteristics
of a diode, (i.e., the variation of current as a function of applied
voltage) are shown in Fig. 14.16(a) and (b). The battery is connected
to the diode through a potentiometer (or reheostat) so that the
applied voltage to the diode can be changed. For different values
of voltages, the value of the current is noted. A graph between V
and I is obtained as in Fig. 14.16(c). Note that in forward bias
measurement, we use a milliammeter since the expected current is large
(as explained in the earlier section) while a micrometer is used in reverse
bias to measure the current. You can see in Fig. 14.16(c) that in forward
FIGURE 14.15 (a) Diode
under reverse bias,
(b) Barrier potential under
reverse bias.
FIGURE 14.16 Experimental circuit arrangement for studying V-I characteristics of
a p-n junction diode (a) in forward bias, (b) in reverse bias. (c) Typical V-I
characteristics of a silicon diode.
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EXAMPLE 14.4
bias, the current first increases very slowly, almost negligibly, till the
voltage across the diode crosses a certain value. After the characteristic
voltage, the diode current increases significantly (exponentially), even for
a very small increase in the diode bias voltage. This voltage is called the
threshold voltage or cut-in voltage (~0.2V for germanium diode and
~0.7 V for silicon diode).
For the diode in reverse bias, the current is very small (~µA) and almost
remains constant with change in bias. It is called reverse saturation
current. However, for special cases, at very high reverse bias (break down
voltage), the current suddenly increases. This special action of the diode
is discussed later in Section 14.8. The general purpose diode are not
used beyond the reverse saturation current region.
The above discussion shows that the p-n junction diode primerly
allows the flow of current only in one direction (forward bias). The forward
bias resistance is low as compared to the reverse bias resistance. This
property is used for rectification of ac voltages as discussed in the next
section. For diodes, we define a quantity called dynamic resistance as
the ratio of small change in voltage ∆V to a small change in current ∆I:
d
V
r
I
∆
=
∆
(14.6)
Example 14.4 The V-I characteristic of a silicon diode is shown in
the Fig. 14.17. Calculate the resistance of the diode at (a) I
D
= 15 mA
and (b) V
D
= –10 V.
FIGURE 14.17
Solution Considering the diode characteristics as a straight line
between I = 10 mA to I = 20 mA passing through the origin, we can
calculate the resistance using Ohm’s law.
(a) From the curve, at I = 20 mA, V = 0.8 V; I = 10 mA, V = 0.7 V
r
fb
= ∆V/∆I = 0.1V/10 mA = 10 Ω
(b) From the curve at V = –10 V, I = –1 µA,
Therefore,
r
rb
= 10 V/1µA= 1.0 × 10
7
Ω
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14.7 APPLICATION OF JUNCTION DIODE AS A RECTIFIER
From the V-I characteristic of a junction diode we see that it allows current
to pass only when it is forward biased. So if an alternating voltage is
applied across a diode the current flows only in that part of the cycle
when the diode is forward biased. This property
is used to rectify alternating voltages and the
circuit used for this purpose is called a rectifier.
If an alternating voltage is applied across a
diode in series with a load, a pulsating voltage will
appear across the load only during the half cycles
of the ac input during which the diode is forward
biased. Such rectifier circuit, as shown in
Fig. 14.18, is called a half-wave rectifier. The
secondary of a transformer supplies the desired
ac voltage across terminals A and B. When the
voltage at A is positive, the diode is forward biased
and it conducts. When A is negative, the diode is
reverse-biased and it does not conduct. The reverse
saturation current of a diode is negligible and can
be considered equal to zero for practical purposes.
(The reverse breakdown voltage of the diode must
be sufficiently higher than the peak ac voltage at
the secondary of the transformer to protect the
diode from reverse breakdown.)
Therefore, in the positive half-cycle of ac there
is a current through the load resistor R
L
and we
get an output voltage, as shown in Fig. 14.18(b),
whereas there is no current in the negative half-
cycle. In the next positive half-cycle, again we get
the output voltage. Thus, the output voltage, though still varying, is
restricted to only one direction and is said to be rectified. Since the
rectified output of this circuit is only for half of the input ac wave it is
called as half-wave rectifier.
The circuit using two diodes, shown in Fig. 14.19(a), gives output
rectified voltage corresponding to both the positive as well as negative
half of the ac cycle. Hence, it is known as full-wave rectifier. Here the
p-side of the two diodes are connected to the ends of the secondary of the
transformer. The n-side of the diodes are connected together and the
output is taken between this common point of diodes and the midpoint
of the secondary of the transformer. So for a full-wave rectifier the
secondary of the transformer is provided with a centre tapping and so it
is called centre-tap transformer. As can be seen from Fig.14.19(c) the
voltage rectified by each diode is only half the total secondary voltage.
Each diode rectifies only for half the cycle, but the two do so for alternate
cycles. Thus, the output between their common terminals and the centre-
tap of the transformer becomes a full-wave rectifier output. (Note that
there is another circuit of full wave rectifier which does not need a centre-
tap transformer but needs four diodes.) Suppose the input voltage to A
FIGURE 14.18 (a) Half-wave rectifier
circuit, (b) Input ac voltage and output
voltage waveforms from the rectifier circuit.
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with respect to the centre tap at any instant
is positive. It is clear that, at that instant,
voltage at B being out of phase will be
negative as shown in Fig.14.19(b). So, diode
D
1
gets forward biased and conducts (while
D
2
being reverse biased is not conducting).
Hence, during this positive half cycle we get
an output current (and a output voltage
across the load resistor R
L
) as shown in
Fig.14.19(c). In the course of the ac cycle
when the voltage at A becomes negative with
respect to centre tap, the voltage at B would
be positive. In this part of the cycle diode
D
1
would not conduct but diode D
2
would,
giving an output current and output
voltage (across R
L
) during the negative half
cycle of the input ac. Thus, we get output
voltage during both the positive as well as
the negative half of the cycle. Obviously,
this is a more efficient circuit for getting
rectified voltage or current than the half-
wave rectifier.
The rectified voltage is in the form of
pulses of the shape of half sinusoids.
Though it is unidirectional it does not have
a steady value. To get steady dc output
from the pulsating voltage normally a
capacitor is connected across the output
terminals (parallel to the load R
L
). One can
also use an inductor in series with R
L
for
the same purpose. Since these additional
circuits appear to filter out the ac ripple
and give a pure dc voltage, so they are
called filters.
Now we shall discuss the role of
capacitor in filtering. When the voltage
across the capacitor is rising, it gets
charged. If there is no external load, it remains charged to the peak voltage
of the rectified output. When there is a load, it gets discharged through
the load and the voltage across it begins to fall. In the next half-cycle of
rectified output it again gets charged to the peak value (Fig. 14.20). The
rate of fall of the voltage across the capacitor depends inversely upon the
product of capacitance C and the effective resistance R
L
used in the circuit
and is called the time constant. To make the time constant large value of
C should be large. So capacitor input filters use large capacitors. The
output voltage obtained by using capacitor input filter is nearer to the
peak voltage of the rectified voltage. This type of filter is most widely
used in power supplies.
FIGURE 14.19 (a) A Full-wave rectifier
circuit; (b) Input wave forms given to the
diode D
1
at A and to the diode D
2
at B;
(c) Output waveform across the
load R
L
connected in the full-wave
rectifier circuit.
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14.8 SPECIAL PURPOSE p-n JUNCTION DIODES
In the section, we shall discuss some devices which are basically junction
diodes but are developed for different applications.
14.8.1 Zener diode
It is a special purpose semiconductor diode, named after its inventor
C. Zener. It is designed to operate under reverse bias in the breakdown
region and used as a voltage regulator. The symbol for Zener diode is
shown in Fig. 14.21(a).
Zener diode is fabricated by heavily doping both p-, and
n- sides of the junction. Due to this, depletion region formed
is very thin (<10
–6
m) and the electric field of the junction is
extremely high (~5×10
6
V/m) even for a small reverse bias
voltage of about 5V. The I-V characteristics of a Zener diode is
shown in Fig. 14.21(b). It is seen that when the applied reverse
bias voltage(V) reaches the breakdown voltage (V
z
) of the Zener
diode, there is a large change in the current. Note that after
the breakdown voltage V
z
, a large change in the current can
be produced by almost insignificant change in the reverse bias
voltage. In other words, Zener voltage remains constant, even
though current through the Zener diode varies over a wide
range. This property of the Zener diode is used for regulating
supply voltages so that they are constant.
Let us understand how reverse current suddenly increases
at the breakdown voltage. We know that reverse current is
due to the flow of electrons (minority carriers) from p → n and
holes from n → p. As the reverse bias voltage is increased, the
electric field at the junction becomes significant. When the
reverse bias voltage V = V
z
, then the electric field strength is
high enough to pull valence electrons from the host atoms on
the p-side which are accelerated to n-side. These electrons
account for high current observed at the breakdown. The
emission of electrons from the host atoms due to the high
electric field is known as internal field emission or field
ionisation. The electric field required for field ionisation is of
the order of 10
6
V/m.
FIGURE 14.20 (a) A full-wave rectifier with capacitor filter, (b) Input and output
voltage of rectifier in (a).
FIGURE 14.21 Zener diode,
(a) symbol, (b) I-V
characteristics.
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EXAMPLE 14.5
FIGURE 14.22 Zener diode as DC
voltage regulator
Zener diode as a voltage regulator
We know that when the ac input voltage of a rectifier fluctuates, its rectified
output also fluctuates. To get a constant dc voltage from the dc
unregulated output of a rectifier, we use a Zener diode. The circuit diagram
of a voltage regulator using a Zener diode is shown in Fig. 14.22.
The unregulated dc voltage (filtered output of a
rectifier) is connected to the Zener diode through a series
resistance R
s
such that the Zener diode is reverse biased.
If the input voltage increases, the current through R
s
and Zener diode also increases. This increases the
voltage drop across R
s
without any change in the
voltage across the Zener diode. This is because in the
breakdown region, Zener voltage remains constant even
though the current through the Zener diode changes.
Similarly, if the input voltage decreases, the current
through R
s
and Zener diode also decreases. The voltage
drop across R
s
decreases without any change in the
voltage across the Zener diode. Thus any increase/
decrease in the input voltage results in, increase/
decrease of the voltage drop across R
s
without any
change in voltage across the Zener diode. Thus the Zener diode acts as a
voltage regulator. We have to select the Zener diode according to the
required output voltage and accordingly the series resistance R
s
.
Example 14.5 In a Zener regulated power supply a Zener diode with
V
Z
= 6.0 V is used for regulation. The load current is to be 4.0 mA and
the unregulated input is 10.0 V. What should be the value of series
resistor R
S
?
Solution
The value of R
S
should be such that the current through the Zener
diode is much larger than the load current. This is to have good load
regulation. Choose Zener current as five times the load current, i.e.,
I
Z
= 20 mA. The total current through R
S
is, therefore, 24 mA. The
voltage drop across R
S
is 10.0 – 6.0 = 4.0 V. This gives
R
S
= 4.0V/(24 × 10
–3
) A = 167 Ω. The nearest value of carbon resistor
is 150 Ω. So, a series resistor of 150 Ω is appropriate. Note that slight
variation in the value of the resistor does not matter, what is important
is that the current I
Z
should be sufficiently larger than I
L
.
14.8.2 Optoelectronic junction devices
We have seen so far, how a semiconductor diode behaves under applied
electrical inputs. In this section, we learn about semiconductor diodes in
which carriers are generated by photons (photo-excitation). All these
devices are called optoelectronic devices. We shall study the functioning
of the following optoelectronic devices:
(i) Photodiodes used for detecting optical signal (photodetectors).
(ii) Light emitting diodes (LED) which convert electrical energy into light.
(iii) Photovoltaic devices which convert optical radiation into electricity
(solar cells).
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EXAMPLE 14.6
(i) Photodiode
A Photodiode is again a special purpose p-n
junction diode fabricated with a transparent
window to allow light to fall on the diode. It is
operated under reverse bias. When the photodiode
is illuminated with light (photons) with energy (h
ν
)
greater than the energy gap (E
g
) of the
semiconductor, then electron-hole pairs are
generated due to the absorption of photons. The
diode is fabricated such that the generation of
e-h pairs takes place in or near the depletion region
of the diode. Due to electric field of the junction,
electrons and holes are separated before they
recombine. The direction of the electric field is such
that electrons reach n-side and holes reach p-side.
Electrons are collected on n-side and holes are
collected on p-side giving rise to an emf. When an
external load is connected, current flows. The
magnitude of the photocurrent depends on the
intensity of incident light (photocurrent is
proportional to incident light intensity).
It is easier to observe the change in the current
with change in the light intensity, if a reverse bias
is applied. Thus photodiode can be used as a
photodetector to detect optical signals. The circuit
diagram used for the measurement of I-V
characteristics of a photodiode is shown in
Fig. 14.23(a) and a typical I-V characteristics in
Fig. 14.23(b).
Example 14.6 The current in the forward bias is known to be more
(~mA) than the current in the reverse bias (~µA). What is the reason
then to operate the photodiodes in reverse bias?
Solution Consider the case of an n-type semiconductor. Obviously,
the majority carrier density (n) is considerably larger than the minority
hole density p (i.e., n >> p). On illumination, let the excess electrons
and holes generated be ∆n and ∆p, respectively:
n
′
= n + ∆n
p
′
= p + ∆p
Here n
′
and p
′
are the electron and hole concentrations* at any
particular illumination and n and p are carriers concentration when
there is no illumination. Remember ∆n = ∆p and n >> p. Hence, the
FIGURE 14.23 (a) An illuminated
photodiode under reverse bias , (b) I-V
characteristics of a photodiode for different
illumination intensity I
4
> I
3
> I
2
> I
1
.
* Note that, to create an e-h pair, we spend some energy (photoexcitation, thermal
excitation, etc.). Therefore when an electron and hole recombine the energy is
released in the form of light (radiative recombination) or heat (non-radiative
recombination). It depends on semiconductor and the method of fabrication of
the p-n junction. For the fabrication of LEDs, semiconductors like GaAs, GaAs-
GaP are used in which radiative recombination dominates.
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EXAMPLE 14.6
fractional change in the majority carriers (i.e., ∆n/n) would be much
less than that in the minority carriers (i.e., ∆p/p). In general, we can
state that the fractional change due to the photo-effects on the
minority carrier dominated reverse bias current is more easily
measurable than the fractional change in the forward bias current.
Hence, photodiodes are preferably used in the reverse bias condition
for measuring light intensity.
(ii) Light emitting diode
It is a heavily doped p-n junction which under forward bias emits
spontaneous radiation. The diode is encapsulated with a transparent
cover so that emitted light can come out.
When the diode is forward biased, electrons are sent from n → p (where
they are minority carriers) and holes are sent from p → n (where they are
minority carriers). At the junction boundary the concentration of minority
carriers increases compared to the equilibrium concentration (i.e., when
there is no bias). Thus at the junction boundary on either side of the
junction, excess minority carriers are there which recombine with majority
carriers near the junction. On recombination, the energy is released in
the form of photons. Photons with energy equal to or slightly less than
the band gap are emitted. When the forward current of the diode is small,
the intensity of light emitted is small. As the forward current increases,
intensity of light increases and reaches a maximum. Further increase in
the forward current results in decrease of light intensity. LEDs are biased
such that the light emitting efficiency is maximum.
The V-I characteristics of a LED is similar to that of a Si junction
diode. But the threshold voltages are much higher and slightly different
for each colour. The reverse breakdown voltages of LEDs are very low,
typically around 5V. So care should be taken that high reverse voltages
do not appear across them.
LEDs that can emit red, yellow, orange, green and blue light are
commercially available. The semiconductor used for fabrication of visible
LEDs must at least have a band gap of 1.8 eV (spectral range of visible
light is from about 0.4 µm to 0.7 µm, i.e., from about 3 eV to 1.8 eV). The
compound semiconductor Gallium Arsenide – Phosphide (GaAs
1–x
P
x
) is
used for making LEDs of different colours. GaAs
0.6
P
0.4
(E
g
~ 1.9 eV) is
used for red LED. GaAs (E
g
~ 1.4 eV) is used for making infrared LED.
These LEDs find extensive use in remote controls, burglar alarm systems,
optical communication, etc. Extensive research is being done for
developing white LEDs which can replace incandescent lamps.
LEDs have the following advantages over conventional incandescent
low power lamps:
(i) Low operational voltage and less power.
(ii) Fast action and no warm-up time required.
(iii) The bandwidth of emitted light is 100 Å to 500 Å or in other words it
is nearly (but not exactly) monochromatic.
(iv) Long life and ruggedness.
(v) Fast on-off switching capability.
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(iii) Solar cell
A solar cell is basically a p-n junction which
generates emf when solar radiation falls on the
p-n junction. It works on the same principle
(photovoltaic effect) as the photodiode, except that
no external bias is applied and the junction area
is kept much larger for solar radiation to be
incident because we are interested in more power.
A simple p-n junction solar cell is shown in
Fig. 14.24.
A p-Si wafer of about 300 µm is taken over
which a thin layer (~0.3 µm) of n-Si is grown on
one-side by diffusion process. The other side of
p-Si is coated with a metal (back contact). On the
top of n-Si layer, metal finger electrode (or metallic
grid) is deposited. This acts as a front contact. The
metallic grid occupies only a very small fraction
of the cell area (<15%) so that light can be incident
on the cell from the top.
The generation of emf by a solar cell, when light falls on, it is due to
the following three basic processes: generation, separation and collection—
(i) generation of e-h pairs due to light (with h
ν
> E
g
)
close to the junction; (ii) separation of electrons and
holes due to electric field of the depletion region.
Electrons are swept to n-side and holes to p-side;
(iii) the electrons reaching the n-side are collected by
the front contact and holes reaching p-side are collected
by the back contact. Thus p-side becomes positive and
n-side becomes negative giving rise to photovoltage.
When an external load is connected as shown in
the Fig. 14.25(a) a photocurrent I
L
flows through the
load. A typical I-V characteristics of a solar cell is shown
in the Fig. 14.25(b).
Note that the I – V characteristics of solar cell is
drawn in the fourth quadrant of the coordinate axes.
This is because a solar cell does not draw current but
supplies the same to the load.
Semiconductors with band gap close to 1.5 eV are
ideal materials for solar cell fabrication. Solar cells are
made with semiconductors like Si (E
g
= 1.1 eV), GaAs
(E
g
= 1.43 eV), CdTe (E
g
= 1.45 eV), CuInSe
2
(E
g
= 1.04
eV), etc. The important criteria for the selection of a
material for solar cell fabrication are (i) band gap (~1.0
to 1.8 eV), (ii) high optical absorption (~10
4
cm
–1
), (iii)
electrical conductivity, (iv) availability of the raw
material, and (v) cost. Note that sunlight is not always
required for a solar cell. Any light with photon energies
greater than the bandgap will do. Solar cells are used
to power electronic devices in satellites and space
vehicles and also as power supply to some calculators. Production of
low-cost photovoltaic cells for large-scale solar energy is a topic
for research.
FIGURE 14.24 (a) Typical p-n junction
solar cell; (b) Cross-sectional view.
FIGURE 14.25 (a) A typical
illuminated p-n junction solar cell;
(b) I-V characteristics of a solar cell.
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EXAMPLE 14.7
Example 14.7 Why are Si and GaAs are preferred materials for
solar cells?
Solution The solar radiation spectrum received by us is shown in
Fig. 14.26.
FIGURE 14.26
The maxima is near 1.5 eV. For photo-excitation, h
ν
> E
g
. Hence,
semiconductor with band gap ~1.5 eV or lower is likely to give better
solar conversion efficiency. Silicon has E
g
~ 1.1 eV while for GaAs it is
~1.53 eV. In fact, GaAs is better (in spite of its higher band gap) than
Si because of its relatively higher absorption coefficient. If we choose
materials like CdS or CdSe (E
g
~ 2.4 eV), we can use only the high
energy component of the solar energy for photo-conversion and a
significant part of energy will be of no use.
The question arises: why we do not use material like PbS (E
g
~ 0.4 eV)
which satisfy the condition h
ν
> E
g
for
ν
maxima corresponding to the
solar radiation spectra? If we do so, most of the solar radiation will be
absorbed on the top-layer of solar cell and will not reach in or near
the depletion region. For effective electron-hole separation, due to
the junction field, we want the photo-generation to occur in the
junction region only.
14.9 DIGITAL ELECTRONICS AND LOGIC GATES
In electronics circuits like amplifiers, oscillators, introduced to you in
earlier sections, the signal (current or voltage) has been in the form of
continuous, time-varying voltage or current. Such signals are called
continuous or analog signals. A typical analog signal is shown in Figure.
14.27(a). Fig. 14.27(b) shows a pulse waveform in which only discrete
values of voltages are possible. It is convenient to use binary numbers
to represent such signals. A binary number has only two digits ‘0’ (say,
0V) and ‘1’ (say, 5V). In digital electronics we use only these two levels of
voltage as shown in Fig. 14.27(b). Such signals are called Digital Signals.
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FIGURE 14.27 (a) Analog signal, (b) Digital signal.
Input Output
A Y
0 1
1 0
(b)
FIGURE 14.28
(a) Logic symbol,
(b) Truth table of
NOT gate.
In digital circuits only two values (represented by 0 or 1) of the input and
output voltage are permissible.
This section is intended to provide the first step in our understanding
of digital electronics. We shall restrict our study to some basic building
blocks of digital electronics (called Logic Gates) which process the digital
signals in a specific manner. Logic gates are used in calculators, digital
watches, computers, robots, industrial control systems, and in
telecommunications.
A light switch in your house can be used as an example of a digital
circuit. The light is either ON or OFF depending on the switch position.
When the light is ON, the output value is ‘1’. When the light is OFF the
output value is ‘0’. The inputs are the position of the light switch. The
switch is placed either in the ON or OFF position to activate the light.
14.9.1 Logic gates
A gate is a digital circuit that follows curtain logical relationship
between the input and output voltages. Therefore, they are generally
known as logic gates — gates because they control the flow of
information. The five common logic gates used are NOT, AND, OR,
NAND, NOR. Each logic gate is indicated by a symbol and its function
is defined by a truth table that shows all the possible input logic level
combinations with their respective output logic levels. Truth tables
help understand the behaviour of logic gates. These logic gates can be
realised using semiconductor devices.
(i) NOT gate
This is the most basic gate, with one input and one output. It produces
a ‘1’ output if the input is ‘0’ and vice-versa. That is, it produces an
inverted version of the input at its output. This is why it is also known
as an inverter. The commonly used symbol together with the truth
table for this gate is given in Fig. 14.28.
(ii) OR Gate
An OR gate has two or more inputs with one output. The logic symbol
and truth table are shown in Fig. 14.29. The output Y is 1 when either
input A or input B or both are 1s, that is, if any of the input is high, the
output is high.
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EXAMPLE 14.8
Apart from carrying out the above mathematical logic operation, this
gate can be used for modifying the pulse waveform as explained in the
following example.
Example 14.8 Justify the output waveform (Y) of the OR gate for the
following inputs A and B given in Fig. 14.30.
Solution Note the following:
• At t < t
1
; A = 0, B = 0; Hence Y = 0
• For t
1
to t
2
; A = 1, B = 0; Hence Y = 1
• For t
2
to t
3
; A = 1, B = 1; Hence Y = 1
• For t
3
to t
4
; A = 0, B = 1; Hence Y = 1
• For t
4
to t
5
; A = 0, B = 0; Hence Y = 0
• For t
5
to t
6
; A = 1, B = 0; Hence Y = 1
• For t > t
6
; A = 0, B = 1; Hence Y = 1
Therefore the waveform Y will be as shown in the Fig. 14.30.
FIGURE 14.30
(iii) AND Gate
An AND gate has two or more inputs and one output. The output Y of
AND gate is 1 only when input A and input B are both 1. The logic
symbol and truth table for this gate are given in Fig. 14.31
FIGURE 14.31 (a) Logic symbol, (b) Truth table of AND gate.
Input Output
A B Y
0 0 0
0 1 0
1 0 0
1 1 1
(b)
(b)
FIGURE 14.29 (a) Logic symbol (b) Truth table of OR gate.
Input Output
A B Y
0 0 0
0 1 1
1 0 1
1 1 1
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EXAMPLE 14.9
EXAMPLE 14.10
Input Output
A B Y
0 0 1
0 1 1
1 0 1
1 1 0
(b)
Example 14.9 Take A and B input waveforms similar to that in
Example 14.8. Sketch the output waveform obtained from AND gate.
Solution
• For t ≤ t
1
; A = 0, B = 0; Hence Y = 0
• For t
1
to t
2
; A = 1, B = 0; Hence Y = 0
• For t
2
to t
3
; A = 1, B = 1; Hence Y = 1
• For t
3
to t
4
; A = 0, B = 1; Hence Y = 0
• For t
4
to t
5
; A = 0, B = 0; Hence Y = 0
• For t
5
to t
6
; A = 1, B = 0; Hence Y = 0
• For t > t
6
; A = 0, B = 1; Hence Y = 0
Based on the above, the output waveform for AND gate can be drawn
as given below.
FIGURE 14.32
(iv) NAND Gate
This is an AND gate followed by a NOT gate. If inputs A and B are both
‘1’, the output Y is not ‘1’. The gate gets its name from this NOT AND
behaviour. Figure 14.33 shows the symbol and truth table of NAND gate.
NAND gates are also called Universal Gates since by using these
gates you can realise other basic gates like OR, AND and NOT (Exercises
14.12 and 14.13).
FIGURE 14.33 (a) Logic symbol, (b) Truth table of NAND gate.
Example 14.10 Sketch the output Y from a NAND gate having inputs
A and B given below:
Solution
• For t < t
1
; A = 1, B = 1; Hence Y = 0
• For t
1
to t
2
; A = 0, B = 0; Hence Y = 1
• For t
2
to t
3
; A = 0, B = 1; Hence Y = 1
• For t
3
to t
4
; A = 1, B = 0; Hence Y = 1
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FASTER AND SMALLER: THE FUTURE OF COMPUTER TECHNOLOGY
The Integrated Chip (IC) is at the heart of all computer systems. In fact ICs are found in
almost all electrical devices like cars, televisions, CD players, cell phones etc. The
miniaturisation that made the modern personal computer possible could never have
happened without the IC. ICs are electronic devices that contain many transistors, resistors,
capacitors, connecting wires – all in one package. You must have heard of the
EXAMPLE 14.10
• For t
4
to t
5
; A = 1, B = 1; Hence Y = 0
• For t
5
to t
6
; A = 0, B = 0; Hence Y = 1
• For t > t
6
; A = 0, B = 1; Hence Y = 1
FIGURE 14.34
(v) NOR Gate
It has two or more inputs and one output. A NOT- operation applied
after OR gate gives a NOT-OR gate (or simply NOR gate). Its output Y is
‘1’ only when both inputs A and B are ‘0’, i.e., neither one input nor the
other is ‘1’. The symbol and truth table for NOR gate is given in
Fig. 14.35.
FIGURE 14.35 (a) Logic symbol, (b) Truth table of NOR gate.
NOR gates are considered as universal gates because you can obtain
all the gates like AND, OR, NOT by using only NOR gates (Exercises 14.14
and 14.15).
Input Output
A B Y
0 0 1
0 1 0
1 0 0
1 1 0
(b)
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microprocessor. The micr
oprocessor is an IC that pr
ocesses all information in a computer,
like keeping track of what keys are pressed, running programmes, games etc. The IC was
first invented by Jack Kilky at Texas Instruments in 1958 and he was awarded Nobel Prize
for this in 2000. ICs are produced on a piece of semiconductor crystal (or chip) by a process
called photolithography. Thus, the entire Information Technology (IT) industry hinges on
semiconductors. Over the years, the complexity of ICs has increased while the size of its
features continued to shrink. In the past five decades, a dramatic miniaturisation in
computer technology has made modern day computers faster and smaller. In the 1970s,
Gordon Moore, co-founder of INTEL, pointed out that the memory capacity of a chip (IC)
approximately doubled every one and a half years. This is popularly known as Moore’s
law. The number of transistors per chip has risen exponentially and each year computers
are becoming more powerful, yet cheaper than the year before. It is intimated from current
trends that the computers available in 2020 will operate at 40 GHz (40,000 MHz) and
would be much smaller, more efficient and less expensive than present day computers.
The explosive growth in the semiconductor industry and computer technology is best
expressed by a famous quote from Gordon Moore: “If the auto industry advanced as rapidly
as the semiconductor industry, a Rolls Royce would get half a million miles per gallon, and
it would be cheaper to throw it away than to park it”.
SUMMARY
1. Semiconductors are the basic materials used in the present solid state
electronic devices like diode, transistor, ICs, etc.
2. Lattice structure and the atomic structure of constituent elements
decide whether a particular material will be insulator, metal or
semiconductor.
3. Metals have low resistivity (10
–2
to 10
–8
Ωm), insulators have very high
resistivity (>10
8
Ωm
–1
), while semiconductors have intermediate values
of resistivity.
4. Semiconductors are elemental (Si, Ge) as well as compound (GaAs,
CdS, etc.).
5. Pure semiconductors are called ‘intrinsic semiconductors’. The presence
of charge carriers (electrons and holes) is an ‘intrinsic’ property of the
material and these are obtained as a result of thermal excitation. The
number of electrons (n
e
) is equal to the number of holes (n
h
) in intrinsic
conductors. Holes are essentially electron vacancies with an effective
positive charge.
6. The number of charge carriers can be changed by ‘doping’ of a suitable
impurity in pure semiconductors. Such semiconductors are known as
extrinsic semiconductors. These are of two types (n-type and p-type).
7. In n-type semiconductors, n
e
>> n
h
while in p-type semiconductors n
h
>> n
e
.
8. n-type semiconducting Si or Ge is obtained by doping with pentavalent
atoms (donors) like As, Sb, P, etc., while p-type Si or Ge can be obtained
by doping with trivalent atom (acceptors) like B, Al, In etc.
9. n
e
n
h
= n
i
2
in all cases. Further, the material possesses an overall charge
neutrality.
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10. There are two distinct band of energies (called valence band and
conduction band) in which the electrons in a material lie. Valence
band energies are low as compared to conduction band energies. All
energy levels in the valence band are filled while energy levels in the
conduction band may be fully empty or partially filled. The electrons in
the conduction band are free to move in a solid and are responsible for
the conductivity. The extent of conductivity depends upon the energy
gap (E
g
) between the top of valence band (E
V
) and the bottom of the
conduction band E
C
. The electrons from valence band can be excited by
heat, light or electrical energy to the conduction band and thus, produce
a change in the current flowing in a semiconductor.
11. For insulators E
g
> 3 eV, for semiconductors E
g
is 0.2 eV to 3 eV, while
for metals E
g
≈ 0.
12. p-n junction is the ‘key’ to all semiconductor devices. When such a
junction is made, a ‘depletion layer’ is formed consisting of immobile
ion-cores devoid of their electrons or holes. This is responsible for a
junction potential barrier.
13. By changing the external applied voltage, junction barriers can be
changed. In forward bias (n-side is connected to negative terminal of the
battery and p-side is connected to the positive), the barrier is decreased
while the barrier increases in reverse bias. Hence, forward bias current
is more (mA) while it is very small (µA) in a p-n junction diode.
14. Diodes can be used for rectifying an ac voltage (restricting the ac voltage
to one direction). With the help of a capacitor or a suitable filter, a dc
voltage can be obtained.
15. There are some special purpose diodes.
16. Zener diode is one such special purpose diode. In reverse bias, after a
certain voltage, the current suddenly increases (breakdown voltage) in
a Zener diode. This property has been used to obtain voltage regulation.
17. p-n junctions have also been used to obtain many photonic or
optoelectronic devices where one of the participating entity is ‘photon’:
(a) Photodiodes in which photon excitation results in a change of reverse
saturation current which helps us to measure light intensity; (b) Solar
cells which convert photon energy into electricity; (c) Light Emitting
Diode and Diode Laser in which electron excitation by a bias voltage
results in the generation of light.
18. There are some special circuits which handle the digital data consisting
of 0 and 1 levels. This forms the subject of Digital Electronics.
19. The important digital circuits performing special logic operations are
called logic gates. These are: OR, AND, NOT, NAND, and NOR gates.
POINTS TO PONDER
1. The energy bands (E
C
or E
V
) in the semiconductors are space delocalised
which means that these are not located in any specific place inside the
solid. The energies are the overall averages. When you see a picture in
which E
C
or E
V
are drawn as straight lines, then they should be
respectively taken simply as the bottom of conduction band energy levels
and top of valence band energy levels.
2. In elemental semiconductors (Si or Ge), the n-type or p-type
semiconductors are obtained by introducing ‘dopants’ as defects. In
compound semiconductors, the change in relative stoichiometric ratio
can also change the type of semiconductor. For example, in ideal GaAs
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EXERCISES
14.1 In an n-type silicon, which of the following statement is true:
(a) Electrons are majority carriers and trivalent atoms are the
dopants.
(b) Electrons are minority carriers and pentavalent atoms are the
dopants.
(c) Holes are minority carriers and pentavalent atoms are the
dopants.
(d) Holes are majority carriers and trivalent atoms are the dopants.
14.2 Which of the statements given in Exercise 14.1 is true for p-type
semiconductos.
14.3 Carbon, silicon and germanium have four valence electrons each.
These are characterised by valence and conduction bands separated
by energy band gap respectively equal to (E
g
)
C
, (E
g
)
Si
and (E
g
)
Ge
. Which
of the following statements is true?
(a) (E
g
)
Si
< (E
g
)
Ge
< (E
g
)
C
(b) (E
g
)
C
< (E
g
)
Ge
> (E
g
)
Si
(c) (E
g
)
C
> (E
g
)
Si
> (E
g
)
Ge
(d) (E
g
)
C
= (E
g
)
Si
= (E
g
)
Ge
14.4 In an unbiased p-n junction, holes diffuse from the p-region to
n-region because
(a) free electrons in the n-region attract them.
(b) they move across the junction by the potential difference.
(c) hole concentration in p-region is more as compared to n-region.
(d) All the above.
14.5 When a forward bias is applied to a p-n junction, it
(a) raises the potential barrier.
(b) reduces the majority carrier current to zero.
(c) lowers the potential barrier.
(d) None of the above.
14.6 In half-wave rectification, what is the output frequency if the input
frequency is 50 Hz. What is the output frequency of a full-wave rectifier
for the same input frequency.
14.7 A p-n photodiode is fabricated from a semiconductor with band gap
of 2.8 eV. Can it detect a wavelength of 6000 nm?
the ratio of Ga:As is 1:1 but in Ga-rich or As-rich GaAs it could
respectively be Ga
1.1
As
0.9
or Ga
0.9
As
1.1
. In general, the presence of
defects control the properties of semiconductors in many ways.
3. In modern day circuit, many logical gates or circuits are integrated in
one single ‘Chip’. These are known as Intgrated circuits (IC).
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ADDITIONAL EXERCISES
14.8 The number of silicon atoms per m
3
is 5 × 10
28
. This is doped
simultaneously with 5 × 10
22
atoms per m
3
of Arsenic and 5 × 10
20
per m
3
atoms of Indium. Calculate the number of electrons and holes.
Given that n
i
= 1.5 × 10
16
m
–3
. Is the material n-type or p-type?
14.9 In an intrinsic semiconductor the energy gap E
g
is 1.2eV. Its hole
mobility is much smaller than electron mobility and independent of
temperature. What is the ratio between conductivity at 600K and
that at 300K? Assume that the temperature dependence of intrinsic
carrier concentration n
i
is given by
where n
0
is a constant.
14.10 In a p-n junction diode, the current I can be expressed as
where I
0
is called the reverse saturation current, V is the voltage
across the diode and is positive for forward bias and negative for
reverse bias, and I is the current through the diode, k
B
is the
Boltzmann constant (8.6×10
–5
eV/K) and T is the absolute
temperature. If for a given diode I
0
= 5 × 10
–12
A and T = 300 K, then
(a) What will be the forward current at a forward voltage of 0.6 V?
(b) What will be the increase in the current if the voltage across the
diode is increased to 0.7 V?
(c) What is the dynamic resistance?
(d) What will be the current if reverse bias voltage changes from 1 V
to 2 V?
14.11 You are given the two circuits as shown in Fig. 14.36. Show that
circuit (a) acts as OR gate while the circuit (b) acts as AND gate.
FIGURE 14.36
14.12 Write the truth table for a NAND gate connected as given in
Fig. 14.37.
FIGURE 14.37
Hence identify the exact logic operation carried out by this circuit.
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14.13 You are given two circuits as shown in Fig. 14.38, which consist
of NAND gates. Identify the logic operation carried out by the two
circuits.
FIGURE 14.38
14.14 Write the truth table for circuit given in Fig. 14.39 below consisting
of NOR gates and identify the logic operation (OR, AND, NOT) which
this circuit is performing.
FIGURE 14.39
(Hint: A = 0, B = 1 then A and B inputs of second NOR gate will be 0
and hence Y=1. Similarly work out the values of Y for other
combinations of A and B. Compare with the truth table of OR, AND,
NOT gates and find the correct one.)
14.15 Write the truth table for the circuits given in Fig. 14.40 consisting of
NOR gates only. Identify the logic operations (OR, AND, NOT) performed
by the two circuits.
FIGURE 14.40
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