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CHAPTER
1
AN INTRODUCTION TO
SEMICONDUCTORS
A
semiconductor is a material whose conductivity is intermediate between a conductor and an insulator.
At room temperature, the resistivity of a semiconductor varies from 10–3 to 106 ohm-cm, whereas that
of a good conductor and a good insulator is of the order of 10–6 ohm-cm and1012 ohm-cm respectively.
A conductor has a positive temperature co-efficient of resistance, whereas a pure semiconductor has a
negative temperature coefficient of resistance. The Ohm’s law relating the current flow through a conductor
and the voltage across it is not valid in case of a semiconductor.
1.1 ENERGY LEVELS IN AN ISOLATED ATOM
In an isolated atom, electrons revolve round the nucleus in different discrete orbits. Assuming that the
orbits are circular, as in the Bohr model of the atomic structure, the radius of the orbit is such that the angular
h
nh
momentum of the electron is an integral multiple of
, i.e., mvr =
, where m is the mass of the electron,
2π
2π
v is the speed of the electron in the circular orbit, h is the Plank’s constant and n = 1, 2, 3, 4…. etc.
As n has only discrete values, the energy of each orbiting electron is also discrete. The discrete values
of energy corresponding to each value of n are represented pictorially by horizontal lines, as shown in
Fig. 1.1. This pictorial representation of discrete energy levels associated with each orbiting electron in
an isolated atom is called an energy level diagram.
n=5
n=4
n=3
n=2
n=1
Fig. 1.1 Discrete energy levels of an isolated atom.
1.2 ENERGY BANDS IN SOLID CRYSTALS
As seen in Fig. 1.1, there are energy gaps between the discrete energy levels of an isolated atom. No
electrons can appear in these gaps. When the atoms of a material are brought closer together to form a
2
Analog Electronic Circuits
solid crystal, then due to an interaction between the atoms, electrons in a particular orbit of one atom have
slightly different energy levels from the electrons in the same orbit of a neighboring atom. The separation
between the energy levels is very small. This large number of discrete and closely spaced energy levels
constitutes an energy band. The width of the band depends on the corresponding energy level and the
inter-atomic distance of the solid. The higher the energy level, the more wide is the band. Since the higher
energy levels are affected more than the lower energy levels by the interactions between the atoms. So
a higher energy level expands into a wide band, while a lower energy level expands into a narrow band.
Moreover, the inter-atomic distances are different for different atoms. Hence the width of energy bands
varies from solid to solid, being larger for an atom for which the interatomic distance is smaller.
The band corresponding to the outermost cell of the atom is the valence band. This band and the
other lower energy bands are completely filled, i.e., occupied by electrons. The upper vacant band is the
conduction band, i.e., the band above the uppermost valence band is the conduction band.
As in an isolated atom, no electrons appear in the gaps between discrete energy levels, the electrons
in a solid crystal also cannot appear in the region between the bands. The region of energy between
the two successive energy bands is called the forbidden band or forbidden gap. The forbidden energygap between the uppermost valence band and the next conduction band is of prime importance for the
conduction of electrons in a material.
1.3 INSULATORS, SEMICONDUCTORS AND CONDUCTORS
The width of the forbidden energy gap is different for different solids and decreases as the inter-atomic
distance decreases. When the inter-atomic distance is small enough, the energy bands overlap. Now
depending on the energy-band structure, materials can be classified as: (a) Insulators, (b) Semiconductors
and (c) Conductors or Metals.
Energy
Energy
Conduction
band (empty)
Forbidden
band
Valence
band (full)
(a)
Energy
Conduction band
(almost empty)
Conducts
band
Forbidden
band
Valence
band (full)
(b)
Valence
band
(c)
Fig. 1.2 Energy-band structure of (a) an insulator, (b) a semiconductor and (c) a conductor or metal.
An Introduction to Semiconductors
3
Insulators
The materials, for which the forbidden energy gap between the filled valence band and the vacant
conduction band is so large (Eg ≈ 6eV) that at room temperature a negligible number of valence electrons
can cross the energy gap and enter the conduction band, are called insulators [Fig. 1.2a]. Since there
remains a very few electrons in the conduction band at room temperature, an insulator is a very poor
conductor of electricity.
Semiconductors
The materials for which the forbidden energy gap between the filled valence band and the vacant
conduction band is smaller (Eg ≈ l eV) so that at room temperature a large number of valence electrons
acquire sufficient energy to escape from the valence band and enter the conduction band are called
semiconductors [Fig. 1.2b]. The electrical conductivity of semiconductor materials is larger than that of
an insulator but less than that of a conductor.
Conductors
The materials, for which the conduction band and the valence band overlap, are called conductors or
metals [Fig. 1.2c]. These materials have electrons in the conduction band even at 0°K. Hence, at room
temperature, there are sufficient free electrons in the conduction band to sustain a flow of heavy current.
These materials (metals) have good electrical conductivity.
1.4 THE INTRINSIC SEMICONDUCTOR
The semiconductor in which the current conduction takes solely by the thermally generated electrons
is known as the intrinsic or pure semiconductor. At absolute zero, all the valence electrons in such a
semiconductor find themselves locked in the outermost shell of the atom; no free electrons are available
for current conduction. Hence, at absolute zero, an intrinsic semiconductor behaves as an insulator. At
room temperature, some of the valence electrons escape from the valence band and enter the conduction
band, thereby creating equal number of holes in the valence band. A hole carries a positive charge equal
in magnitude to that of an electron.
1.5 THE EXTRINSIC SEMICONDUCTORS
Addition of a very small amount of certain impure atoms into the pure semiconductor material can
generate sufficient free electrons and holes. These impurities can alter the electrical property of material
significantly. The process of adding impurities inside a semiconductor material is known as doping. A pure
semiconductor material when subjected to the doping process is termed as an extrinsic semiconductor.
Depending upon the type of the doped impurities, extrinsic semiconductors are divided into two
classes: n-type and p-type.
n -type Semiconductor
The pure semiconductor material of group IV such as germanium (Ge) or silicon (Si), when doped by
pentavalent impure atoms of group V such as arsenic, antimony or phosphorus, is called the n-type
semiconductor. Each impure atom contains five valence electrons in its outer shell. Four of these
electrons form a covalent bond with the four electrons of the four neighboring Ge or Si atoms. The
fifth valence electron of the impure atom is loosely bound to its nucleus and becomes free at room
4
Analog Electronic Circuits
Ge
Ge
Ge
Free
electron
Ge
As
Ge
Ge
Ge
Ge
Fig. 1.3 Formation of n-type semiconductor.
temperature. In this way, a very small amount of impure atoms (1 part in 107) produces a huge
number of free electrons in the doped Ge or Si material. These free electrons are the majority
current carriers in the n-type semiconductor. However, there are always thermally generated holes*
and electrons in the semiconductor material due to rupture of covalent bonds at room temperature.
Electrons are added with those donated by the impure atoms and the holes become the minority
carriers of current. Thus in the n-type semiconductor, electrons are the majority current carriers,
and holes are the minority carriers. The formation of n-type semiconductor is shown pictorially in
Fig. 1.3. The pentavalent impure atoms that donate electrons to the intrinsic semiconductor are called
donors. The donor atom, after losing an electron, becomes an immobile positive ion. Since the total
number of free electrons in an n-type semiconductor are equal to the number of the immobile positive
ions plus the thermally generated holes, the semiconductor material, as a whole, is electrically neutral.
*An electron vacancy in a covalent bond is defined as a hole.
p -type Semiconductor
The pure semiconductor material of group IV such as germanium (Ge ) or silicon ( Si ), when doped by
trivalent impure atoms of group III such as boron, aluminium, gallium or indium, is called the p-type
semiconductor. Each impure atom contains three valence electrons in its outer shell. Each of these
electrons forms a covalent bond with three electrons of the four neighboring Ge or Si atoms. Hence one
valence electron of a Ge or a Si atom does not find an electron to form a covalent bond. This means that
the deficiency of one electron in the outer shell of the impure atom creates a vacancy or hole, where the
unbound valence electron of Ge or Si can jump creating a new vacancy or hole behind it. In this way,
a very small amount of impure atoms produces a huge number of holes in the doped Ge or Si material.
Thus, holes are the majority carriers and the thermally generated electrons are the minority carriers of
current in the p-type semiconductor material. The formation of p-type semiconductor is shown pictorially
in Fig. 1.4.
5
An Introduction to Semiconductors
Ge
Ge
Ge
Ge
B
Ge
o
hole
Ge
Ge
Ge
Fig. 1.4 Formation of p-type semiconductor.
The holes move in the opposite direction to that of the valence electrons. The trivalent impure atoms
that produce holes in the intrinsic semiconductor are called acceptor atoms. The acceptor atoms become
negatively charged immobile atoms in a p-type semiconductor since they accept electrons to complete
the covalent bonds. The number of the negatively charged immobile acceptor atoms and the thermally
generated electrons in a p-type semiconductor is equal to the total number of holes in the material so that
the semiconductor material, as a whole, is electrically neutral.
1.6 A BIASED n-TYPE SEMICONDUCTOR
When an n-type semiconductor is placed between the two terminals of a battery (Fig.1.5), the free electrons
flow towards the positive terminal of the battery leaving immobile positive ions in the vicinity of the
negative terminal. The electrons reaching the positive terminal disappear there, while at the same time the
immobile positive ions at the other end attract electrons from the negative terminal of the battery. Thus
electrons flow continuously from the negative terminal to the positive terminal of the battery through
the semiconductor, giving rise to a current in the opposite direction. The strength of the current depends
on the applied voltage and the conductivity of the semiconductor material.
Immobile
donor atom
Electron
– +
–
+
–
–
+
–
+
+
+
– +
+
–
–
+
–
Electrons
Electron
Electron
Fig. 1.5 Current-flow in a biased n-type semiconductor.
6
Analog Electronic Circuits
1.7 A BIASED p-TYPE SEMICONDUCTOR
When a p-type semiconductor is placed between the two terminals of a battery (Fig. 1.6), the holes flow
towards the negative terminal of the battery leaving immobile negative ions in the vicinity of the positive
terminal. The holes reaching the negative terminal combine with the electrons coming from the negative
terminal of the battery and disappear. As one hole disappears in the vicinity of the negative terminal,
an electron gets free from the negatively charged acceptor ions at the other end by the force exerted by
positive terminal of the battery on the ions, enters the positive terminal and is lost there. By losing the
electron, the acceptor atom steals an electron from the neighboring covalent bond, thereby creating a
hole. The process continues till there is battery voltage. Thus holes flow continuously from the positive
terminal to the negative terminal of the battery through the semiconductor, giving rise to a current. The
strength of the current depends on the applied voltage and the conductivity of the semiconductor material.
Immobile
acceptor atoms
+
Hole
+
–
–
+
– +
+
–
+
–
–
–
+
–
+
+
–
Holes
Electron
Electron
Fig.1.6 Current-flow in a biased p-type semiconductor.
EXERCISE
1. What is a semiconductor? How does it differ from a conductor?
2. What is the energy-level diagram of an atom? Sketch it.
3. How are energy bands formed in a solid crystal? What are the factors on which the width of the
band depends? Define valence band, conduction band and forbidden energy gap.
4. Distinguish between an insulator, a semiconductor and a metal on the basis of their band structures.
5. What are intrinsic and extrinsic semiconductors?
6. What are an n-type and a p-type semiconductors? Explain their formation.
7. What are the majority and minority current carriers in an n-type and a p-type semiconductors?
Define the terms: doping, donor and acceptor atoms.
8. Explain with diagrams the flow of current in a biased n-type and p-type semiconductors.
CHAPTER
2
SEMICONDUCTOR JUNCTION
DIODES AND THEIR APPLICATIONS
W
hen p-type and n-type semiconductor materials are brought together, a p–n junction is formed. A
p–n junction works in the same way, as does a vacuum diode. So, it is also called a p–n junction
diode or a semiconductor junction diode or, simply a junction diode. It is a two-terminal device and
extensively used in modern electronic circuits.
2.1 SEMICONDUCTOR JUNCTION DIODE
A semiconductor junction diode is prepared by converting part of a p-type semiconductor into n-type
or vice-versa by adding appropriate impurity, so that a p–n junction is formed over an extended area.
Metallic contacts with leads are made from the p-type and n–type materials for external connection. A
semiconductor junction diode is shown schematically in Fig. 2.1(a), while its circuit symbol is shown
in Fig. 2.1(b).
(a)
(b)
Fig. 2.1 Semiconductor junction diode: (a) Schematic representation and (b) Circuit symbol.
The p-type material of the diode is called the anode and the n-type material is called the cathode. In the
circuit symbol of Fig. 2.1(b), the arrowhead represents the anode and the bar represents the cathode.
When the p–n junction is just formed, the p side of the junction consists plenty of holes produced by
impurity atoms, an equal number of negatively ionized immobile acceptor atoms and a very small number
of thermally generated holes and electrons, while the n side consists plenty of donated electrons, an equal
number of positively ionized immobile donor atoms and a very small number of thermally generated
electrons and holes. The thermally generated holes in the p region combine with the holes produced by
the acceptor atoms and take part as the majority carriers of current. The thermally generated electrons
remain as the minority current carriers. Similar is the case with the thermally generated electrons in the
n-region leaving the holes as the minority current carriers. Fig. 2.2 shows the various charge carriers in
the p and n regions. The thermally generated electrons and holes are not shown for the sake of simplicity.
In this figure, the hollow circles and ‘–’ sign within the circles in the p-region represent the holes and the
negatively ionized acceptor atoms respectively, while the solid circles and ‘+’ sign within the circles in
the n-region represent the electrons and the positively ionized donor atoms respectively. The holes and
electrons are the mobile charges, while the positive and negative ions are immobile charges.
8
Analog Electronic Circuits
Fig. 2.2 Distribution of charge carriers in p and n layers just at the time of formation
of the junction (minority carriers are not shown).
2.2 JUNCTION BARRIER POTENTIAL AND DEPLETION REGION
The hole concentration on the p side of a p–n junction is much greater than that of the n–side, while the
electron concentration of the n–side is much greater than that of the p–side. Therefore, the holes diffuse
(move from a place where they are in excess to a place where they are lacking) from the p–side to the
n side and the electrons from the n–side to the p–side of the junction. After crossing the junction, the
holes recombine with the electrons in the n-region and the electrons with the holes in the p-region. This
constitutes a recombination current across the junction. The two components of the majority-carrier
current flowing across the junction are indicated in Fig. 2.3 (b) by Ir(h) (hole flow), and Ir(e) (electron
flow). The arrowhead on the respective line represents the direction of hole and electron flow. Since the
direction of current due to electron flow is opposite to that of the electron flow, the two components of the
recombination current are additive. As the holes and electrons cross the junction, the immobile negative
ions are left unneutralized in the p-region and positive ions in the n-region near the junction. These
unneutralized immobile ions are called uncovered charges. Because of the presence of the uncovered
charges near the junction, the two regions have different potentials and an electric field is produced
across the junction. This field is called the barrier field. It is directed from the n-side to the p–side of
the junction and opposes the flow of holes from the p to n and of electrons from n to p side. So the net
recombination current decreases. Note that so long as the recombination process goes on, the number of
uncovered ions on each side of the junction and hence junction barrier potential increases.
Let us now consider the current flow across the junction due to the minority carriers. Electrons in the
p region are attracted by the bound positive ions in the n region, and the holes in the n region are attracted
by the bound negative ions in the p region. This constitutes a hole and electron currents across the junction.
They are represented in Fig. 2.3 by It(h) and It(e) respectively. The magnitude of these currents does not
depend on the barrier field but depends on temperature. Since the arrowhead on each line indicates the
direction of flow of the respective carrier, the two components of the minority currents flow in the same
direction and hence additive. However, the direction of the net current flow due to minority carriers is
opposite to that of the net recombination current.
The equilibrium is established when the barrier potential across the junction attains a value which
makes the recombination current just equal to the current due to thermally generated minority carriers.
Under this condition, Ir(h) = It (h) and Ir(e) = It(e) and the net current across the junction is zero. The battery
placed across the junction with its positive terminal connected to the n region and the negative terminal
connected to the p region, as shown in Fig. 2.3(a) represents the junction barrier potential produced by
the uncovered charges at equilibrium.
9
Semiconductor Junction Diodes and their Applications
The narrow region adjacent to and on each side of the junction is devoid or depleted of mobile charge
carriers. So, this region is called the depletion region. This is also called the space-charge region or the
transition region, because over this region a net charge density exists. Outside this region, the net charge
density is zero owing to the presence of the immobile ions and an equal number of the opposite charges.
Barrier
potential
p
–
–
n
–
–
–
–
–
+
–
+
–
–
+
+
p
n
Ir(h)
+
+
+
It(h)
It(e)
+
+
+
Depletion region
(a)
Ir(e)
(b)
Fig. 2.3. (a) Junction-barrier potential and the depletion region and
(b) Flow of thermally generated minority carriers.
Here [ Ir(h) hole flow, Ir(e) electron flow, It(h) thermally generated hole flow,
It(e) thermally generated electron flow.]
2.3 FORWARD AND REVERSE BIASING OF A JUNCTION DIODE
When voltage is applied across the junction of a p–n junction diode, the diode is said to be under
biased condition. If the voltage is applied by connecting the positive terminal of a battery with the
p material and the negative terminal of the battery with the n material of the diode, it is said to be forwardbiased. The schematic and symbolic representations of a forward-biased junction diode are shown in
Fig. 2.4 (a), (b) respectively. On the other hand, if the negative terminal of the battery is connected with
the p material and the positive terminal with the n material, the diode is said to be under reversed-biased
condition. The schematic and symbolic representation of a reversed-biased junction diode is shown in
Fig. 2.5 (a), (b) respectively.
Fig. 2.4 Forward biasing of a junction diode: (a) Schematic representation and (b) Symbolic representation.
10
Analog Electronic Circuits
p
n
I
I
–
V
+
–
(a)
V
+
(b)
Fig. 2.5 Reverse biasing of a junction diode:
(a) Schematic representation and (b) Symbolic representation.
2.4 ACTION OF A JUNCTION DIODE UNDER BIASED CONDITION
Under biased condition, the width of the depletion region of a junction diode and hence the junctionbarrier potential change from its value at equilibrium. When the diode is forward-biased, as shown in Fig.
2.6 (a), the positive and negative terminals of the battery repel the holes in the p region and the electrons
in the n region towards the junction respectively. Hence, the width of the depletion region decreases,
thereby decreasing the junction barrier potential. As a result, a large number of holes in the p region and
electrons in the n region cross the junction. After crossing the junction, the holes recombine with the
electrons in the n region and the electrons with the holes in the p region. Thus the recombination current
increases. As one hole recombines with an electron in the n region, an electron enters the n region from
the negative terminal of the battery. Similarly, as one electron recombines with a hole in the p region, a
covalent bond in the p region breaks and a valence electron enters the positive terminal of the battery from
the p region. Since the hole and electron flow occur in the opposite directions, they constitute an electric
current in the same direction in the external circuit. However, the flow of the minority carriers (holes
from p to n and electrons from n to p regions) remains unaffected, since this current does not depend on
the barrier potential, but depends only on temperature. The variation of diode current I as a function of
voltage V across the diode under forward-biased condition is shown in Fig. 2.6 (b).
(a)
(b)
Fig. 2.6 (a) Flow of holes and electrons in a forward-biased junction diode and
(b) Volt-ampere characteristic curve under forward-biased condition.