NCERT Textbook: Semiconductor Electronics - Notes | Study Physics Class 12 - NEET

 Page 1


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
Chapter Fourteen
SEMICONDUCTOR
ELECTRONICS:
MATERIALS, DEVICES
AND SIMPLE CIRCUITS
2022-23
Page 2


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
Chapter Fourteen
SEMICONDUCTOR
ELECTRONICS:
MATERIALS, DEVICES
AND SIMPLE CIRCUITS
2022-23
Physics
468
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 ( s) or resistivity
( ? = 1/ s ), the solids are broadly classified as:
(i) Metals: They possess very low resistivity (or high conductivity).
? ~ 10
–2
 – 10
–8
 O m
s ~ 10
2
 – 10
8
 S m
–1
(ii) Semiconductors: They have resistivity or conductivity intermediate
to metals and insulators.
? ~ 10
–5
 – 10
6
 O m
s ~ 10
5
 – 10
–6
 S m
–1
(iii)Insulators: They have high resistivity (or low conductivity).
? ~ 10
11
 – 10
19
 O m
s ~ 10
–11
 – 10
–19
 S m
–1
The values of ? and s 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
2022-23
Page 3


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
Chapter Fourteen
SEMICONDUCTOR
ELECTRONICS:
MATERIALS, DEVICES
AND SIMPLE CIRCUITS
2022-23
Physics
468
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 ( s) or resistivity
( ? = 1/ s ), the solids are broadly classified as:
(i) Metals: They possess very low resistivity (or high conductivity).
? ~ 10
–2
 – 10
–8
 O m
s ~ 10
2
 – 10
8
 S m
–1
(ii) Semiconductors: They have resistivity or conductivity intermediate
to metals and insulators.
? ~ 10
–5
 – 10
6
 O m
s ~ 10
5
 – 10
–6
 S m
–1
(iii)Insulators: They have high resistivity (or low conductivity).
? ~ 10
11
 – 10
19
 O m
s ~ 10
–11
 – 10
–19
 S m
–1
The values of ? and s 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
2022-23
469
Semiconductor Electronics:
Materials, Devices and
Simple Circuits
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 + 6 p 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
2022-23
Page 4


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
Chapter Fourteen
SEMICONDUCTOR
ELECTRONICS:
MATERIALS, DEVICES
AND SIMPLE CIRCUITS
2022-23
Physics
468
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 ( s) or resistivity
( ? = 1/ s ), the solids are broadly classified as:
(i) Metals: They possess very low resistivity (or high conductivity).
? ~ 10
–2
 – 10
–8
 O m
s ~ 10
2
 – 10
8
 S m
–1
(ii) Semiconductors: They have resistivity or conductivity intermediate
to metals and insulators.
? ~ 10
–5
 – 10
6
 O m
s ~ 10
5
 – 10
–6
 S m
–1
(iii)Insulators: They have high resistivity (or low conductivity).
? ~ 10
11
 – 10
19
 O m
s ~ 10
–11
 – 10
–19
 S m
–1
The values of ? and s 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
2022-23
469
Semiconductor Electronics:
Materials, Devices and
Simple Circuits
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 + 6 p 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
2022-23
Physics
470
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 + 6 p 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.
2022-23
Page 5


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
Chapter Fourteen
SEMICONDUCTOR
ELECTRONICS:
MATERIALS, DEVICES
AND SIMPLE CIRCUITS
2022-23
Physics
468
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 ( s) or resistivity
( ? = 1/ s ), the solids are broadly classified as:
(i) Metals: They possess very low resistivity (or high conductivity).
? ~ 10
–2
 – 10
–8
 O m
s ~ 10
2
 – 10
8
 S m
–1
(ii) Semiconductors: They have resistivity or conductivity intermediate
to metals and insulators.
? ~ 10
–5
 – 10
6
 O m
s ~ 10
5
 – 10
–6
 S m
–1
(iii)Insulators: They have high resistivity (or low conductivity).
? ~ 10
11
 – 10
19
 O m
s ~ 10
–11
 – 10
–19
 S m
–1
The values of ? and s 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
2022-23
469
Semiconductor Electronics:
Materials, Devices and
Simple Circuits
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 + 6 p 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
2022-23
Physics
470
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 + 6 p 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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Semiconductor Electronics:
Materials, Devices and
Simple Circuits
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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