Department of Chemistry
School of Engineering
Presidency University
STUDY MATERIAL
Module 1: Introduction to electronic materials
Conductors, Semiconductors & Insulators: Definition of conductors,
semiconductor and insulators based on band theory.
Semiconductors: Introduction, production of electronic grade silicon from
Czochralski process (CZ) and Float Zone (FZ) methods, Chemical and electronic
properties & applications of inorganic semiconductors (SiGe, GaAs, InP).
The electrons in the outermost orbitals of the atoms determine its electrical
properties.
The electron theory of solids aims to explain the electrical, thermal and magnetic
properties of solids.
This theory has been developed in three main stages.
1. Classical free electron theory 2. Quantum free electron theory 3. Band
theory of solids.
Classical free electron theory: Drude and Lorentz developed this theory in 1900.
According to this theory the metals containing free electrons obey the laws of
Classical Mechanics (These laws describe how objects move under the influence
of forces, and how energy, momentum, and angular momentum are conserved
in isolated systems).
Quantum free electron theory: Somerfield developed this theory during 1928.
According to this theory free electrons obey the Quantum laws (describe the
behavior of matter and energy at the atomic and subatomic levels).
Band theory of solids or Zone theory: Bloch stated this theory in 1928. According
to this theory, the free electrons move in a periodic field provided by the lattice
and the theory is also called Band theory of solids (quantum mechanical model
explaining how electrons are arranged in solids, forming energy bands and gaps
that determine electrical conductivity (wave-particle duality, quantization, and
uncertainty))
Origin of Energy band formation in Solids
When we consider isolated atom, the electrons are tightly bound and
have discrete, sharp energy levels.
, When two identical atoms are brought closer the outer most orbits of these
atoms overlap and
interact.
• If more atoms are brought together more levels are formed and for a
solid of N atoms, each of the energy levels of an atom splits into N
levels of energy.
• The levels are so close together that they form an almost continuous
band.
• The width of this band depends on the degree of overlap of
electrons of adjacent atoms and is largest for outer most atomic
electrons.
Explanation
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.
Energy Band diagram
Let us consider what happens in the case of Si or Ge crystal containing N atoms.
For Si (AN 14), the outermost orbit is the third orbit (n = 3), while for Ge (AN 32)
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.
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 Eg. The lower band which is 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.
School of Engineering
Presidency University
STUDY MATERIAL
Module 1: Introduction to electronic materials
Conductors, Semiconductors & Insulators: Definition of conductors,
semiconductor and insulators based on band theory.
Semiconductors: Introduction, production of electronic grade silicon from
Czochralski process (CZ) and Float Zone (FZ) methods, Chemical and electronic
properties & applications of inorganic semiconductors (SiGe, GaAs, InP).
The electrons in the outermost orbitals of the atoms determine its electrical
properties.
The electron theory of solids aims to explain the electrical, thermal and magnetic
properties of solids.
This theory has been developed in three main stages.
1. Classical free electron theory 2. Quantum free electron theory 3. Band
theory of solids.
Classical free electron theory: Drude and Lorentz developed this theory in 1900.
According to this theory the metals containing free electrons obey the laws of
Classical Mechanics (These laws describe how objects move under the influence
of forces, and how energy, momentum, and angular momentum are conserved
in isolated systems).
Quantum free electron theory: Somerfield developed this theory during 1928.
According to this theory free electrons obey the Quantum laws (describe the
behavior of matter and energy at the atomic and subatomic levels).
Band theory of solids or Zone theory: Bloch stated this theory in 1928. According
to this theory, the free electrons move in a periodic field provided by the lattice
and the theory is also called Band theory of solids (quantum mechanical model
explaining how electrons are arranged in solids, forming energy bands and gaps
that determine electrical conductivity (wave-particle duality, quantization, and
uncertainty))
Origin of Energy band formation in Solids
When we consider isolated atom, the electrons are tightly bound and
have discrete, sharp energy levels.
, When two identical atoms are brought closer the outer most orbits of these
atoms overlap and
interact.
• If more atoms are brought together more levels are formed and for a
solid of N atoms, each of the energy levels of an atom splits into N
levels of energy.
• The levels are so close together that they form an almost continuous
band.
• The width of this band depends on the degree of overlap of
electrons of adjacent atoms and is largest for outer most atomic
electrons.
Explanation
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.
Energy Band diagram
Let us consider what happens in the case of Si or Ge crystal containing N atoms.
For Si (AN 14), the outermost orbit is the third orbit (n = 3), while for Ge (AN 32)
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.
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 Eg. The lower band which is 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.
