Energy bands consisting of a large number of closely spaced energy levels exist in crystalline materials. The bands can be thought of as the collection of the individual energy levels of electrons surrounding each atom. The wavefunctions of the individual electrons, however, overlap with those of electrons confined to neighboring atoms. The Pauli exclusion principle does not allow the electron energy levels to be the same so that one obtains a set of closely spaced energy levels, forming an energy band. The energy band model is crucial to any detailed treatment of semiconductor devices. It provides the framework needed to understand the concept of an energy bandgap and that of conduction in an almost filled band as described by the empty states.

1. Dr. B.R. Ambedkar National Institute of Technology,
Jalandhar
TOPIC- ENERGY BAND GAP
SUBJECT- MATERIAL SCIENCE(NANO SCIENCE) PHX-301
GROUP-5 Submitted To: Dr. Shishram Rebari
YOGESHWER(17109083)
SHUBHAM SHARMA(17109067)
SUBHASH YADAV(17109070)
SURENDER KUMAR YADAV(17109074)

2. PREFACE:
INTRODUCTION
WHAT ARE ENERGY BANDS?
WHAT IS BAND GAP?
WHAT ARE BAND GAP SIZES?
ENERGY BAND THEORY
FORMATION OF ENERGY BANDS
CLASSIFICATION OF ENERGY BANDS:
VALENCE BAND
CONDUCTION BAND
FORBIDDEN ENERGY BAND
INSULATORS, CONDUCTORS AND SEMICONDUCTORS

3. INTRODUCTION:
Energy band gap is usually referred to the energy difference between the conduction band and
the valence band. The conduction band is the outermost energy band where the free electrons
lie and below that there is the valence band.
An electron residing in the valence band can not jump to the conduction band until and unless
it is provided the amount of energy needed for the electron to cross the energy barrier between
the aforementioned bands, which is just the band gap energy.
As soon as the electron is provided energy equal or greater than the band gap energy, it can go
to the conduction band, become a free electron which is the main reason behind the high
conductivity of metal.

4. WHAT ARE ENERGY BANDS?
In gaseous substances, the arrangement of molecules are spread apart and are not so close to
each other. In liquids, the molecules are closer to each other. But, in solids, the molecules are
closely arranged together, due to this the atoms of molecules tend to move into the orbitals of
neighbouring atoms. Hence, the electron orbitals overlap when atoms come together.
In solids, several bands of energy levels are formed due to the intermixing of atoms in solids. We
call these set of energy levels as energy bands.

5. WHAT IS BAND GAP?
A band gap is the distance between the valence band of electrons and the conduction band.
Essentially, the band gap represents the minimum energy that is required to excite an electron up
to a state in the conduction band where it can participate in conduction. The lower energy level is
the valence band, and thus if a gap exists between this level and the higher energy conduction
band, energy must be input for electrons to become free. The size and existence of this band gap
allows one to visualize the difference between conductors, semiconductors, and insulators.

6. BAND GAP SIZES:
The size of this band gap gives the materials some of their distinct properties. In insulators, the
electrons in the valence band are separated by a large band gap from the conduction band. This
means that there is a large "forbidden" gap in energies preventing electrons from the valence
band from jumping up into the conduction band and participating in conduction. This is provides
an explanation for why insulators do not conduct electricity well.
In conductors, the valence band overlaps with the conduction band. This overlap causes the
valence electrons to be essentially free to move into the conduction band and participate in
conduction. Since it is not a full overlap, only a fraction of the valence electrons can move
through the material, but this is still enough to make conductors conductive.

7. BAND GAP SIZES:
In semiconductors, the gap is small enough that it can be bridged by some sort of excitation -
perhaps from the Sun in the case of photovoltaic cells. The gap is essentially some size "in-
between" that of a conductor or insulator. In this model, a finite number of electrons are able to
reach the conduction band and conduct small amounts of electricity. The excitation of this
electron also allows additional conduction processes to occur as a result of the electron hole left
behind. An electron from an atom close by can occupy this space, creating a chain reaction of
holes and electron movement that creates current. A small amount of doping material can
drastically increase the conductivity of this material.

8. A band gap diagram showing the different sizes of band
gaps for conductors, semiconductors, and insulators.
These distances can be seen in diagrams known as band diagrams.

9. ENERGY BAND THEORY:
According to Bohr’s theory, every shell of an atom contains a discrete amount of energy at
different levels. Energy band theory explains the interaction of electrons between the outermost
shell and the innermost shell. Based on the energy band theory, there are three different energy
bands:
1.Valence band
2.Forbidden energy gap
3.Conduction band

10. FORMATION OF ENERGY BANDS:
In an isolated atom, the electrons in each orbit possess definite energy. But, in the case of solids, the
energy level of the outermost orbit electrons are affected by the neighbouring atoms.
When two isolated charges are brought close to each other, the electrons in the outermost orbit
experiences an attractive force from the nearest or neighbouring atomic nucleus. Due to this reason, the
energies of the electrons will not be at the same level, the energy levels of electrons are changed to a value
which is higher or lower than that of the original energy level of the electron.
The electrons in the same orbit exhibit different energy levels. The grouping of this different energy levels
is known as energy band.
However, the energy of the inner orbit electrons are not much affected by the presence of neighbouring
atoms.

11. CLASSIFICATION OF ENERGY BANDS:
VALENCE BAND:
The electrons in the outermost shell are known as valence electrons. These valence electrons contain a
series of energy levels and form an energy band known as valence band. The valence band has the highest
occupied energy.
CONDUCTION BAND:
The valence electrons are not tightly held to the nucleus due to which a few of these valence electrons
leave the outermost orbit even at room temperature and become free electrons. The free electrons conduct
current in conductors and are therefore known as conduction electrons. The conduction band is one that
contains conduction electrons and has the lowest occupied energy levels.
FORBIDDEN ENERGY BAND:
The gap between the valence band and the conduction band is referred to as forbidden gap. As the name
suggests, the forbidden gap doesn’t have any energy and no electrons stay in this band. If the forbidden energy
gap is greater, then the valence band electrons are tightly bound or firmly attached to the nucleus. We require
some amount of external energy that is equal to the forbidden energy gap.

12. The above figure shows the conduction band, valence
band and the forbidden energy gap.

13. CONDUCTORS:
Gold, Aluminium, Silver, Copper, all these metals
allow an electric current to flow through them.
There is no forbidden gap between the valence band
and conduction band which results in the overlapping
of both the bands.The number of free electrons available
at room temperature is large.

14. INSULATORS:
Glass and wood are examples of the insulator.
These substances do not allow electricity to pass through them.
They have high resistivity and very low conductivity.
The energy gap in the insulator is very high up to 7eV.
The material cannot conduct because the movement of the
electrons from the valence band to the conduction band is
not possible.
.

15. SEMICONDUCTORS:
Germanium and Silicon are the most preferable material
whose electrical properties lie in between semiconductors
and insulators. The energy band diagram of semiconductor
is shown where the conduction band is empty and the valence
band is completely filled but the forbidden gap between the two
bands is very small that is about 1eV. For Germanium, the forbidden
gap is 0.72eV and for Silicon, it is 1.1eV. Thus, semiconductor
requires small conductivity.

16. N TYPE SEMICONDUCTORS
When a pentavalent impurity (5 electrons in outershell ) is added to a pure Si
semiconductor, then it becomes N type semiconductor.
Examples of pentavalent impurity: P , As, Sb, Bi etc.
The order of energy between Ed and Ec is 10 to 30 meV.
At room temperature of 300K ,the available thermal energy
is approximately 30 meV.
So the electrons of Ed will go in conduction band by taking
energy from the thermal energy. In this way the conuctivity of
the intrinsic semiconductor can be increased by doping.

18. P TYPE SEMICONDUCTORS
When a trivalent impurity such as B, Al,Ga,In (3 electrons in outershell ) is added to a pure
Si semiconductor, then it becomes P type semiconductor.
The three valence electrons forms covalent bond, but a hole is created at the site of fourth
electron as it is missing.The electron from the neighbouring site can fill this hole and
another hole is generated at that site and it continues..
Such an impurity is called acceptor impurity since it accepts
electron into the impurity centre. Si Or Ge doped in this way
contains many holes as charge carriers and therefore called
P-type semiconductors.
In a p type semiconductors, holes are majority carriers and
thermally generated electrons are the minority carriers.