2. I n t r o d u c t i o n
W h a t i s b a n d t h e o r y ?
Ty p e s o f B a n d s
B a n d S t r u c t u r e
B a n d s t r u c t u r e s i n
I n s u l a t o r s
B a n d s t r u c t u r e s i n
S e m i c o n d u c t o r s
Ty p e s o f
S e m i c o n d u c t o r s
B a n d G a p
F i l l i n g o f B a n d s
A p p l i c a t i o n s
B a n d s t r u c t u r e s i n C o n d u c t o r s
C o n c l u s i o n
3. In 1928, Felix Bloch had the idea
to take the quantum theory and
apply it to solids.
Band Theory was developed with
some help from the knowledge
gained during the quantum
revolution in science.
In 1927, Walter Heitler and Fritz London
discovered bands very closely spaced orbitals
with not much difference in energy.
Introduction
4. Band theory is a quantum model in solid state which gives the possible energies for electrons in a solid and gives an
understanding of electrical conductivity. It comes from the theory of molecular orbitals.
In this image, orbitals are
represented by the black
horizontal lines, and they
are being filled with an
increasing number of
electrons. Thus a band is
formed where the orbitals
have been filled.
7. The valence band is the band of
electron orbitals that electrons can
jump out of, moving into the
conduction band when excited.
It is generally completely full in
semi-conductors When heated.
Electrons from this band jump out of the
band across the band gap and into the
conduction band, making the material
conductive.
Types Of Bands
Valence Band
Electrons jumping
into the
conduction band,
becoming free
electrons.
8. The term band
structure refers
to the size of
various bands,
the gap between
adjacent bands
and the
occupation of the
levels in the bands
by electrons.
9. In insulators, the
band gap between
the valence band
the the conduction
band is so large
that electrons
cannot make the
energy jump from
the valence band to
the conduction
band.
Band Structure In
Insulators
10. Band structure
in Conductors
Metals are
conductors.
There is no
band gap
between
their
valence and
conduction
bands, since
they
overlap.
There is a
continuous
availability of
electrons in
these closely
spaced
orbitals.
11. Semiconductors have a small energy gap between the valence
band and the conduction band. Electrons can make the jump
up to the conduction band, but not with the same ease as they
do in conductors.
Band structure in Semiconductors
13. Intrinsic semiconductor
Extrinsicsemiconductor
Extrinsic types of semiconductor are those where a
small amount of impurity has been added to the
basic intrinsic material. This 'doping' uses an
element from a different periodic table group and
in this way it will either have more or less electrons
in the valence band than the semiconductor itself.
An intrinsic type of semiconductor material made
to be very pure chemically. For every electron that
jumps into the conduction band, the missing
electron will generate a hole that can move freely
in the valence band. As a result it possesses a very
low conductivity level.
15. Page 01
Page 02
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.
Band Gap
16. At thermodynamic
equilibrium, the
likelihood of a state of
energy E being filled
with an electron is
given by the Fermi–
Dirac distribution, a
thermodynamic
distribution that takes
into account the Pauli
exclusion principle.
KB
𝜇 T
KB
Boltzmann's
constant and
temperature
𝜇 is the total
chemical
potential
T is the product of
of electrons, or
Fermi level . The
Fermi level of a
solid is directly
related to the
voltage on that solid
18. The band theory represents a one-electron
theory, in which an electron moves in a
periodic potential representing the nucleus
and the averaged potential of other electrons,
in the sense of Spartree's self-consistent field.
It is really broader than a one-electron theory.
Important advances have been made in the
last few years in the approximate solution of
Spacher Ödinger's equation for a periodic
potential, in the detailed understanding of the
band structure of particular semiconductors,
and in the use of experiments to clarify many
important points of these band structures.
