https://www.youtube.com/c/EngineeringPhysicsbySanjiv
SEMICONDUCTOR PHYSICS
https://youtu.be/CXFtbpYaBXw
CHAPTER – 3 SEMICONDUCTOR PHYSICS
Session 1 : Formation of Energy Bands
Intrinsic and Extrinsic semiconductors
Direct and Indirect gap Semiconductors
Formation of Energy Bands :
In an isolated atom, the electrons are tightly bound and have discrete sharp energy levels. When
two atoms are completely isolated from each other, there is no interaction of electrons in these two
atoms and both atoms can have identical energy levels. However, as the spacing between the two
atoms becomes smaller, i.e. when two identical atoms are brought closer, the two atoms form an
interacting system. The wave functions of the electrons of different atoms begin to overlap and
energy levels corresponding to these wave functions spilt into two levels. This is in accordance
with Pauli‟s Exclusion Principle which states that “No two electrons in a given interacting system
can have same quantum state and hence same energy.” Thus there must be a spitting of discrete
energy levels of isolated atoms into new levels belonging to the pair rather than to individual
atom.
When a number of isolated atoms come close to each other, various interactions occur between
neighbouring atoms. The forces of attraction and repulsion between atoms find a balance and a
proper inter-atomic spacing for a solid is adjusted. In this process, important changes occur in the
electron energy level configurations and these changes result in varied electrical properties of
solid.
In a solid, many atoms are brought together, so that the split energy levels form essentially a
continuous band of energies.
Pushing the atoms together, the initial quantized
energy level will split into a band of discrete energy
levels.
Prepared by – Sanjiv Badhe
Page 1 of 7
https://www.youtube.com/c/EngineeringPhysicsbySanjiv
SEMICONDUCTOR PHYSICS
https://youtu.be/CXFtbpYaBXw
Formation of Enegry Bands (example)
In a solid, many atoms are brought together, so that the split energy levels form essentially a
continuous band of energies. In the following figure, the imaginary formation of a diamond crystal
from N number of Carbon atoms is shown.
Each isolated carbon atom has an electronic structure 1s2 2s2 2p2. Thus each atom has two 1s
states, two 2s states, six 2p states and the higher states. Hence for N atoms, there will be 2N, 2N
and 6N available states of type 1s, 2s, and 2p respectively. As the inter-atomic spacing decreases,
these energy levels split into bands, beginning with the outer (n=2) shell. As the 2s and 2p bands
grow, they merge into a single band composed of mixture of energy levels. There are 8N available
states in this 2s-2p band. As the inter-atomic distance approaches the equilibrium inter-atomic
spacing, this band splits into bands separated by an energy gap Eg. The upper band (called as
conduction band) contains 4N states and the lower band (called as valence band) also contains 4N
states.
The lower 1s band is filled with original 2N electrons,
which were already there in 1s energy levels. The
remaining 4N electrons from 2s and 2p, now occupy states
in the valence band or conduction band. At 00 K, the
electrons occupy the lowest energy states available to them.
Hence, for diamond, valence band is completely filled and
conduction band is completely empty at 00 K.
Thus energy bands for Diamond can be drawn as shown
here –
Prepared by – Sanjiv Badhe
Page 2 of 7
https://www.youtube.com/c/EngineeringPhysicsbySanjiv
SEMICONDUCTOR PHYSICS
https://youtu.be/CXFtbpYaBXw
Conduction band, Valance band and Energy Gap :
Conduction band is defined as the lowest empty band in the energy band diagram.
Valence band is defined as uppermost filled band in the energy band diagram.
Forbidden gap or Energy gap is defined as difference between top of the valence band and bottom
of the conduction band.
If energy of top of the valence band is Ev and energy of bottom of the conduction band is Ec then
the energy gap (Eg) is given by Eg = Ec – Ev.
3.1.2 Classification of Solids on the basis of band theory :
There are many energy bands in the solid. As far as the electrical conductivity of the solid is
concerned, only the valence band and conduction band are important. Completely filled band and
completely empty band do not contribute to the conduction. The electrons in the inner shell do not
take part in the conduction.
Electrons in the conduction band are free and can move freely under the influence of electric field.
The electrons in the valence band are attached to the lattice and are not free to move. If they
acquire sufficient energy to cross the forbidden gap Eg, they can occupy the conduction band states
and are available for conduction. Hence, Eg is the parameter which decides whether the material
acts as conductor, insulator or semiconductor.
On the basis of band theory, solids are classified into three categories – insulator, semiconductor
and conductor.
Semiconductors
Semiconductor is a material, which has conductivity level somewhere between the extremes of an
insulators and a conductor. In terms of energy bands, semiconductors are defined as those
materials, which have almost an empty conduction band and almost filled valence band with a
narrow energy gap of the order of 1 eV between them.
Prepared by – Sanjiv Badhe
Page 3 of 7
https://www.youtube.com/c/EngineeringPhysicsbySanjiv
SEMICONDUCTOR PHYSICS
https://youtu.be/CXFtbpYaBXw
Why silicon is preferred over germanium?
Silicon and Germanium are two most widely used semiconductors. Silicon is preferred over
Germanium because of its superior thermal properties. The maximum operational temperature for
Germanium devices is 80 0C while Silicon devices may be used at up to 160 0C. Also, at room
temperature, silicon crystal has almost no free electrons compared with Germanium crystal.
Covalent Bonds in Semiconductors :
Semiconductors like Germanium and Silicon have crystalline structure (i.e. definite geometrical
arrangement is followed by atoms). An isolated silicon atom has four electrons in its valence orbit.
Hence to produce eight electrons in the valence orbit to get stability, a silicon atom combines with
four neighboring silicon atoms as shown below –
The forces that hold the atoms together are known as covalent bonds. The neighboring atoms form
covalent bonds by sharing four electrons with each other.
Intrinsic Semiconductor :
Intrinsic semiconductor is one that is made of semiconductor material in its extremely pure form.
Pure Silicon and pure Germanium are examples of intrinsic semiconductors.
At absolute zero temperature, the electrons in the outer shell of intrinsic semiconductor are tightly
bound with the covalent bonds. Hence, there are no free electrons and it behaves as insulator.
However, at room temperature, some valence electrons absorb enough energy to enable them to
break free from their covalent bonds. When this occurs, the liberated electrons are free to move
about in the crystal. When battery is connected to this crystal, free electrons are attracted to the
positive terminal of the battery and constitute electric current. Greater the temperature, greater is
the current. Free electron means that its motion is quite sensitive to applied electric field.
Generation of free electrons can also be explained on the basis of band theory. The energy band
diagram of intrinsic semiconductor is as shown in following fig. –
Prepared by – Sanjiv Badhe
Page 4 of 7
https://www.youtube.com/c/EngineeringPhysicsbySanjiv
SEMICONDUCTOR PHYSICS
https://youtu.be/CXFtbpYaBXw
In intrinsic semiconductor, at 0 0K, the valence band is completely filled and conduction band is
completely empty. These bands are separated by energy gap Eg. In valence band, electrons are
present but vacant energy states are not there so that they can move freely. In conduction band,
vacant energy states are present but electrons are not there to move through these states freely.
However, as the temperature increases, some of the valence band electrons get enough energy to
overcome the energy gap and jump to the conductions band. Now, we have some vacant energy
states in the valence band, which are called, as „holes‟ and number of electrons, which can move
freely through holes when electric field is applied. Also, in conduction band, we have some
electrons, which can move, freely through already available vacant states when electric field is
applied.
Thus, in intrinsic semiconductor, electrons and holes are generated in pairs. At any temperature,
the number of holes valence band and the number of electrons in conduction band are same. As
the temperature increases, the number of electron hole pairs increase. Hence the conductivity of
the intrinsic semiconductor is directly proportional to the temperature.
Recombination :
Occasionally, it happens that the electron in the conduction band looses its energy and falls back
in the valence band. The lost energy is given out in the form of radiation (heat or light). This
merging of a free electron and a hole is called as „recombination‟.
Recombination occurs continuously in a semiconductor. Incoming heat energy keeps producing
electron hole pairs by lifting valence electrons to the conduction band. The time for which the
electron remains in the conduction band is called as the lifetime. Lifetime varies from a few
nanoseconds to several microseconds. After the lifetime of excited electron gets over, it falls back
into the valence band. This concept is used in the production of LEDs and semiconductor lasers.
Doped or Extrinsic Semiconductor :
Doping means adding impurity atoms to the crystal to increase either the number of free electrons
or the number of holes. When the crystal is doped, it is called as an extrinsic semiconductor. There
are two types of extrinsic semiconductors depending on the type of impurity (doping material).
n-type semiconductor :
In n-type semiconductor, a pentavalent impurity such as Antimony (Sb), Arsenic (As),
Phosphorous (P) is added to pure semiconductor to get extra conduction band electrons. The
pentavalent atom (Sb) has five electrons in its valence orbit, out of which four electrons form
covalent bonds with four neighbouring semiconductor (Si) atoms and fifth electron remains
loosely bound as shown below-
Prepared by – Sanjiv Badhe
Page 5 of 7
https://www.youtube.com/c/EngineeringPhysicsbySanjiv
SEMICONDUCTOR PHYSICS
https://youtu.be/CXFtbpYaBXw
This loosely bound electron can be excited to conduction band easily and can be made free. As
pentavalent atoms donate one electron to the conduction band of pure silicon, they are called as
donor atoms.
From the energy band structure viewpoint, the donor atoms introduce filled states called „donor
levels‟ just below the conduction band. The donor levels have energy approximately 0.1 eV below
the lowest level in the conduction band. Hence, donor electrons in donor levels can be easily
excited to the conduction band. Once they come in conduction band, they can move freely when
electric field is applied. This number of donated electrons in conduction band is much more as
compared to the number of electron hole pairs. Hence, in n-type semiconductor, the electrons are
majority carriers and holes are minority carriers.
p-type of semiconductor :
In p-type semiconductor, a trivalent impurity such as Boron (B), Aluminum (Al) is added to pure
semiconductor to get extra vacant states (holes) in the valence band. The trivalent atom (Al) has
three electrons in its valence orbit. All these three electrons form covalent bond wih four
surrounding semiconductor atoms (Si). But one bond is left incomplete and gives rise to a hole as
shown below –
Valence band electrons can move freely through the holes when electric field is applied. Trivalent
atoms accept one electron from a Silicon atom and in a process causes the semiconductor atom to
have a hole. Hence, they are known as acceptor atoms.
From the energy band structure viewpoint, the acceptor atoms introduce available energy states
called acceptor levels just above the valence band. The electrons from valence band can easily
jump to these acceptor levels leaving hole in the valence band. In p-type semiconductor, the
number of holes in valence band is much more than the number conduction band electrons. Hence,
the current is mainly due to holes. Thus, in p-type semiconductor, holes are majority carriers and
electrons are minority carriers.
Prepared by – Sanjiv Badhe
Page 6 of 7
https://www.youtube.com/c/EngineeringPhysicsbySanjiv
SEMICONDUCTOR PHYSICS
https://youtu.be/CXFtbpYaBXw
DIRECT AND INDIRECT BAND GAP:
p2 2k 2
where p is momentum,  is Planck constant

2m
2m
and k is propagation constant. Thus E  k 2 which is an equation of parabola.
The energy of electron is given by E 
The graph of E vs k is parabola as shown below-
The upper parabola in the conduction band represents free electrons and lower parabola in the
valence band represents holes.
Prepared by – Sanjiv Badhe
Page 7 of 7