Priyanka Jakhar

1. Class 12 th Physics
Priyanka Jakhar
Physics Lecturer
GGIC Vijay Nagar
Ghaziabad U.P.
Semiconductor Part 2

2. The resistivity of semiconductors decreases with temperature because the number of charge carriers
increases rapidly with increase in temperature making the fractional change

3. Intrinsic Semiconductor:--
An intrinsic(pure) semiconductor, also called an undoped semiconductor or i-type semiconductor,
is a pure semiconductor without any significant dopant species present. The number of charge
carriers is therefore determined by the properties of the material itself instead of the amount of
impurities. In intrinsic semiconductors the number of excited electrons and the number
of holes are equal: 𝒏 𝒆 = 𝒏 𝒉 .
1. A semiconductor in which holes and electrons are created only by thermal excitation across the energy gap is
called an intrinsic semiconductor.
2. A pure crystal of silicon or germanium is an intrinsic semiconductor.
3. In an intrinsic semiconductor the number of holes in the valence band is equal to number of electrons in the
conduction band.
4. The Fermi level for an intrinsic semiconductor lies at midway in the forbidden gap.

4. Crystalline structure
At temperature 0K –
•In the crystal structure, the four valence electron of the Ge
atom forms four covalent bond by sharing of electron with
the neighbouring atoms
•Each covalent bond is made of two atoms, each one from
each atom
•By forming covalent bond, each Ge atom in the crystal
behaves as if the outermost orbit of each atom is complete
with 8 electrons, having no free electrons in the crystal
At room temperature
•The conduction is possible if the electrons break away from
the covalent bonds and are free by the thermal energy
•When electron breaks away from the covalent bond, the
empty space or vacancy left in the bond is called a hole
•An electron from the neighbouring atom can break away
and can be attracted by the hole, creating hole in the other
place
•In the crystal structure, thus, we can see, electrons break
the covalent bond and keep moving. Similarly, due to
attraction of hole and electron, hole also keeps moving in a
crystal

5. Energy band theory
There is an energy gap of about 1 eV between the
valence and the conduction band
At temperature 0K –
•In terms of energy band theory, the valence band is
full and the conduction band is totally empty
•As no electrons are available for conduction, the Ge
crystal behaves like a electrical insulator
At room temperature -
•The thermal vibrations of the atoms provide energy to
the electrons in the valence band to cross the energy
gap and move into the conduction band as free
electrons
•This results in electrical conductivity of the
semiconductor
•As electrons move from the valence band to the
conduction band, a vacancy is created in the valence
band. This vacancy is called a hole
•As electrons move in the conduction band, the holes
move in the valence band and electrical conduction in
semiconductors is possible
At a higher temperature, when electric field is applied,

6. Important points related to Intrinsic semiconductor
(1) In intrinsic semiconductors, free electrons and holes are the charge carriers. At all the
temperatures, the number of free electrons 𝒏 𝒆 is equal to the number of holes 𝒏 𝒉 , i.e., 𝒏 𝒆 = 𝒏 𝒉 =
𝒏𝒊
𝒏𝒊 is known as intrinsic carrier concentration.
(2) With the increase in temperature 𝒏𝒊 increases. At room temperature :
For silicon (Si), 𝒏𝒊 = 1.5 1016 /m3
For germanium (Ge), 𝒏𝒊 = 2.5 1019 /m3
Above room temperature, for every 10ºC rise in temperature, the value of 𝒏𝒊 becomes double.
(3) In semiconductor apart from generation of free electrons and holes, a simultaneous process of
recombination of free electron and holes also takes place. At equilibrium, rate of generation is
equal to rate of recombination. Hence, at a particular temprature, 𝒏𝒊 remains constant.
(4) We know that conductivity of a metal s = 𝒏𝒆m where
n = free electron density in metal, e = charge on electron and
m = mobility of free electron. Therefore, if m 𝒆 and m 𝒉 are the
mobility of free electron and holes in a semiconductor and s 𝒆 and s 𝒉 are their conductivities
respectively,
s 𝒆 = 𝒏 𝒆 e m 𝒆
and s 𝒉 = 𝒏 𝒉 em 𝒉
where 𝒏 𝒆 = 𝒏 𝒉 = 𝒏𝒊 = intrinsic carrier concentration
Net conductivity s = s 𝒆 +s 𝒉 = 𝒏 𝒆 em 𝒆 + 𝒏 𝒉 em 𝒉 or s = 𝒏𝒊e (m 𝒆 + m 𝒉 )
(5) As the temperature increases, the number of electron hole pair (𝒏𝒊 ) generated under effect of

7. Generation of carriers (free electrons and holes)
The process by which free electrons and holes are generated in pair is called generation of
carriers.
When electrons in a valence band get enough energy, then they will absorb this energy and jumps
into the conduction band. The electron which is jumped into a conduction band is called free
electron and the place from where electron left is called hole. Likewise, two type of charge carriers
(free electrons and holes) gets generated.
Recombination of carriers (free electrons and holes)
The process by which free electrons and the holes get eliminated is called recombination of
carriers. When free electron in the conduction band falls in to a hole in the valence band, then the
free electron and hole gets eliminated.

8. Extrinsic Semiconductor:--
1. It is an impure semiconductor made by doping process thereby reducing the band gap up to 0.01 eV.
2. In this case of N-type semiconductor, the donar energy level is very close to the unfilled energy band
(Conduction band). So it can easily donate an electron to that unfilled state.
3. In this case of P-type semiconductor, the acceptor energy level is very close to the filled energy band
(Valance band). So it can easily accept the electrons from the filled state.

9. Extrinsic Semiconductor
N- Type P-Type
1. It is donor type.
2. Impurity atom is pentavalent.
3. Donor level lies close to the bottom of
the conduction band.
4. Electrons are the majority carriers and
holes are the minority carriers.
1. It is acceptor type.
2. Impurity atom is trivalent.
3. Acceptor level lies close to the top of the
valence band.
4. Holes are the majority carriers and
electrons are the minority carriers.

10. Doping :-- The process of adding desired impurity in a semiconductor is known
as doping and the semiconductor obtained after doping is known as extrinsic
semiconductor or impurity semiconductor.
The process of adding an impurity to an intrinsic or pure material is called doping and the impurity
is called a dopant.
After doping, an intrinsic material becomes an extrinsic material.
There are two types of dopants, n-type dopants and p-type dopants; n-type dopants act as electron
donors, and p-type dopants act as electron acceptors.
When a suitable impurity is added to a semiconductor in a very small amount, its conductivity
increases by many times.
Dopants should be such that it should not disturb the lattice of original semiconductor.
The necessary condition is the size of atoms of dopants should be nearly equal to the size of
atoms of semiconductor atom.
Concentration of dopants in semiconductor is expressed as parts per million (ppm).
The different methods of doping semiconductors are given below:
i) The impurity atoms are added to the semiconductor in its molten state.
ii) The pure semiconductor is bombarded by ions of impurity atoms.
iii) When in the semiconductor crystal container the impurity atoms are heated, the
impurity atoms diffuse into the hot crystal.

11. BASIS OF COMPARISON INTRINSIC SEMICONDUCTOR EXTRINSIC SEMICONDUCTOR
Doping
Doping or addition of impurities does
not happen in intrinsic
semiconductors.
A small amount of impurity is doped
in a pure semiconductor for
preparation of extrinsic
semiconductor.
Electrical Conductivity
Electrical conductivity is a function of
temperature alone.
The electrical conductivity depends
upon the temperature as well as on
the impurity atoms doped in the
structure.
The Number Of Holes And
Electrons
The number of free electrons present
in the conduction band is equal to
the number of holes in the valence
band.
The number of electrons and holes
are not equal.
Fermi Level
The Fermi level is at the center of
forbidden energy gap and is
unchanged with change in
temperature.
The Fermi level shifts upward or
downward with change in
temperature.
Intrinsic Semiconductors Vs. Extrinsic Semiconductors

12. Electrical Conductivity
The electrical conductivity of
intrinsic semiconductors is very
poor.
The electrical conductivity of extrinsic
semiconductor is fair good.
Use
Intrinsic semiconductors are not
practically used.
Extrinsic semiconductors are
practically used.
Impurities
The pure form of silicon and
germanium crystal is used in an
intrinsic semiconductor.
The impurity like arsenic, antimony,
phosphorus, aluminium , indium etc
are added to the pure form of silicon
and germanium to form extrinsic
semiconductors.
Band/Energy Gap
The band gap between conduction
and valence band is small in intrinsic
semiconductors.
In extrinsic semiconductors the band
gap is bigger.
Classification
Does not have any further
classification.
Can be classified into n–type and p-
type.

13. p-type semiconductor
•When pure Si or Ge which has four valency electrons is doped with controlled amount of
trivalent atoms, like Gallium, Indium, Boron or Aluminium , we get a p-type semiconductor
•The three valence electron from the impure atom will combine with three electrons of the Si
or Ge atom to form 3 covalent bonds
•There will be one unbounded electron in the Si atom which would try to form a covalent
bond with the neighbouring Si atom
•This Si-Si covalent bond creates a deficiency of electron in Si atom. Thus, creating a hole
•This hole is compensated by the breakage of Si-Si covalent bond in the neighbourhood .
Hence, electron moves towards the hole, resulting in hole formation at some other place
•The trivalent atoms are called acceptor atoms and conduction of electricity is due to the
motion of holes
•Thus in p-type semiconductors, holes are the majority carriers and electrons are minority
carriers

14. Energy band theory
•Si or Ge doped with impurities like Aluminium , produces energy level which
is situated in the energy gap slightly above the valence band
•This is called as acceptor energy level
•At room temperature, the electrons in the valence band can easily be
transferred to the acceptor level. This produces a large number of holes in
the valence band.
•The valence band becomes the hole conducting band

15. Few Important Points Related to p-Type Semiconductor
(1) If 𝒏 𝒆 , 𝒏 𝒉 and 𝑵 𝑨 are the number of free electrons, number of holes and number of negatively
charged acceptor ions in p type semiconductor, then 𝒏 𝒉 = 𝒏 𝒆 + 𝑵 𝑨 Therefore, this
semiconductor is electrically neutral.
(2) On connecting battery across the p-type semiconductor, electrons move towards positive
terminal and holes move towards negative terminal, whereas negatively charged acceptor ions
remains stationary. So in this type of semiconductor, electrons and holes are also the charge
carriers, not the fixed acceptor ion .
Net current in the circuit, I = 𝑰 𝒆 + 𝑰 𝒉
(3) In p-type semiconductor 𝒏 𝒉 >> 𝒏 𝒆 , therefore, holes are the majority charge carriers and
electrons are the minority charge carriers. Since, majority charge carriers have positive charge
therefore, it is said to be p-type semiconductor.
(4) Conductivity of a p-type semiconductor
s = 𝒏 𝒆 em 𝒆 + 𝒏 𝒉 e m 𝒉 = e (𝒏 𝒆 m 𝒆 + 𝒏 𝒉 m 𝒉 )
where all the symbols have their usual meanings. With the increase in temperature, number of
electron-hole pair produced due to thermal energy increases and hence conductivity increases.
(5) In a p-type semiconductor, if 𝒏 𝒆 and 𝒏 𝒉 are the concentration of electron and hole respectively
at any temperature and 𝒏𝒊 is the concentration of intrinsic semiconductor at same temperature,
then
(i) 𝒏 𝒆 < 𝒏𝒊 (ii) 𝒏 𝒉 > 𝒏𝒊 (iii) 𝒏 𝒆 𝒏 𝒉 = 𝒏𝒊 2
At normal temperature 𝒏 𝒉  𝑵 𝑨

16. n-type semiconductor
•When pure Si or Ge which has four valency electrons is doped with controlled amount of
pentavalent atoms, like Arsenic, Phosphorus, Antimony or Bismuth, we get a n-type
semiconductor
•The four valence electron from the impure atom will combine with four electrons of the Si or
Ge atom to form 4 covalent bonds
•The fifth electron of the impure atom is free to move. Thus, each atom of the impure
substance, donates a free electron for conduction. Hence, it is called as donor atom
•Giving the free electron for conduction, the impure atom becomes positively charged, giving
rise to a hole
•Thus in n-type semiconductors, electrons are the majority carriers and holes are minority
carriers

17. Energy band theory
•Comparing Si or Ge doped with impurities like Arsenic with a pure Si or Ge, the lowest
energy level of the conduction band is less
•The electrons occupy discrete energy levels called the donor energy level between the
valence band and the conduction band
•This donor energy level is below the bottom of the conduction band
•Thus, very small energy supplied can excite the electron from the donor level to the
conduction band, hence, conductivity of semiconductor becomes remarkably improved

18. Few Important Points Related to p-Type Semiconductor
(1) If 𝒏 𝒆 , 𝒏 𝒉 and 𝑵 𝑫 are the number of free electrons, number of holes and number of positive
donar ions in n type semiconductor, then 𝒏 𝒆 = 𝒏 𝒉 + 𝑵 𝑫 Therefore, this semiconductor is
electrically neutral.
(2) On connecting battery across the ends of a n-type semiconductor, electrons move toward
positive terminal and holes moves towards negative terminal whereas positively charged donor
ions remain stationary. Therefore the moving free electrons and holes are the charge carriers but
not the fixed donor ion .Net current in the circuit,
I = 𝑰 𝒆 + 𝑰 𝒉
(3) In n-type semiconductor 𝒏 𝒆 >> 𝒏 𝒉 , electrons are the majority charge carriers and holes are the
minority charge carriers. Since, charge on majority carriers is negative, so they are known as n-
type semiconductor.
4) Conductivity of a p-type semiconductor
s = 𝒏 𝒆 em 𝒆 + 𝒏 𝒉 e m 𝒉 = e (𝒏 𝒆 m 𝒆 + 𝒏 𝒉 m 𝒉 )
Here, all the symbols have their usual meanings. With the increase in temperature, the number of
electron hole pair generated due to thermal energy increases, hence its conductivity increases.
(5) If 𝒏 𝒆 and 𝒏 𝒉 are the concentration of electrons and holes respectively at any temperature in a
n-type semiconductor and 𝒏𝒊 is the concentration in intrinsic semiconductor at same temperature,
(i) 𝒏𝒊 < 𝒏 𝒆(ii) 𝒏𝒊 > 𝒏 𝒉 (iii) 𝒏 𝒆 𝒏 𝒉 = 𝒏𝒊 2
At normal temperature 𝒏 𝒆  𝑵 𝑫

19. Basis for Comparison Donor Impurities Acceptor Impurities
Basic The impurities that increases
conductivity by donating charge is
known as donor impurities.
Those impurities that accepts the
charge for increasing conductivity is
known as acceptor impurities.
Also referred as pentavalent impurities trivalent impurities
Number of valence electrons 5 3
Forms n-type semiconductor p-type semiconductor
Group position in periodic table Group V Group III
Examples Phosphorus, Bismuth. Aluminium, Boron.
Donor Impurities / Acceptor Impurities

20. BASIS OF DIFFERENCE p TYPE SEMICONDUCTOR n TYPE SEMICONDUCTOR
Group of Doping Element In P type semiconductor III
group element is added as
doping element.
In n type semiconductor V
group element is added as
doping element.
Nature of Doping Element Impurity added creates
vacancy of electrons (holes)
called as Acceptor Atom.
Impurity added provides extra
electrons and is known as
Donor Atom.
Type of impurity added Trivalent impurity like Al, Ga, In
etc. are added.
Pentavalent impurity like P, As,
Sb, Bi etc. are added.
Majority Carriers Holes are majority carriers Electrons are majority carriers
Minority Carriers Electrons are minority carriers Holes are minority carriers
The difference between a p-type semiconductor and n-type
semiconductor

21. Density of Electrons and Holes The hole density is much
greater than the electron
density.
𝒏 𝒉 >> 𝒏 𝒆
The electron density is much
greater than the hole density.
𝒏 𝒆 >> 𝒏 𝒉
Energy level The acceptor energy level is
close to the valence band and
away from the conduction
band.
The donor energy level is close
to the conduction band and
away from the valence band.
Fermi level Fermi level lies between
acceptor energy level and the
valence band.
Fermi level lies between donor
energy level and the
conduction band.
Movement of Majority carriers Majority carriers move from
higher to lower potential.
Majority carriers move from
lower to higher potential.