Semiconductor seminar ppt

1. Semiconductor
Physics

2. Introduction
• Semiconductors are materials whose electronic
properties are intermediate between those of Metals
and Insulators.
• They have conductivities in the range of 10 -4 to 10
+4S/m.
• The interesting feature about semiconductors is that
they are bipolar and current is transported by two
charge carriers of opposite sign.
• These intermediate properties are determined by
1.Crystal Structure bonding Characteristics.
2.Electronic Energy bands.

3. • Silicon and Germanium are elemental semiconductors
and they have four valence electrons which are
distributed among the outermost S and p orbital's.
• These outer most S and p orbital's of Semiconductors
involve in Sp3 hybridanisation.
• These Sp3 orbital's form four covalent bonds of equal
angular separation leading to a tetrahedral arrangement
of atoms in space results tetrahedron shape, resulting
crystal structure is known as Diamond cubic crystal
structure

4. Semiconductors are mainly two types
1. Intrinsic (Pure) Semiconductors
2. Extrinsic (Impure)
Semiconductors

5. Intrinsic Semiconductor
• A Semiconductor which does not have any kind
of impurities, behaves as an Insulator at 0k and
behaves as a Conductor at higher temperature is
known as Intrinsic Semiconductor or Pure
Semiconductors.
• Germanium and Silicon (4th group elements) are
the best examples of intrinsic semiconductors and
they possess diamond cubic crystalline structure.

6. Si
Si
Si
Si
Si
Valence Cell
Covalent bonds
Intrinsic Semiconductor

7. E
Ef
Ev
Valence band
Ec
Conduction band
Ec
Electron
energy
Distance
KE of
Electron
= E - Ec
KE of Hole
=
Ev - E
Fermi energy level

8. Carrier Concentration in Intrinsic
Semiconductor
When a suitable form of Energy is supplied to a
Semiconductor then electrons take transition from
Valence band to Conduction band.
Hence a free electron in Conduction band and
simultaneously free hole in Valence band is formed.
This phenomenon is known as Electron - Hole pair
generation.
In Intrinsic Semiconductor the Number of Conduction
electrons will be equal to the Number of Vacant sites or
holes in the valence band.

9. )
1
......(
..........
)
(
)
(
)
(
)
(
band
the
of
top



c
E
dE
E
F
E
z
n
E
F
dE
E
Z
dn
Calculation of Density of
Electrons
Let ‘dn’ be the Number of Electrons available between
energy interval ‘E and E+ dE’ in the Conduction band
Where Z(E) dE is the Density of states in the energy
interval E and E + dE and F(E) is the Probability of
Electron occupancy.

10. dE
E
E
m
h
dE
E
Z c
e
2
1
2
3
3
)
(
)
2
(
4
)
( 
 

Since the E starts at the bottom of the Conduction band Ec
dE
E
m
h
dE
E
Z e
2
1
2
3
3
)
2
(
4
)
( 


We know that the density of states i.e., the number of energy
states per unit volume within the energy interval E and E + dE
is given by
dE
E
m
h
dE
E
Z 2
1
2
3
3
)
2
(
4
)
(



11. )
exp(
)
(
exp
)
(
)
exp(
1
)
(
res
temperatu
possible
all
For
)
exp(
1
1
)
(
kT
E
E
kT
E
E
E
F
kT
E
E
E
F
kT
E
E
kT
E
E
E
F
F
F
f
F
f












Probability of an Electron occupying an energy state E
is given by

12. )
2
.....(
)
exp(
)
(
)
exp(
)
2
(
4
)
exp(
)
(
)
2
(
4
)
exp(
)
(
)
2
(
4
)
(
)
(
2
1
2
3
3
2
1
2
3
3
2
1
2
3
3
band
the
of
top




















c
c
c
c
E
c
F
e
E
F
c
e
E
F
c
e
E
dE
kT
E
E
E
kT
E
m
h
n
dE
kT
E
E
E
E
m
h
n
dE
kT
E
E
E
E
m
h
n
dE
E
F
E
z
n



Substitute Z(E) and F(E) values in Equation (1)

13. )
3
.....(
)
(
exp
)
(
)
exp(
)
2
(
4
)
(
exp
)
(
)
exp(
)
2
(
4
)
exp(
)
(
)
exp(
)
2
(
4
0
2
1
2
3
3
0
2
1
2
3
3
0
2
1
2
3
3























dx
kT
x
x
kT
E
E
m
h
n
dx
kT
x
E
x
kT
E
m
h
n
dE
kT
E
E
E
kT
E
m
h
n
dx
dE
x
E
E
x
E
E
c
F
e
c
F
e
c
F
e
c
c



To solve equation 2, let us put

14. )
exp(
)
2
(
2
}
2
)
{(
)
exp(
)
2
(
4
2
3
2
2
1
2
3
2
3
3
kT
E
E
h
kT
m
n
kT
kT
E
E
m
h
n
c
F
e
c
F
e









)
3
(
2
)
(
)
exp(
)
(
2
1
2
3
0
2
1
equation
in
substitute
kT
dE
kT
x
x
that
know
we





The above equation represents
Number of electrons per unit volume of the Material

15. Calculation of density of
holes
)
1
......(
..........
)}
(
1
){
(
)}
(
1
{
)
(
band
the
of
bottom
 



Ev
dE
E
F
E
z
p
E
F
dE
E
Z
dp
Let ‘dp’ be the Number of holes or Vacancies in the
energy interval ‘E and E + dE’ in the valence band
Where Z(E) dE is the density of states in the energy interval
E and E + dE and
1-F(E) is the probability of existence of a hole.

16. dE
E
m
h
dE
E
Z h
2
1
2
3
3
)
2
(
4
)
( 


Density of holes in the Valence band is
Since Ev is the energy of the top of the valence
band
dE
E
E
m
h
dE
E
Z v
h
2
1
2
3
3
)
(
)
2
(
4
)
( 
 


17. )
exp(
)
(
1
exp
)}
exp(
1
{
1
)
(
1
}
)
exp(
1
1
{
1
)
(
1
1
kT
E
E
E
F
values
T
higher
for
ansion
above
in
terms
order
higher
neglect
kT
E
E
E
F
kT
E
E
E
F
f
f
f














Probability of an Electron occupying an energy state
E is given by

18. )
2
....(
)
exp(
)
(
)
exp(
)
2
(
4
)
exp(
)
(
)
2
(
4
)}
(
1
){
(
2
1
2
3
3
2
1
2
3
3
band
the
of
bottom

















v
v
E
v
F
h
E
F
v
h
Ev
dE
kT
E
E
E
kT
E
m
h
p
dE
kT
E
E
E
E
m
h
p
dE
E
F
E
z
p


Substitute Z(E) and 1 - F(E) values in Equation (1)

19. 

























0
2
1
2
3
3
0
2
1
2
3
3
2
1
2
3
3
)
exp(
)
(
)
exp(
)
2
(
4
)
)(
exp(
)
(
)
exp(
)
2
(
4
)
exp(
)
(
)
exp(
)
2
(
4
dx
kT
x
x
kT
E
E
m
h
p
dx
kT
x
E
x
kT
E
m
h
p
dE
kT
E
E
E
kT
E
m
h
p
dx
dE
x
E
E
x
E
E
F
v
h
v
F
h
E
v
F
h
v
v
v



To solve equation 2, let us put

20. )
exp(
)
2
(
2
2
)
)(
exp(
)
2
(
4
2
3
2
2
1
2
3
2
3
3
kT
E
E
h
kT
m
p
kT
kT
E
E
m
h
p
F
v
h
F
v
h









The above equation represents
Number of holes per unit volume of the Material

21. Intrinsic Carrier Concentration
In intrinsic Semiconductors n = p
Hence n = p = n i is called intrinsic Carrier
Concentration
)
2
exp(
)
(
)
2
(
2
)
2
exp(
)
(
)
2
(
2
)}
exp(
)
2
(
2
)}{
exp(
)
2
(
2
{
4
3
2
3
2
4
3
2
3
2
2
3
2
2
3
2
2
kT
E
m
m
h
kT
n
kT
E
E
m
m
h
kT
n
kT
E
E
h
kT
m
kT
E
E
h
kT
m
n
np
n
np
n
g
h
e
i
c
v
h
e
i
F
v
h
c
F
e
i
i
i




















22. Fermi level in intrinsic Semiconductors
sides
both
on
logarithms
taking
)
exp(
)
(
)
2
exp(
)
exp(
)
2
(
)
exp(
)
2
(
)
exp(
)
2
(
2
)
exp(
)
2
(
2
p
n
tors
semiconduc
intrinsic
In
2
3
2
3
2
2
3
2
2
3
2
2
3
2
kT
E
E
m
m
kT
E
kT
E
E
h
kT
m
kT
E
E
h
kT
m
kT
E
E
h
kT
m
kT
E
E
h
kT
m
c
v
e
h
F
F
v
h
c
F
e
F
v
h
c
F
e




















23. E
Ef
Ev
Valence band
Ec
Conduction band
Ec
Electron
energy
Temperature
*
*
e
h m
m 

24. Thus the Fermi energy level EF is located in the
middle of the forbidden band.
)
2
(
that
know
tor we
semiconduc
intrinsic
In
)
2
(
)
log(
4
3
)
(
)
log(
2
3
2
2
3
c
v
F
h
e
c
v
e
h
F
c
v
e
h
F
E
E
E
m
m
E
E
m
m
kT
E
kT
E
E
m
m
kT
E
















25. Extrinsic Semiconductors
• The Extrinsic Semiconductors are those in which
impurities of large quantity are present. Usually,
the impurities can be either 3rd group elements or
5th group elements.
• Based on the impurities present in the Extrinsic
Semiconductors, they are classified into two
categories.
1. N-type semiconductors
2. P-type semiconductors

26. When any pentavalent element such as
Phosphorous,
Arsenic or Antimony is added to the intrinsic
Semiconductor , four electrons are involved in
covalent bonding with four neighboring pure
Semiconductor atoms.
The fifth electron is weakly bound to the parent
atom. And even for lesser thermal energy it is
released Leaving the parent atom positively ionized.
N - type
Semiconductors

27. N-type
Semiconductor
Si
Si
Si
P
Si
Free electron
Impure atom
(Donor)

28. The Intrinsic Semiconductors doped with pentavalent
impurities are called N-type Semiconductors.
The energy level of fifth electron is called donor level.
The donor level is close to the bottom of the conduction
band most of the donor level electrons are excited in to
the conduction band at room temperature and become
the Majority charge carriers.
Hence in N-type Semiconductors electrons are Majority
carriers and holes are Minority carriers.

29. E Ed
Ev
Valence band
Ec
Conduction band
Ec
Electron
energy
Distance
Donor levels
Eg

30. Carrier Concentration in N-type
Semiconductor
• Consider Nd is the donor Concentration i.e., the
number of donor atoms per unit volume of the
material and Ed is the donor energy level.
• At very low temperatures all donor levels are filled
with electrons.
• With increase of temperature more and more donor
atoms get ionized and the density of electrons in the
conduction band increases.

31. )
exp(
)
2
(
2 2
3
2
kT
E
E
h
kT
m
n c
F
e 



The density of Ionized donors is given
by
)
exp(
)}
(
1
{
kT
E
E
N
E
F
N F
d
d
d
d



At very low temperatures, the Number of electrons in
the conduction band must be equal to the Number of
ionized donors.
)
exp(
)
exp(
)
2
(
2 2
3
2
kT
E
E
N
kT
E
E
h
kT
m F
d
d
c
F
e 




Density of electrons in conduction band is given
by

32. Taking logarithm and rearranging we get
2
)
(
0
.,
)
2
(
2
log
2
2
)
(
)
2
(
2
log
)
(
2
)
2
(
2
log
log
)
(
)
(
2
3
2
2
3
2
2
3
2
c
d
F
e
d
c
d
F
e
d
c
d
F
e
d
F
d
c
F
E
E
E
k
at
h
kT
m
N
kT
E
E
E
h
kT
m
N
kT
E
E
E
h
kT
m
N
kT
E
E
kT
E
E



















At 0k Fermi level lies exactly at the middle of the donor lev
and the bottom of the Conduction band

33. Density of electrons in the conduction band
kT
E
E
h
kT
m
N
kT
E
E
h
kT
m
N
kT
E
E
kT
E
E
kT
E
h
kT
m
N
kT
E
E
kT
E
E
kT
E
h
kT
m
N
kT
E
E
kT
E
E
kT
E
E
h
kT
m
n
c
d
e
d
c
F
e
d
c
d
c
F
c
e
d
c
d
c
F
c
e
d
c
d
c
F
c
F
e
2
)
(
exp
]
)
2
(
2
[
)
(
)
exp(
}
]
)
2
(
2
[
)
(
log
2
)
(
exp{
)
exp(
}
]
)
2
(
2
[
)
(
log
2
)
(
exp{
)
exp(
}
}
)
2
(
2
log
2
2
)
(
{
exp{
)
exp(
)
exp(
)
2
(
2
2
1
2
1
2
1
2
3
2
2
1
2
3
2
2
1
2
3
2
2
1
2
3
2
2
3
2






























34. kT
E
E
h
kT
m
N
n
kT
E
E
h
kT
m
N
h
kT
m
n
kT
E
E
h
kT
m
n
c
d
e
d
c
d
e
d
e
c
F
e
2
)
(
exp
)
2
(
)
(
2
}
2
)
(
exp
]
)
2
(
2
[
)
(
{
)
2
(
2
)
exp(
)
2
(
2
4
3
2
2
1
2
3
2
2
1
2
3
2
2
3
2
2
1














Thus we find that the density of electrons in the
conduction band is proportional to the square root of the
donor concentration at moderately low temperatures.

35. Variation of Fermi level with temperature
To start with ,with increase of temperature Ef increases
slightly.
As the temperature is increased more and more donor
atoms are ionized.
Further increase in temperature results in generation of
Electron - hole pairs due to breading of covalent bonds
and the material tends to behave in intrinsic manner.
The Fermi level gradually moves towards the intrinsic
Fermi level Ei.

36. P-type semiconductors
• When a trivalent elements such as Al, Ga or Indium have
three electrons in their outer most orbits , added to the
intrinsic semiconductor all the three electrons of Indium are
engaged in covalent bonding with the three neighboring Si
atoms.
• Indium needs one more electron to complete its bond. this
electron maybe supplied by Silicon , there by creating a
vacant electron site or hole on the semiconductor atom.
• Indium accepts one extra electron, the energy level of this
impurity atom is called acceptor level and this acceptor
level lies just above the valence band.
• These type of trivalent impurities are called acceptor
impurities and the semiconductors doped the acceptor
impurities are called P-type semiconductors.

37. Si
Si
Si
In
Si
Hole
Co-Valent
bonds
Impure atom
(acceptor)

38. E
Ea
Ev
Valence band
Ec
Conduction band
Ec
Electron
energy
temperature
Acceptor levels
Eg

39. • Even at relatively low temperatures, these
acceptor atoms get ionized taking electrons
from valence band and thus giving rise to holes
in valence band for conduction.
• Due to ionization of acceptor atoms only holes
and no electrons are created.
• Thus holes are more in number than electrons
and hence holes are majority carriers and
electros are minority carriers in P-type
semiconductors.

40. • Equation of continuity:
• As we have seen already, when a bar of n-type
germanium is illuminated on its one face, excess charge
carriers are generated at the exposed surface.
• These charge carriers diffuse through out the material.
Hence the carrier concentration in the body of the
sample is a function of both time and distance.
• Let us now derive the differential equation which governs
this fundamental relationship.
• Let us consider the infinitesimal volume element of area
A and length dx as shown in figure.

41. • If tp is the mean lifetime of the holes, the holes lost
per sec per unit volume by recombination is p/tp .
• The rate of loss of charge within the volume under
consideration
p
t
p
eAdx

If g is the thermal rte of generation of hole-electron
pairs per unit volume, rate of increase of charge wthin
the volume under consideration
eAdxg


42. • If i is the current entering
the volume at x and i + di
the current leaving the
volume at x + dx, then
decrease of charge per
second from the volume
under consideration = di
• Because of the above
stated three effects the
hole density changes with
time.
• Increase in the number of
charges per second
within the volume
p
dt
dp
eAdx

Increase = generation - loss
dI
t
p
eAdx
eAdxg
dt
dp
eAdx
p
p




43. Since the hole current is the sum of the diffusion current and the drift current
E
Ape
dx
dp
AeD
I h
p 



Where E is the electric field intensity within the volume. when no external
field is applied, under thermal equilibrium condition, the hole density
attains a constant value .
0
p
.
conditions
m
equilibriu
under
ion
recombinat
to
due
loss
of
therate
to
equal
is
holes
of
generation
of
rate
that the
indicates
equation
this
0
dt
dp
and
0
di
conditions
e
under thes
0
p
t
p
g 



44. dx
pE
d
x
p
D
t
p
p
dt
dp
eq
combain
h
p
p
s
)
(
)
(
.
5
&
4
,
3
...
,.
2
2
0








This is called equation of conservation of charge or the continuity equation.
x
E
n
x
n
D
t
n
n
t
n
x
E
p
x
p
D
t
p
p
t
p
x
pE
x
p
D
t
p
p
t
p
p
e
p
n
e
p
p
p
n
h
n
p
p
n
n
n
h
p
p

































)
(
)
(
material
type
-
p
in the
electrons
g
considerin
are
we
if
)
(
)
(
material
type
-
n
in the
holes
g
considerin
are
we
if
)
(
)
(
used.
be
should
s
derivative
partial
x,
and
both t
of
function
a
is
p
if
2
2
0
2
2
0
2
2
0




45. Direct band gap and indirect band gap
semiconductors:
• We known that the energy spectrum of an electron
moving in the presence of periodic potential field is
divided into allowed and forbidden zones.
• In crystals the inter atomic distances and the internal
potential energy distribution vary with direction of the
crystal. Hence the E-k relationship and hence energy
band formation depends on the orientation of the
electron wave vector to the crystallographic axes.
• In few crystals like gallium arsenide, the maximum of
the valence band occurs at the same value of k as the
minimum of the conduction band as shown in below.

46. Valence band
Conduction
band
g
E
k
E
k
E
g
E
Valence
band
Conduction
band

47. • In few semiconductors like silicon the maximum of
the valence band does not always occur at the same k
value as the minimum of the conduction band as
shown in figure. This we call indirect band gap
semiconductor.
• In direct band gap semiconductors the direction of
motion of an electron during a transition across the
energy gap remains unchanged.
• Hence the efficiency of transition of charge carriers
across the band gap is more in direct band gap than
in indirect band gap semiconductors.

48. Hall effect
When a magnetic field is applied perpendicular to a current carrying
conductor or semiconductor, voltage is developed across the
specimen in a direction perpendicular to both the current and the
magnetic field. This phenomenon is called the Hall effect and voltage
so developed is called the Hall voltage.
Let us consider, a thin rectangular slab carrying current (i) in the x-
direction.
If we place it in a magnetic field B which is in the y-direction.
Potential difference Vpq will develop between the faces p and q which
are perpendicular to the z-direction.

49. i
B
P
Q
X
Y
Z
+ + +
+ +
VH
+
+
+
+
+
+
+
+ +
+
+
+
+
+
+
+
+ + +
+
-
P – type semiconductor

50. i
B
X
Y
Z
VH
+
-
_
_ _
_
_ _
_
_
_ _
_
_ _
_
_
_
_ _ P
Q
N – type semiconductor

51. Magnetic deflecting force
city
drift velo
is
v
Where
)
(
)
(
d
B
v
E
qE
B
v
q
d
H
H
d




Hall eclectic deflecting force
H
qE
F 
When an equilibrium is reached, the magnetic deflecting force on
the charge carriers are balanced by the electric forces due to
electric Field.
)
( B
v
q
F d 


52. ne
J
vd 
The relation between current density and drift velocity is
Where n is the number of charge carriers per unit volume.
JB
E
ne
t
coefficien
Hall
R
JB
R
E
JB
ne
E
B
ne
J
E
B
v
E
H
H
H
H
H
H
d
H










1
)
,.
(
)
1
(
)
(
)
(

53. If VH be the Hall voltage in equilibrium ,the Hall electric field.
IB
t
V
R
B
t
I
R
V
JBd
R
V
dt
I
J
d
V
JB
R
JB
E
R
d
V
E
H
H
H
H
H
H
H
H
H
H
H
H








)
(
density
current
and
dt
is
section
cross
its
Then
sample,
the
of
thickness
the
is
t
If
1
slab.
the
of
width
the
is
d
Where

54. • Since all the three quantities EH , J and B
are measurable, the Hall coefficient RH and
hence the carrier density can be found out.
• Generally for N-type material since the Hall
field is developed in negative direction
compared to the field developed for a P-
type material, negative sign is used while
denoting hall coefficient RH.