Transcript Slide 1

EXTRINSIC SEMICONDUCTOR
In an extrinsic semiconducting material, the charge
carriers originate from impurity atoms added to the original
material is called impurity [or] extrinsic semiconductor.
• This Semiconductor obtained by doping TRIVALENT and
PENTAVALENT
impurites
in
a
TETRAVALENT
semiconductor. The electrical conductivity of
pure
semiconductors may be changed even with the addition
of few amount of impurities.
DOPING
The method of adding impurities to a pure
semiconductor is known as DOPING, and the impurity
added is called the dopping agent(Ex-Ar,Sb,P,Ge and
Al).
The addition of impurity would increases the no.
of free electrons and holes in a semiconductor and
hence increases its conductivity.
SORTS OF SEMICONDUCTOR according to ADDITION
OF IMPURITIES
n-type semiconductor
p-type semiconductor
N – type semiconductor
When pentavalent impurity is added to the intrinsic
semiconductors, n type semi conductors are formed.
Conduction band
Ec
Ed
Eg
Ev
Valence band
n - type semiconductor
At T = 0K
Donors levels
occupied
 When small amounts of pentavalent impurity such as
phosphorous are added during crystal formation, the impurity
atoms lock into the crystal lattice[ see above Fig).
 Consider a silicon crystal which is doped with a fifth
column element such as P, As or Sb.
 Four of the five electrons in the outermost orbital of the
phosphorus atom take part in the tetrahedral bonding with the
four silicon neighbours.
 The fifth electron cannot take part in the discrete covalent
bonding. It is loosely bound to the parent atom.
 It is possible to calculate an orbit for the fifth electron
assuming that it revolves around the positively charged
phosphorus ion, in the same way as for the “1s” electron around
the hydrogen nucleus.
 The electron of the phosphorus atom is moving in the
electric field of the silicon crystal and not in free space, as is the
case in the hydrogen atom.

This brings in the dielectric constant of the crystal into the
orbital calculations, and the radius of the electron orbit here
turns out to be very large, about 80 Å, as against 0.5 Å for the
hydrogen orbit. Such a large orbit evidently means that the fifth
electron is almost free and is at an energy level close to the
conduction band.
 At OK, the electronic system is in its lowest energy state, all
the valence electron will be in the valence band and all the
phosphorous atoms will be un-ionised.
 The energy levels of the donor atoms are very close to the
conduction band.
 In the energy level diagram, the energy level of the fifth
electron is called donor level. The donor level is so close to the
bottom of the conduction band.
 Most of the donor level electrons are excited into the
conduction band at room temperature and become majority
charge carriers.
Conduction band
Ec
Ed
Conduction band
Ec
Ed
Eg
Ev
Donors levels
ionised
Eg
Ev
Valence band
Valence band
At T > 0K
At T = 300K
Donors levels
ionised
If the thermal energy is sufficiently high, in addition to the
ionization of donor impurity atoms, breaking of covalent
bonds may also occur thereby giving rise to generation of
electron hole pair.
Fermi energy
The Fermi energy for n – type semiconductor is given by
EF






( Ec  Ed )
kT
Nd


ln 

3/ 2
2
2
  2 me* kT 


 2



h2



 

At 0 K, E F  ( E c  E d )
2
Variation of Fermi level with temperature
The Fermi energy is given by,
kT
 E  Ec 
EF   d
ln

2
2


Nd
 2 me * kT
2

h2

3/ 2
 2 me * kT 
2

h2


Let
 E  E  kT  N 
  d c   ln  d 
 2  2  Nx 
1
3/ 2
 Nx
E
T
Variation of Fermi level with donor concentration with temperature
As T increases, Fermi level drops. Also for a given
temperature the Fermi level shift upward as the
concentration increases.
We can say that EF decreases slightly with increase
in temperature.
As the temperature is increased, more and more
donor atoms are ionized. For a particular temperature all
the donor, atoms are ionized.
Further increase in temperature results in generation of
electron-hole pairs due to the breaking of covalence
bonds and the material tends to behave in intrinsic
manner. The Fermi level gradually moves towards the
intrinsic Fermi level Ei .
P -Type Semiconductor
When trivalent impurity is added to
semiconductor, P type semi conductors are formed.
intrinsic
Al has three electrons in the outer orbital. While
substituting for silicon in the crystal, it needs an extraelectron to complete the tetrahedral arrangement of bonds
around it.
The extra electron can come only from one of
the neighbouring silicon atoms, thereby creating a vacant
electron site (hole) on the silicon.
The aluminium atom with the extra electron becomes a
negative charge and the hole with a positive charge can be
considered to resolve around the aluminium atom, leading to
the same orbital calculations as aboveT.
Conduction band
Ec
Eg
Ea
Ev
p - type semiconductor
Valence band
At T = 0K
Since the trivalent impurity accepts an electron, the
energy level of this impurity atom is called acceptor level.
This acceptor level lies just above the valence bond.
Even at relatively low temperatures, these acceptor
atoms get ionized taking electrons from valence bond and
thus giving to holes in the valence bond for conduction.
Due to ionization of acceptor atoms, only holes and no
electrons are created.
If the temperature is sufficiently high, in addition to the
above process, electron-hole pairs are generated due to the
breaking of covalent bonds.
Thus holes are more in number than electrons and hence
holes are majority carriers and electrons are minority carriers
Conduction band
Ec
Eg
Acceptors have
accepted electrons
from valence band
Ea
Ev
Valence band
(a) At T > 0K
(b) At T = 300K
Fermi Energy
The Fermi energy for p – type semiconductor is given by
EF



Na
 E  Ea  kT
 v
ln 

3/
2
2


2 m*h kT 
 

2
 2


h

 
At 0 K,



2 



Ev  Ea
EF 
kT
At 0K, Fermi level is exactly at the middle of the acceptor
level on the top of the valence band.
VARIATION OF FERMI LEVEL WITH
TEMPERATURE
EF



kT
Na
 Ev  Ea 

ln 

3/ 2
2
2


2 mh* kT 
 2

 
h2

 
where Ny = 2
and therefore EF =







=
 Na 
kT
 Ev  E a 

ln 




2
2


 Ny 
 2 mh * kT 


2
h


3/ 2
 Ev  Ea  kT  N a 
ln


 Ny 
 2  2


From the above eqn, it is seen that EF increases slightly
as the temperature increases.
As the temperature increases, more and more acceptor
atoms are ionised.
For a particular temperature all the acceptor
atoms are ionized.
Further increase in temperature results in generation of
electron-hole pair due to the breaking of covalent bonds
and the material tend to behave in intrinsic manner.
The Fermi level gradually moves towards the
intrinsic Fermi level.
E
Na
Na
T
Variation of Fermi level with acceptor concentration and temperature
Hall Effect
When a piece of conductor (metal or semi
conductor) carrying a current is placed in a transverse
magnetic field, an electric field is produced inside the
conductor in a direction normal to both the current and
the magnetic field.
This phenomenon is known as the Hall Effect and
the generated voltage is called the Hall voltage.
Y
B
I
G
F
D
O
E
C
X
EH
A
B
Z
Hall effect
Consider a conventional current flow through the strip
along OX and a magnetic field of induction B is applied along
axis OY.
Case – I: If the Material is N-Type Semi Conductor
(or) Metal

If the strip is made up of metal or N-type semiconductor,
the charge carriers in the strip will be electrons.

As conventional current flows along OX, the electrons
must be moving along XO.

If the velocity of the electrons is `v’ and charge of the
electrons is `e’, the force on the electrons due to the magnetic
field
F =  Bev, which acts along OZ.
 This causes the electrons to be deflected and the
electrons accumulate at the face ABEF.

Face ABEF will become negative and the face OCDG
becomes positive.

A potential difference is established across faces ABEF
and OCDG, causing a field EH.
Y
B
n
ce o
Forectron
el
F
G
B
v
F
D
O
E
C
X
I
A
B
Z
Hall effect for n type semiconductor
This field gives rise to a force of `eEH’ on the electrons in
the opposite direction. (i.e, in the negative Z direction)
At equilibrium, eEH = Be (or) EH = B
If J is the current density, then, J =  ne
where `n’ is the concentration of current carriers.
v=
J
 ne
Substitute the value of `’ in eqn
BJ
EH =
 ne
The Hall Effect is described by means of the Hall
coefficient `RH’ in terms of current density `J’ by the relation,
EH = RHBJ
(or) RH = EH/ BJ
RH 
BJ
1

 neBJ
ne
All the three quantities EH, J and B are measurable,
the Hall coefficient RH and hence the carrier density `n’ can
be found out.
Case – (ii) If the material is a P-type semi conductor

If the strip is a P-type semiconductor, the charge
carriers in the strip will be holes.

The holes will constitute current in the direction of
conventional current.

Holes move along the direction of the conventional
Y
current itself along ox
B
B
v
n
eo
c
r
Fo le
ho
F
G
F
D
O
E
C
X
I
A
B
Z
Hall effect for p type semiconductor
If `e’ is the charge of the hole, the force experienced by
the holes due to magnetic field is, F = Be , which acts along
OZ.
This causes the holes to accumulate on the face ABEF
– making it positive, and leaving the face OCDG as negative.
P-type semiconductor, RH = 1/pe , where p = the density of
holes.
Determination of Hall coefficient
The Hall coefficient is determined by measuring
the Hall voltage that generates the Hall field.
If `w’ is the width of the sample across which the Hall
voltage is measured, then
EH = VH/ w
We know that,
RH = EH/ BJ
Substituting the value of EH in the above eqn
RH = VH/ wBJ
(or) VH = RHwBJ
If the thickness of the sample is `t’, the its cross sectional
area A = wt, and the current density,
I
I

J=
A wt
Substitute the value of `J ’
RH I B
RH w.B.I
VH =
=
(or) RH =
t
wt
VH t
IB
VH will be opposite in sign for P and N type semiconductors.
A rectangular slab of the given material having
thickness `t’ and width `w’ is taken.
A current of `I’ amperes is passed through this sample by
connecting it to a battery, `Ba’.
The sample is placed between two pole pieces of an
electromagnet such that the field `B’ is perpendicular to I
Y
B
G
I
D
O
F
t
A
w
E
B
Z
Ba
A
Rh
C
X
VH
The hall voltage `VH’ is then measured by placing
two probes at the two side faces of the slab. If the
magnetic flux density is `B’ and `VH’ is the hall voltage, then
the Hall coefficient,
Y
B
G
I
D
O
F
t
A
w
E
C
X
VH
B
Z
Ba
A
Rh
Experimental setup for the measurement of Hall voltage
RH = VHt / IB (m3/coulomb)
For n-type material, n = nee (or)
For p-type material, p = p e  h (or)
e 
h 
n
   n . RH
ne
p
pe
  p . RH
Applications of Hall effect
(1) Determination of N-type of semiconductor
For a N-type semiconductor, the Hall coefficient
is negative whereas for a P-type semiconductor, it is positive.
Thus from the direction of the Hall voltage developed, one
can find out the type of semiconductor.
(2) Calculation of carrier concentration
Once Hall coefficient RH is measured, the
carrier concentration can be obtained,
n
1
eR H
(or )
p 
1
eR H
(3)Determination of mobility
We know that, conductivity,  n = n e e (or)
Also, P = p e h (or)
p
n 
  p . RH
pe
Thus by measuring `’ and RH, ’ can be calculated.
(4) Measurement of magnetic flux density.
Using a semiconductor sample of known `RH’, the
magnetic flux density can be deduced from, RH =
B
VH t
RH I
DILUTE MAGNETIC SEMICONDUCTORS
Introduction
•
Integrated circuits and high-frequency devices made of
semiconductors, used for information processing and
communications, have had great success using the charge of
electrons in semiconductors.
Mass storage of information–indispensable for
information technology–is carried out by magnetic
recording (hard disks, magnetic tapes, magneto optical
disks) using spin of electrons in ferromagnetic materials.
Dilute or diluted magnetic semiconductors (DMS)
also referred to as semi magnetic semiconductors, are
alloys whose lattices are made up in part of
substitutional magnetic atoms.
DMS= Semiconductors with dilute concentration of
magnetic dopants.
The most important feature of these materials is carrier
mediated magnetism which can be easily controlled with
voltage. The advantage is that, unlike the conventional
magnets, DMS are compatible with semiconductors and can
be used as efficient sources for spin injection.
Three types of semiconductors: (A) a magnetic semiconductor(e.g.
some spinels), in which a periodic array of magnetic element is
present, (B) a dilute magnetic semiconductor(e.g. (GaMn)As,(InMn)P,
ZnCoO etc), an alloy between nonmagnetic semiconductor and
magnetic element and (C) a non-magnetic semiconductor(e.g. GaAs,
InP, Cu2O, NiO etc), which contains no magnetic ions.
Materials
The most common SMSC are II-VI compounds (like CdTe,
ZnSe, CdSe, CdS, etc.), with transition metal ions (e.g. Mn, Fe
or Co) substituting their original cations. There are also
materials based on IV-VI (e.g. PbTe, SnTe) and recently III-V
(e.g. GaAs, InSb) crystals.
The wide variety of both host crystals and magnetic atoms
provides materials which range from wide gap to zero gap
semiconductors, and which reveal many different types of
magnetic interaction.
Formation of DMS
Several of the properties of these materials may be tuned
by changing the concentration of the magnetic ions.
The most relevant feature of DMS, is the coexistence and
interaction of two different electronic sub systems:
delocalized conduction (s-type) and valence (p-type) band
electrons and localized (d or f-type) electrons of magnetic
ions.
In particular the spd exchange interaction leads to strong
band splitting, which result in giant magneto optical effects .
The most studied III-V DMS system is GaxMn1-xAs
with x up to 0.07. The solubility limit of magnetic elements in
III-V semiconductors is very low, but in order to have
ferromagnetism in DMS, a sizable amount of magnetic ions
are needed.
This can only be accomplished by means of
nonequilibrium crystal growth techniques, such as low
temperature molecular beam epitaxy (MBE).
The upper concentration limit of magnetic ions is
around 10 %.
The highest conclusively reported Tc of DMS is around
110 K for 5 % doped GaAs. It is of great technological
importance to find DMS systems with Tc above room
temperature, before one attempts to make a DMS based
device.
Applications
Diluted magnetic semiconductors (DMS) are expected to
play an role in interdisciplinary materials science and future
electronics because charge and spin degrees of freedom
accommodated into a single material exhibits interesting
magnetic, magneto-optical, magnetoelectronic and other
properties.
It is expected that magnetoelectronic important chips
will be used in quantum computers.
An inherent advantage of magnetoelectronics over
electronics is the fact that magnet tend to stay magnetized for
long.
Hence this arises interest in industries to replace the
semiconductor-based components of computer with magnetic
ones, starting from RAM.
These DMS materials are very attractive for integration of
photonic (light-emitting diodes), electronic (field effect
transistors), and magnetic (memory) devices on a single
substrate.
Some important application areas of DMS are listed below.
•Photonics plus spintronics (Spin+electronics = Spintronics)
•Improved spin transistor
•Transistors spin toward quantum computing
•Magnetic spins to store quantum information
•Microscope to view magnetism at atomic level
•Ballistic magneto resistance
•Missile guidance
•Fast accurate position and motion sensing of
mechanical components in precision aengineering and
in robotics
•In automotive sensors
Importance of DMS based devices
Information is stored (written) into spins as a particular spin
orientation (up or down)
The spins, being attached to mobile electrons, carry the
information along a conductor
The information can be stored or is read at a terminal.
Spintronics devices are attractive for memory storage and
magnetic sensors applications
Spin-based electronics promises a radical alternative to
charge-based electronics, namely the possibility of logic
operations with much lower power consumption than
equivalent charge-based logic operations
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