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Chương 6 Tính chất điện-điện môi
Định luật Ohm
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• Ohm's Law: V = I R voltage drop (volts = J/C)
C = Coulomb
resistance (Ohms) current (amps = C/s)
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• Conductivity,
• Resistivity, :
-- a material property that is independent of sample size and
geometry
RA
l
surface area
of current flow
current flow
path length
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Which will have the greater resistance?
Analogous to flow of water in a pipe
Resistance depends on sample geometry and
size.
D
2D
R1 2
D
2
2
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D2
2
R2
2D
2
2
D2
R1
8
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Further definitions
J = E <= another way to state Ohm’s law
J current density
E electric field potential = V/
flux a like area surface
current
A
I
Electron flux conductivity voltage gradient
J = (V/ )
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• Room temperature values (Ohm-m)-1 = ( m)-1= S m-1
CONDUCTIVITY: COMPARISON
Silver 6.8 x 10 7
Copper 6.0 x 10 7
Iron 1.0 x 10 7
METALS conductors
Silicon 4 x 10 -4
Germanium 2 x 10 0
GaAs 10 -6
SEMICONDUCTORS
semiconductors
Polystyrene <10 -14
Polyethylene 10 -15 -10 -17
Soda-lime glass 10
Concrete 10 -9
Aluminum oxide <10 -13
CERAMICS
POLYMERS
insulators
-10 -10 -11
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What is the minimum diameter (D) of the wire so that V < 1.5 V?
(=6.07 x 107 (Ohm-m)-1)
EXAMPLE:
Cu wire I = 2.5 A - +
V
Solve to get D > 1.87 mm
< 1.5 V
2.5 A
6.07 x 107 (Ohm-m)-1
100 m
I
V
AR
4
2D
100 m
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Energy levels of an isolated atom
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ELECTRON ENERGY BAND STRUCTURES
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BAND STRUCTURE REPRESENTATION
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Metals Insulators Semiconductors
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CONDUCTION & ELECTRON TRANSPORT
• Metals (Conductors): -- for metals empty energy states are adjacent to filled states.
-- two types of band
structures for metals
-- thermal energy
excites electrons
into empty higher
energy states.
- partially filled band
- empty band that
overlaps filled band
filled band
Energy
partly filled band
empty band
GAP
fille
d s
tate
s
Partially filled band
Energy
filled
band
filled band
empty band
fille
d s
tate
s
Overlapping bands
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• Insulators: -- wide band gap (> 4 eV)
-- few electrons excited
across band gap
Energy
filled band
filled valence band
fille
d s
tate
s
GAP
empty
band conduction
• Semiconductors: -- narrow band gap (< 4 eV)
-- more electrons excited
across band gap
Energy
filled band
filled valence band
fille
d s
tate
s
GAP ?
empty
band conduction
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where, E is the electron energy, Ef is the Fermi energy, and T
is the absolute temperature. Its physical meaning is that: f(E)
is the probability of occupancy for an electron energy
state at energy E by an electron. That is, the probability
that this state is occupied by an electron is f(E), and the
probability that it is vacant is 1 - f(E).
The Fermi energy is the maximum energy occupied by
an electron at 0K.
Fermi function
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CHARGE CARRIERS IN INSULATORS AND SEMICONDUCTORS
Two types of electronic charge carriers:
Free Electron
– negative charge
– in conduction band
Hole
– positive charge – in valence band
Move at different speeds - drift velocities
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INTRINSIC SEMICONDUCTORS
Pure material semiconductors: e.g., silicon &
germanium
Group IVA materials
Compound semiconductors
– III-V compounds
• Ex: GaAs & InSb
– II-VI compounds
• Ex: CdS & ZnTe
– The wider the electronegativity difference between
the elements the wider the energy gap.
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INTRINSIC SEMICONDUCTION IN TERMS OF
ELECTRON AND HOLE MIGRATION
electric field electric field electric field
• Electrical Conductivity given by:
# electrons/m3 electron mobility
# holes/m3
hole mobility he epen
Concept of electrons and holes:
+ -
electron hole pair creation
+ -
no applied applied
valence electron Si atom
applied
electron hole pair migration
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NUMBER OF CHARGE CARRIERS
Intrinsic Conductivity
)s/Vm 45.085.0)(C10x6.1(
m)(10219
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hei
en
For GaAs ni = 4.8 x 1024 m-3
For Si ni = 1.3 x 1016 m-3
• Ex: GaAs
he epen
• for intrinsic semiconductor n = p = ni
= ni|e|(e + h)
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INTRINSIC SEMICONDUCTORS:
CONDUCTIVITY VS T
• Data for Pure Silicon: -- increases with T
-- opposite to metals
material
Si
Ge
GaP
CdS
band gap (eV)
1.11
0.67
2.25
2.40
Selected values from Table 18.3,
Callister & Rethwisch 8e.
ni eEgap /kT
ni e e h
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Intrinsic semiconductor - A semiconductor in
which properties are controlled by the
element or compound that makes the
semiconductor and not by dopants or
impurities.
Extrinsic semiconductor - A semiconductor
prepared by adding dopants, which determine
the number and type of charge carriers.
Doping - Deliberate addition of controlled
amounts of other elements to increase the
number of charge carriers in a semiconductor.
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Extrinsic semiconductor
(doped with an electron donor)
Without thermal
excitation
With thermal
excitation
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Energy bands
Intrinsic
semiconductor
Extrinsic semiconductor
(doped with an electron
donor)
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Extrinsic semiconductor
(doped with an electron acceptor)
Without thermal
excitation
With thermal
excitation
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Energy bands
Intrinsic
semiconductor
Extrinsic semiconductor
(doped with an electron
acceptor)
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Defect semiconductor
(excess semiconductor Zn1+xO)
Zn+ ion serves as an electron donor.
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Energy bands of Zn1+xO
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Defect semiconductor
(deficit semiconductor Ni1-xO)
Ni3+ ion serves as an electron acceptor.
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Energy bands of Ni1-xO
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Temperature Effect - When the temperature of a
metal increases, thermal energy causes the
atoms to vibrate
Effect of Atomic Level Defects - Imperfections in
crystal structures scatter electrons, reducing
the mobility and conductivity of the metal
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T
where = temperature coefficient of
electrical resistivity
Change of resistivity with temperature
for a metal
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roo
ks/
Co
le, a
div
isio
n o
f T
ho
mso
n L
earn
ing,
Inc.
T
ho
mso
n L
earn
ing™
is
a tr
adem
ark u
sed h
erei
n u
nder
lic
ense
.
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= q n
For a metal, σ decreases with increasing
temperature because μ decreases with
increasing temperature.
For a semiconductor, σ increases with
increasing temperature because n and/or
p increases with increasing temperature.
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where Eg = energy band gap between conduction and
valence bands,
k = Boltzmann's constant,
and T = temperature in K.
The factor of 2 in the exponent is because the
excitation of an electron across Eg produces an
intrinsic conduction electron and an intrinsic hole.
,en/2kTEg
For a semiconductor
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Taking natural logarithms,
Changing the natural logarithms to
logarithms of base 10,
.eσσ/2kTE
og
.2kT
Eσlnσln
g
o
.(2.3)2kT
Eσlogσlog
g
o
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Conductivity of an ionic solid
, )A + C(n q = An q + Cn q =
where n = number of Schottky defects
per unit volume
C = mobility of cations,
A = mobility of anions.
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,nnn ei
where n = total concentration of conduction
electrons,
ni = concentration of intrinsic conduction
electrons,
ne = concentration of extrinsic conduction
electrons.
An n-type semiconductor
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,eDD
, +N = n De
. e nkT2/Eg-
i
. e n/kTE- D
e
. < < nn ei
.pp i
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However
,
.pp i
No extrinsic holes, thus
pi = ni
Thus,
p = ni
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enn
. 0 p
. qp + qn = pn
nqn
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, p + p = p ei
where p = total concentration of
conduction holes
pi = concentration of intrinsic holes,
pe = concentration of extrinsic holes.
A p-type semiconductor
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, A-
e-
+A
, h+
+ A-
A
, N = p Ae
, e pkT2/Eg-
i
. e-
p/kTEA
e
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p < < p ei
.nn i
. p =n i
p p e
. 0n
. qp + qn = pn qn p
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THE MASS-ACTION LAW
Product of n and p is a constant
for a particular semiconductor
at a particular temperature
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.ppnn ii
.nnp 2i
Siforcm101.5n 310i
.Geforcm102.5n 313
i
Intrinsic semiconductor
This equation applies
whether the semiconductor
is doped or not.
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De Nnn
DD NN
.Nn D
. N
n =
n
n = p
D
2i
2i
Consider an n-type semiconductor.
(Donor exhaustion)
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ANpp e
A-A NN
.Np A
. N
n =
n =
2i
2i
Apn
Consider an p-type semiconductor.
(Donor exhaustion)
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Conducting polymers
THE NOBEL PRIZE IN CHEMISTRY, 2000:
CONDUCTIVE POLYMERS
Professor Alan J. Heeger at the University of California at Santa Barbara, USA
Professor Alan G. MacDiarmid at the University of Pennsylvania, USA and
Professor Hideki Shirakawa at the University of Tsukuba, Japan
rewarded the Nobel Prize in Chemistry for 2000 “for the discovery and development of electrically conductive polymers”.
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of other materials, from quartz (insulator) to copper
(conductor).
Polymers may also have conductivities
corresponding to those of semiconductors.
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Chemical structures of some conductive polymers. From top left
clockwise: polyacetylene; polyphenylene vinylene; polypyrrole (X = NH)
and polythiophene (X = S); and polyaniline (X = NH/N) and
polyphenylene sulfide (X = S).
A key property of a conductive polymer is the presence of conjugated
double bonds along the backbone of the polymer. In conjugation, the
bonds between the carbon atoms are alternately single and double.
The presence of C5 makes
it impossible for the π
electrons of the C6-C7 pi
bond to join the conjugated
system on the first four
carbons.
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Conjugation is not enough to make the polymer
material conductive. In addition – and this is what the
dopant does – charge carriers in the form of extra
electrons or ”holes” have to be injected into the
material.
The “doped” form of polyacetylene had a conductivity of
105 Siemens per meter, which was higher than that of any
previously known polymer. As a comparison, Teflon has a
conductivity of 10–16 S.m–1and silver and copper 108 S.m–1.
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• The halogen doping that transforms
polyacetylene to a good conductor of electricity is
oxidation (or p-doping).
• Reductive doping (called n-doping) is also
possible using, e.g., an alkali metal.
The doped polymer is thus a salt. However, it is not the counter
ions, I3– or Na+, but the charges on the polymer that are the
mobile charge carriers.
Mechanism of polymer conductivity – role
of doping
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Ferroelectric - A material that shows spontaneous
and reversible dielectric polarization.
Piezoelectric – A material that develops voltage upon
the application of a stress and develops strain when
an electric field is applied.
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The (a) direct and (b) converse piezoelectric effect.
In the direct piezoelectric effect, applied stress
causes a voltage to appear.
In the converse effect (b), an applied voltage
leads to development of strain.
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