Download Electrical properties

I. ELECTRICAL CONDUCTION
• 12.2 Ohm's Law:
V = I R in most cases V = DV = V2 – V1
voltage drop (volts)
resistance (Ohms)
current (amps)
• Resistivity, r and Conductivity, s:
--geometry-independent forms of Ohm's Law
E: electric
field
intensity
• Resistance:
DV I
 r
L
A
rL
L
R

A As
resistivity
(Ohm-m)
J: current density
conductivity
I
s
r
3
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12.6 Conduction in Terms of Band and Atomic Bonding Models
Metallic character
Excitation barrier is much smaller than heat (RT), noise or any background
excitations. Practically anything excite electrons to the conduction band
An intrinsic semiconductor has a band gap or barrier for the electrons to get
into the conduction band
This barrier need a photon excitation, an external bias potential
Usually RT cannot excite the electron to the conduction band.
For instance, a photon of light ~4eV
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12.7 Electron Mobility
J = sE
Scattering Events
Electric field drifts electrons in the
opposite direction to the field
b/c electrons are –ve
The actual speed of electrons is
much higher than the drift velocity
Scattering is due to the strike with
the nuclei
When the actual velocity of the
electrons is similar to the drift
velocity, the system is in the ballistic
regime
d
 e=
E
In the ballistic regime there is
practically no barrier for the electrons
Examples: in vacuum tubes, ~in
carbon nanotubes (CNT),
superconductors*
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II. SEMICONDUCTIVITY
Conductivity of semiconducting materials is lower than from metals
Sensitive to minute concentrations of impurities
Intrinsic: pure material
Extrinsic: doped with impurity atoms
12.10 Intrinsic Semiconduction
Band structure
Si (1.1 eV)
Ge (0.7 eV)
GaAs (IIIA-VA)
InSb (IIIA-VA)
CdS (IIB-VIA)
ZnTe (IIB-VIA)
We have electrons as carriers in metals and “electrons” and ‘holes’ as carriers
in semiconductors
n-type extrinsic semiconductor
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s  n e e
p-type extrinsic semiconductor
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s  p e h
p-type extrinsic semiconductor
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Intrinsic carrier increases rapidly
with temperature
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n-type silicon
1021/m3
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12.14 The Hall Effect
How we can determine the type of carriers?
Use magnetic fields
The Hall voltage
The Hall coefficient
1
RH 
ne
s
e 
e  RH s
ne
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RH I x Bz
VH 
d
p-n rectifying junction
Flow of electrons in one direction only
convert alternating current to direct current
Processing: diffuse P into one side of a Bdoped crystal.
--No applied potential, no net current flow. -Forward bias: carriers flow through p-type and
n-type regions; holes and electrons recombine at
p-n junction; current flows.
--Reverse bias: carrier
flow away from p-n junction;
carrier conc. greatly reduced
at junction; little current flow.
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• Results:
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The Junction Transistor
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The Junction Transistor
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The MOSFET
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12.17 Electrical properties of polymers
Usually poor conductors of electricity
Mechanism not well-understood
Conduction in polymers of high purity is electronic
Conducting Polymers
Conductivities of 1.5x107 (W-m)-1
Even polyacetylene
Due to alternating single-double bonds
Do = oE
Dielectric material
Electric dipole structure
Charge separation
Q
C
V
A
C  o
l
o= permittivity of vacuum
= 8.85x10-12 F/m
Do = oE + P
A
C 
l

r 
o
Dielectric Behavior
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12.19 Field vectors and polarization
p = qd
Surface charge density or
dielectric displacement (C/m2)
Do = oE
For the dielectric case
D=  E
Do = oE + P
where P is the polarization (C/m2)
or total dipole moment per unit of volume of the dielectric
P= o(r – 1)E
Electronic Polarization
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Ionic polarization
Orientation polarization
12.21 Frequency Dependence of the dielectric constant
Response to alternating fields
Reorientation time --- relaxation frequency
12.22 Dielectric Strength
Substance
Dielectric Strength (MV/m)
Air
3
Quartz
8
Strontium titanate
8
Neoprene rubber
12
Nylon
14
Pyrex glass
14
Silicone oil
15
Paper
16
Bakelite
24
Polystyrene
24
Teflon
60
Frequency dependence of the dielectric constant
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SUMMARY
• Electrical conductivity and resistivity are:
--material parameters.
--geometry independent but not at small scale (nano)
• Electrical resistance is:
--a geometry and material dependent parameter.
• Conductors, semiconductors, and insulators...
--different in whether there are accessible energy
states for conductance electrons.
• For metals, conductivity is increased by
--reducing deformation
--reducing imperfections
--decreasing temperature.
• For pure semiconductors, conductivity is increased by
--increasing temperature
--doping (e.g., adding B to Si (p-type) or P to Si (n-type).
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