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3
• 12.2 Ohm's Law: V = I R in most cases V = V = V2 – V1
voltage drop (volts) resistance (Ohms)current (amps)
VIe-
A(cross sect. area)
L
• Resistivity, and Conductivity, :
--geometry-independent forms of Ohm's Law
VL
IA
E: electricfieldintensity
resistivity(Ohm-m)
J: current density
I
conductivity• Resistance:
R
LA
L
A
I. ELECTRICAL CONDUCTION
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12.6 Conduction in Terms of Band and Atomic Bonding Models
Metallic characterExcitation barrier is much smaller than heat (RT), noise or any background excitations. Practically anything excite electrons to the conduction band
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An intrinsic semiconductor has a band gap or barrier for the electrons to get into the conduction bandThis barrier need a photon excitation, an external bias potentialUsually RT cannot excite the electron to the conduction band.For instance, a photon of light ~4eV
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Scattering EventsElectric field drifts electrons in the opposite direction to the fieldb/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
In the ballistic regime there is practically no barrier for the electrons
Examples: in vacuum tubes, ~in carbon nanotubes (CNT), superconductors*
J = E
Ed
e
=
12.7 Electron Mobility
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12.10 Intrinsic Semiconduction
II. SEMICONDUCTIVITYConductivity of semiconducting materials is lower than from metalsSensitive to minute concentrations of impuritiesIntrinsic: pure materialExtrinsic: doped with impurity atoms
Band structureSi (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
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n-type extrinsic semiconductor
nee
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p-type extrinsic semiconductor
peh
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p-type extrinsic semiconductor
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Intrinsic carrier increases rapidly with temperature
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n-type silicon1021/m3
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12.14 The Hall Effect
d
BIRV zxH
H
How we can determine the type of carriers?Use magnetic fieldsThe Hall voltage
The Hall coefficient
neRH
1
nee
He R
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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 B-doped crystal.
• Results:--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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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 electricityMechanism not well-understoodConduction in polymers of high purity is electronic
Conducting PolymersConductivities of 1.5x107 (-m)-1
Even polyacetyleneDue to alternating single-double bonds
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Dielectric Behavior
Dielectric materialElectric dipole structureCharge separation
V
QC
l
AC
or
Do = oE
Do = oE + P
o= permittivity of vacuum = 8.85x10-12 F/m
l
AC o
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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 caseD= E
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P= o(r – 1)E
Do = oE + P where P is the polarization (C/m2)or total dipole moment per unit of volume of the dielectric
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Orientation polarization
Ionic polarization
Electronic Polarization
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Response to alternating fields
12.21 Frequency Dependence of the dielectric constant
Reorientation time --- relaxation frequency
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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
12.22 Dielectric Strength
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Frequency dependence of the dielectric constant
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15
• 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).
SUMMARY