kwang kim yonsei university [email protected]
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Foundations of Materials Science and Engineering Lecture Note 11 (Electrical Properties of Materials ) June 3, 2013. Kwang Kim Yonsei University [email protected]. 8 O 16.00. 7 N 14.01. 34 Se 78.96. 53 I 126.9. 39 Y 88.91. Electrical Properties. ISSUES TO ADDRESS. - PowerPoint PPT PresentationTRANSCRIPT
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Kwang Kim Yonsei University
Foundations of Materials Science and Engineering
Lecture Note 11(Electrical Properties of Materials)
June 3, 2013
39Y
88.91
8O
16.00
53I
126.9
34Se
78.96
7N
14.01
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Electrical Properties
ISSUES TO ADDRESS...• How are electrical conductance and resistance characterized?
• What are the physical phenomena that distinguish conductors, semiconductors, and insulators?
• For metals, how is conductivity affected by imperfections, temperature, and deformation?
• For semiconductors, how is conductivity affected by impurities (doping) and temperature?
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Electric Conduction – classical model
• Metallic bonds make free movement of valence electrons possible.
• Outer valence electrons are completely free to move between posi-tive ion cores.
• Positive ion cores vibrate with greater amplitude with increasing temperature.
• The motion of electrons are random and restricted in absence of elec-tric field.
• In presence of electric field,
electrons attain directed drift
velocity.
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Electric Conduction
• Ohm's Law: V = I Rvoltage drop (volts = J/C) C = Coulomb
resistance (Ohms)current (amps = C/s)
1
• Conductivity,
• Resistivity, : -- a material property that is independent of sample size and geometry
RAl
surface area of current flow
current flow path length
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Electrical Properties
• 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
D2
2
8D2
2
R2
2D2
2
D2
R1
8
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Definitions
Further definitions
J = <= another way to state Ohm’s law
J current density
electric field potential = V/
flux a like area surface
currentAI
Electron flux conductivity voltage gradient
J = (V/ )
ARI V
JAI
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Conductivity: Comparison
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Example: Conductivity Problem
What is the minimum diameter (D) of the wire so that V < 1.5 V?
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
IV
AR
4
2D
100 m
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Electron Energy Band Structures
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Band Structure
• Valence band – (filled) highest occupied energy levels• Conduction band – (empty) lowest unoccupied energy
levels
Valence band
Conductionband
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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 st
ates
Partially filled band
Energy
filled band
filled band
empty band
fille
d st
ates
Overlapping bands
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Energy Band Structures: Insulators & Semiconductors
• Insulators: -- wide band gap (> 2 eV) -- few electrons excited across band gap
Energy
filled band
filled valence band
fille
d st
ates
GAP
empty
bandconduction
• Semiconductors: -- narrow band gap (< 2 eV) -- more electrons excited across band gap
Energy
filled band
filled valence band
fille
d st
ates
GAP?
empty
bandconduction
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Charge Carriers
Two types of electronic charge carriers:
Free Electron – negative charge – in conduction band
Hole – positive charge
– vacant electron state in the valence band
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Metals: Resistivity vs. T, Impurities
• Presence of imperfections increases resistivity -- grain boundaries -- dislocations -- impurity atoms -- vacancies
These act to scatterelectrons so that theytake a less direct path.
• Resistivity increases with:
=
deformed Cu + 1.12 at%Ni
T (ºC)-200 -100 0
123456
Res
istiv
ity,
(1
0-8
Ohm
-m)
0
Cu + 1.12 at%Ni
“Pure” Cu
d -- %CW
+ deformation
i
-- wt% impurity
+ impurity
t
-- temperature
thermal
Cu + 3.32 at%Ni
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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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Conduction: Electron and Hole Migration
electric field electric field electric field
• Electrical Conductivity given by:
# electrons/m3 electron mobility
# holes/m3
hole mobilityhe 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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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
ni e Egap / kT
ni e e h
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Intrinsic vs. Extrinsic Conduction
• Intrinsic: -- case for pure Si -- # electrons = # holes (n = p)• Extrinsic: -- electrical behavior is determined by presence of impurities that introduce excess electrons or holes -- n ≠ p
3+
• p-type Extrinsic: (p >> n)
no applied electric field
Boron atom
4+ 4+ 4+ 4+
4+
4+4+4+4+
4+ 4+ hep
hole
• n-type Extrinsic: (n >> p)
no applied electric field
5+
4+ 4+ 4+ 4+
4+
4+4+4+4+
4+ 4+
Phosphorus atom
valence electron
Si atom
conductionelectron
een
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Electrical Properties
HOMO : Highest Occupied Molecular Orbital
LUMO : Lowest Unoccupied Molecular Orbital
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Extrinsic Semiconductors : Conductivity vs. T
• Data for Doped Silicon: -- increases doping -- reason: imperfection sites lower the activation energy to produce mobile electrons.
• Comparison: intrinsic vs extrinsic conduction... -- extrinsic doping level: 1021/m3 of a n-type donor impurity (such as P). -- for T < 100 K: "freeze-out“, thermal energy insufficient to excite electrons. -- for 150 K < T < 450 K: "extrinsic" -- for T >> 450 K: "intrinsic"
Con
duct
ion
elec
tron
conc
entra
tion
(1021
/m3 )
T (K)6004002000
0
1
2
3
freez
e-ou
t
extri
nsic
intri
nsic
doped
undoped
EF
EV
EC
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n-type Si
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p-type Si
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p-n Rectifying Junction
• Allows flow of electrons in one direction only (e.g., useful to convert alternating current to direct current).• Processing: diffuse P into one side of a B-doped 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: carriers flow away from p-n junction; junction region depleted of carriers; little current flow.
++
+ ++
- ---
-p-type n-type
+ -
++ +
++
--
--
-
p-type n-type
+++
+
+
---
--
p-type n-type- +
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Energy Band Bending
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LED from p-n Rectifying Junction
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Properties of Rectifying Junction
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Junction Transistor
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MOSFET Transistor Integrated Circuit Device
• Integrated circuits - state of the art ca. 50 nm line width– ~ 1,000,000,000 components on chip– chips formed one layer at a time
Fig. 18.26, Callister & Rethwisch 8e.
• MOSFET (metal oxide semiconductor field effect transistor)
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Electrical Properties of Ceramics
• Basic properties of dielectric: Dielectric constant:- Q = CVQ = ChargeV = VoltageC = CapacitanceC = ε0A/d ε0 = permeability of free space = 8.854 x 10-12 F/m
• When the medium is not free space C = Kε0A/d Where K is dielectric constant of the material between the
plates
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Dielectric Strength and Loss Factor
• Dielectric strength is measure of ability of material to hold energy at high voltage.
Defined as voltage gradient at which failure occurs.
Measured in volts/mil.• Dielectric loss factor: Current leads voltage by 90
degrees when a loss free dielectric is between plates of capacitor.
• When real dielectric is used, current leads voltage by 900 – δ where δ is dielectric loss angle.
• Dielectric loss factor = K tan δ measure of electric energy lost.
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Ferroelectric Ceramics
• Experience spontaneous polarization
BaTiO3 -- ferroelectric below its Curie temperature (120ºC)
If cooling takes place in electric field, dipoles align in the direction of the field.
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Piezoelectric Materials
stress-free with applied stress
Piezoelectricity – application of stress induces voltage – application of voltage induces dimensional change
Mechanicalforce
Electricresponse