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
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
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?
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.
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
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
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
Conductivity: Comparison
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
Electron Energy Band Structures
Band Structure
• Valence band – (filled) highest occupied energy levels• Conduction band – (empty) lowest unoccupied energy
levels
Valence band
Conductionband
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
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
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
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
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.
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
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
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
Electrical Properties
HOMO : Highest Occupied Molecular Orbital
LUMO : Lowest Unoccupied Molecular Orbital
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
n-type Si
p-type Si
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- +
Energy Band Bending
LED from p-n Rectifying Junction
Properties of Rectifying Junction
Junction Transistor
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)
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
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.
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.
Piezoelectric Materials
stress-free with applied stress
Piezoelectricity – application of stress induces voltage – application of voltage induces dimensional change
Mechanicalforce
Electricresponse