Download Introduction to Materials Science, Chapter 18, Electrical properties

Introduction to Materials Science, Chapter 18, Electrical properties
Chapter 18
Electrical properties
 Electrical conduction
• How many moveable electrons are there in a
material (carrier density)?
• How easily do they move (mobility) ?
 Semiconductivity
• Electrons and holes
• Intrinsic and extrinsic carriers
• Semiconductor devices: p-n junctions and
transistors
 Conduction in polymers and ionic materials
 Dielectric behavior
Optional reading: 18.14, 18.21, 18.24, 18.26
University of Virginia, Dept. of Materials Science and Engineering
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Introduction to Materials Science, Chapter 18, Electrical properties
Electrical Properties of Metals
Electrical potential, V --> Current, I
[volts, J/C]
Ohm's law:
[amperes, C/s]
I = V/R
R is the electrical resistance
[ohms, ]
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Introduction to Materials Science, Chapter 18, Electrical properties
R due to intrinsic resistivity  [-m]
+ geometry (length l, area A through
which the current passes)
R = l/A
In most materials (e.g. metals), the
current is carried by electrons
(electronic conduction).
In ionic crystals, the charge carriers
are ions (ionic conduction).
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Introduction to Materials Science, Chapter 18, Electrical properties
Electrical Properties of Metals
Electrical
conduct)
conductivity
(ability
to
 = 1/
Electric field intensity: E = V/l
Ohm's law can be rewritten in terms
of the current density J = I/A
J=E
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Introduction to Materials Science, Chapter 18, Electrical properties
Electrical conductivity varies between
different materials by over
27 orders of magnitude,
the greatest variation of any physical
property
 (.cm)-1
Metals:  > 105 (.m)-1
Semiconductors: 10-6 <  < 105 (.m)-1
Insulators:  < 10-6 (.m)-1
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Introduction to Materials Science, Chapter 18, Electrical properties
Energy Band Structures (I)
Atoms form a solid  valence electrons interact
 two quantum mechanical effects.
Heisenberg's uncertainty principle: constrain
electrons to a small volume  raises their energy
called promotion.
Pauli exclusion principle limits the number of
electrons with the same energy.
Result: valence electrons form wide electron
energy bands in a solid.
Bands separated by gaps, where electrons cannot
exist.
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Introduction to Materials Science, Chapter 18, Electrical properties
Energy Band Structures and Conductivity
 Fermi Energy (EF) - highest filled state at 0 K
 Conduction band -partially filled or empty band
 Valence band – highest partially or completely
filled band
Semiconductors and insulators, valence band is filled,
and no more electrons can be added (Pauli's principle).
> 2 eV
insulator
semiconductor
Electrical conduction --> electrons gain energy in
an electric field.
Not possible in these materials:
forbidden band gap
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Introduction to Materials Science, Chapter 18, Electrical properties
Probability an electron reaches the
conduction band is ~exp(-Eg/2kT)
Eg is band gap
Probability < 10-24 no electrons in the
conduction band in a solid of 1 cm3
Requires Eg/2kT > 55
At room temperature, 2kT = 0.05 eV 
Eg > 2.8 eV an insulator
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Introduction to Materials Science, Chapter 18, Electrical properties
Energy Band Structures and Conductivity
(semiconductors and insulators)
 Semiconductors and insulators: electrons
must jump across band gap into
conduction band to find conducting
states above Ef
 Energy needed  heat or radiation
 Difference: semiconductors electrons
reach conduction band at room
temperature: not in insulators
 Electron promoted to conduction band
leaves a hole (positive charge) in the
valence band
it also participates in conduction.
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Introduction to Materials Science, Chapter 18, Electrical properties
Energy Band Structures and Conductivity (metals)
Metals: highest occupied band is partially
filled or bands overlap
Conduction occurs by promoting electrons
into conducting states: start right above
Fermi level.
Energy provided by an electric field is
sufficient to excite many electrons into
conducting states.
Cu
Mg
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Introduction to Materials Science, Chapter 18, Electrical properties
Energy Band Structures and Bonding
(metals, semiconductors, insulators)
Metals: valence electrons form an
“electron gas”
Insulators: valence electrons tightly
bound to (or shared with) the
individual atoms: ionic + covalent
Semiconductors:
bonding
mostly
covalent
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Introduction to Materials Science, Chapter 18, Electrical properties
Energy Band Structures and Conductivity
Metals
Semiconductors and Insulators
University of Virginia, Dept. of Materials Science and Engineering
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Introduction to Materials Science, Chapter 18, Electrical properties
Electron Mobility
 Force on electron is -eE, e = charge
 No obstacles  electron speeds up in an
electric field.
Vacuum (TV tube) or perfect crystal
 Real solid: electrons scattered by
collisions with imperfections and thermal
vibrations
 friction  resistance
 net drift velocity of electrons
vd = eE
e – electron mobility
[m2/V-s]. 1 / Friction
E
Scattering
events
Transfers part of energy
supplied by electric field
into lattice as heat.
Electric heater
Net electron motion
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Introduction to Materials Science, Chapter 18, Electrical properties
Electron Mobility
 Electrical conductivity proportional to
number of free electrons per unit volume,
Ne, and electron mobility, e
 = Nee e
(m) = Metal
(s) = Semicon
Na (m)
Ag (m)
Al (m)
Si (s)
GaAs (s)
InSb (s)
Nmetal >> Nsemi
metal < semi
Mobility (RT)
 (m2V-1s-1)
0.0053
0.0057
0.0013
0.15
0.85
8.00
Carrier Density
Ne (m-3)
2.6 x 1028
5.9 x 1028
1.8 x 1029
1.5 x 1010
1.8 x 106
metal >> semi
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Introduction to Materials Science, Chapter 18, Electrical properties
Conductivity / Resistivity of Metals
Total resistivity tot (Matthiessen rule)
total = thermal+impurity+deformation
Increases with T, with deformation, and with
alloying.
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Introduction to Materials Science, Chapter 18, Electrical properties
Conductivity / Resistivity of Metals
Influence of temperature:
Increasing thermal vibrations and density of vacancies
T = o + aT
Impurities:
• Solid solution
I
=
Aci(1-ci)
ci is impurity concentration
• Two-phase alloy ( and  phases):
i = V +  V 
Plastic deformation:
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Introduction to Materials Science, Chapter 18, Electrical properties
Materials of Choice for Metal Conductors
 Silver: One of best for electrical conduction
but high cost
 Copper: inexpensive, abundant, high , but
soft
 Cu-Be alloy: Precipitation hardening, solid
solution alloying, cold working decrease
conductivity.
 Aluminum: low weight, more resistant to
corrosion but half as good as Cu
 Nickel-chromium alloy: low  (high R),
resistant to high temperature oxidation
Heating elements
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Introduction to Materials Science, Chapter 18, Electrical properties
Semiconductivity
Intrinsic semiconductors: conductivity
defined by electronic structure of pure
material
Extrinsic semiconductors - electrical
conductivity is defined by impurity atoms
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Introduction to Materials Science, Chapter 18, Electrical properties
Intrinsic semiconductors (I)
Number of electrons in conduction band
Ne  n = C T3/2 exp(-Eg/2kT) Eg is band gap
Conducting
Electrons
Conduction band
Eg
Holes (positive
charge carriers
Valence band
T=0K
T = 300 K
Electron promoted into the conduction band 
hole (positive charge) in valence band.
In electric field, electrons and holes move in opposite
direction and participate in conduction.
Si (Eg = 1.1 eV) one out of every 1013 atoms contributes
an electron to conduction band at room T.
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Introduction to Materials Science, Chapter 18, Electrical properties
Intrinsic semiconductors (II)
 = n|e|e + p|e|h
p, hole concentration, h hole mobility
n, electron concentration, e, mobility
e > h
and n = p 
 = n|e|(e + h) = p|e|(e + h)
n (and p) increase exponentially with T
e and h decrease about linearly with T
 Conductivity of intrinsic semiconductors
increases with temperature
(different from metals!)
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Introduction to Materials Science, Chapter 18, Electrical properties
Intrinsic semiconductors (III)
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Introduction to Materials Science, Chapter 18, Electrical properties
Extrinsic semiconductors
 defined by impurity atoms
Si extrinsic at room T if impurity
concentration is one atom per 1012
(remember estimate of number of electrons
promoted to conduction band at 300 K)
Different concentrations of p and n
p-type if p > n and n-type if n > p.
Doping (addition of a small concentration
of impurity atoms)
Methods: diffusion or ion implantation.
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Introduction to Materials Science, Chapter 18, Electrical properties
n-type extrinsic semiconductors (I)
Excess electron carriers produced by substitutional
impurities: more valence electrons per atom than
semiconductor matrix
Example: phosphorus with 5 valence electrons is
an electron donor in Si which has 4 electrons that
bond.
Fifth outer electron of P is weakly bound in donor
state (~0.01 eV); easily promoted to conduction
band. P is a donor impurity.
Elements in columns V and VI of periodic table are
donors for semiconductors in column IV, Si or Ge
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Introduction to Materials Science, Chapter 18, Electrical properties
n-type extrinsic semiconductors (II)
Hole in donor state is far from the valence
band and is immobile
Conduction occurs mainly by the donated
electrons (n-type). ND ~ n
 ~ n|e|e ~ ND |e|e
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Introduction to Materials Science, Chapter 18, Electrical properties
p-type extrinsic semiconductors (I)
Excess holes: substitutional impurities that have
fewer valence electrons per atom than matrix
Bond with neighbor is incomplete: a hole weakly
bound to the impurity atom.
Elements in columns III of periodic table (B, Al,
Ga) are donors for semiconductors in column IV,
Si and Ge.
Impurities are called acceptors, NA = NBoron ~p
University of Virginia, Dept. of Materials Science and Engineering
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Introduction to Materials Science, Chapter 18, Electrical properties
p-type extrinsic semiconductors (II)
Energy state corresponding to hole
(acceptor state) is close to top of valence
band
Electron easily hops from valence band to
complete the bond leaving a hole behind.
Conduction occurs mainly by the holes
(p-type)
 ~ p|e|p ~ NA |e|p
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