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Chapter 12:
Electrical Properties
Learning Objectives...
• 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, deformation, and temperature?
• For semiconductors, how is conductivity affected by imperfections, impurities (doping)
F
i d
h i
d i i ff
db i
f i
i
i i (d i )
and Temperature?
Relevant Reading for this Lecture...
• Pages 483-541
1
ELECTRICAL CONDUCTION
V I
 
A
L
resistance (Ohms)
V = I R
• Ohm's Law:
voltage drop (volts)
current (amps)
A
e-
(cross
sect.
area)
Cross‐sectional Area
I
V
L
• Resistivity,  and Conductivity, :
these terms are independent of sample geometry or shape
this equation is another form of Ohm's Law (recall normalization with )
RA

resistivity (Ohm‐m)
L
• Resistance:
L
L

R
A A
conductivity (Ohm‐m)‐1
 nq
e
e
e

I

More about this later
2
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Electrical Properties
• Which will have the greater resistance?
2

D
R1 
2

D 
2 
2
  



2D
R2 

2D 

 2 
2
 

8 
D 2

 R1

D2 8
• Analogous to flow of water in a pipe
• Resistance depends on sample geometry and
size.
Chapter 12 - 3
3
Electrical Conductivity: Comparison
(at room temperature!)
Material
• Metals
Silver
Copper
Aluminum
Iron
(Ohm‐m)‐1
6.8 x 107
6.0 x 107
3.8 x 107
1.0 x 107
(Ohm‐m)‐1
Material
• Ceramics
10
Soda lime glass
Soda-lime
10-10
-9
10
Concrete
10-13
Alumina (Al2O3)
conductors
• Semiconductors
Silicon
Germanium
GaAs
4.0 x 10-4
2.2 x 10 0
1.0 x 10-6
• Polymers
Polystyrene
Polyethylene
<10
10-13
-15
10 – 10-17
insulators
semiconductors
4
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EX: CONDUCTIVITY PROBLEM
e-
Cu wire -
100m
I = 2.5A
+
V
What is the minimum diameter (D) of the Cu wire so that V < 1.5V?
100m
< 1.5V
L
V
R

2.5A
A
I
2
D
7
‐1
6.07 x 10 (Ohm‐m)
4
Solve to get D > 1.88 mm
5
Pauli Exclusion Principle gives rise to energy bands
Figure 12.2 in Callister
Quantum Mechanics states that no two electrons can occupy the same state
same state
6
http://www.aps.org/p
ublications/apsnews/2
00701/images/Wolfga
ng_Pauli_1.jpg
Electrons not accompanying the same state
h
Energy‐level diagram for a hypothetical Nɑ4 molecule. The four shared, outer orbital electrons are “split” into four slightly different energy levels (the Pauli exclusion principle).
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Metals are good conductors since their valence band is only partially filled.
Adapted from Fig. 12.3,
Callister & Rethwisch 4e.
7
Know this!
Metal
e.g., Cu
Metal
e.g., Mg
Semiconductor
Insulator
>2eV
<2eV
Adapted from Fig. 12.4,
Callister & Rethwisch 4e.
Ef = Fermi energy.
This is the boundary between the filled and unfilled energy levels.
For electrons to conduct, they must move to where there are unfilled energy levels.
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CONDUCTION & ELECTRON TRANSPORT
 nq
• Metals:
e
+
Only those e‐ that can get into the empty energy levels can “conduct”
ne = # of e‐
qe = Charge of e‐
e = e‐ mobility
Cu is like this.
Energy
Mg is like this.
empty
band
GAP
partly
filled
valence
band
filled
band
filled states
the cases at right
for metals show that
nearby energy states
are accessible by
th
thermal fluctuations
l fl t ti
e
per m3
net e- flow
Energy
• Energy States:
e
‘My level’ – highest filled state
empty
band
filled states
s
‐‐ Thermal energy puts
many electrons into
a higher energy state.
a higher energy state.
-
Fermi
filled
valence
band
filled
band
http://www.bayarea.net/~kins/
AboutMe/GIFs/Fermi_2.jpg
9
ENERGY STATES: INSULATORS AND SEMICONDUCTORS
• Semiconductors:
‐Higher energy states are not
g p
accessible due to band gap.
Energy
empty
band
filled sta
ates
GAP
10
filled
valence
band
filled
band
wide band gap (> 2 eV)
‐Higher energy states
separated by a smaller gap.
Energy
Engineered material: Gaps are tunable –
more to come…
empty
band
?
GAP
filled states
• Insulators:
filled
valence
band
filled
band
narrow band gap (< 2 eV)
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Insulators: A parallel‐plate capacitor involves an insulator, or dielectric, between two metal electrodes. The charge density buildup at the capacitor surface is related to the dielectric constant of the material
E, Electric field strength (V/m)
A
D  okE
D, charge density (C/m2) k, dielectric constant (material property)
l
o electric permittivity in vacuum, constant, 8.9x10‐
constant,
8.9x 0 12C/(Vm)
= C = Q/V→C= A/l
 k
charge
Capacitance
11
o
Q
A
C  C 
V
l
 electric permittivity
Note your text uses r for k
voltage Dielectric Constants & Strength
Dielectric constant r
60 Hz 1 MHz
Dielectric strength
(V/mil)*
• Ceramics
Titanate ceramics
Mica
Soda-lime glass
Porcelain
--6.9
6.0
15 – 10,000
5.4 – 8.7
6.9
6.0
50 – 300
1000 – 2000
250
40 – 400
• Polymers
Polystyrene
Polyethylene
2.6
2.3
2.6
2.3
500 – 700
450 – 500
* 0.001 in = 1 mil
12
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METALS: RESISTIVITY VS T, IMPURITIES
• Imperfections increase resistivity
6
(10-8 Ohm-m)
Resistivity, 
R
‐ grain boundaries
‐ dislocations
‐ impurity atoms
‐ vacancies
5
4
3
2
1
0
2a
3.3
These act to scatter electrons so that they
take a less direct path, thus .
i
t%N
   [1  a(T  T )]
o
rt
i
i
t%N at%N a is temperature coefficient of a
6
resistivity, o is intrinsic (no impurity) 2
1
.
1
2
1.
+
+
u
resistivity
C
Cu
ed
Ni
m
r
o
at%
2
def
1
.
• Resistivity
• +1
Cu
u
C
increases with:
re”
Why????
“Pu
‐ temperature
‐
wt% impurity
-200 -100
0 T (°C)
‐ %Cold Work
+
Cu
Adapted from Fig. 18.8, Callister 6e. (Fig. 18.8 adapted from J.O. Linde, Ann. Physik 5, p. 219 (1932); and C.A. Wert and R.M. Thomson, Physics of Solids, 2nd ed., McGraw‐Hill Book Company, New York, 1970.)
13
Variation in electrical resistivity with composition for various copper alloys with small levels of elemental additions (at T = 20°C).   Aci 1  ci 
A – composition independent constant
ci – concentration of impurities
p
14
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PURE SEMICONDUCTORS: CONDUCTIVITY VS T
• Data for Pure Silicon:
Energy
‐  increases with T
‐ opposite to metals
104
103
102
101
electrons
can cross
filled
gap at
valence
higher T
band
filled
band
material
Si
Ge
GaP
CdS
pure
p
(undoped)
10-2
50 100
GAP
filled states
electrical
l t i l conductivity,
d ti it 
(Ohm-m)-1
100
10-1
empty
band
?
1000
T(K)
Adapted from Fig. 19.15, Callister 5e. (Fig. 19.15 adapted from G.L. Pearson and J. Bardeen, Phys. Rev. 75, p. 865, 1949.)
band gap (eV)
1.11
0.67
2.25
2.40
Selected values from Table 18.2, Callister 6e.
15
CONDUCTION IN TERMS OF ELECTRON AND HOLE MIGRATION
Light (shown), heat, some input of energy
some input of energy
is required to excite e‐ from valence band to conduction band leaving a positively charged hole behind.
Conduction can be either by negative carriers, y g
,
electrons (n‐type) and/or positive carriers, holes (p‐type). Electrons move towards (+) potential and holes move to (‐) potential
• Electrical Conductivity given by:
## holes/m
holes/m3
  n q e  p q h
electron mobility hole mobility
# electrons/m3
charge of e‐
16
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In class problem
What fraction of the conductivity of intrinsic silicon at room temperature is due to (a) electrons and (b) holes?
 nq
  n q e  p q h
e
e
e
per m3
ne = # of e‐
qe = Charge of e‐
e = e‐ mobility
Here n = p
From Table 12.3, =0.736
From Table 12.3, = 0.263
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   oe
 Eg
2 kT
Arrhenius equation; Why 2? Produce two charge carriers – electron and hole
Eg 1
Determining the activation energy for conduction
   oe 2k T
ln   ln  o 
18
Eg 1
2k T
y  B  mx
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INTRINSIC VS EXTRINSIC CONDUCTION
• Intrinsic semiconductors: # of thermally generated electrons = # of holes (broken bonds)
• Extrinsic
Extrinsic semiconductors: Impurities are added to the semiconductors: Impurities are added to the
semiconductor that contribute additional electrons or holes. Doping = intentional impurities
• Si is the primary material in semiconductors
– Large band gap (1.1 eV); allows Si to operate at warmer temperatures (150oC)
– Can form a native oxide, SiO2, for insulating barriers (important in fabrication)
• Si can be made into large (12 inch dia.), high purity, single crystal ingots. • Doping of Si
– Si has 4 outer shell electrons (group IV)
– n‐type: Phosphorous, arsenic (group V), donate extra electron
– p‐type: boron (group III) for Si
19
n‐type
4 valence electrons of As allow it to bond like Si, but the fifth electron is left orbiting As site – the energy to release the fifth electron into the CB is small
  n e e
20
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p‐type
• Boron has only 3 valance electrons. When it substitutes for a Si atoms, one of its bonds has a missing electron (hole)
• Hole tunnels around, and can be liberated by thermal vibration of Si atoms, from the B site into the VB.
21
  p e h
p‐type
n‐type
?‐type
?‐type
22
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Why 2? Produce two charge carriers –
electron and hole
Why the increase?
Arrhenius plot of electrical conductivity for an n‐type semiconductor over a wide temperature range. At low temperatures (high 1/T), the material is extrinsic. At high temperatures (low 1/T), the material is intrinsic. In between is the exhaustion range, in which all “extra electrons” have been promoted to the
to the
why?
23
In class problem
Calculate the conductivity for the saturation range of silica doped with 10‐ppb boron.
The calculated density of B atoms/m3 is also the density of electron holes in this
p‐type semiconductor at saturation. 10/109
= 10 ‐8
Hence solve for n
Hence solve for n
n = 10‐8
X
6.02x1023 atoms B
10.81 g B
X 2.33x106 g/m3 Si = 1.30 x1021
amu B
Density of Si
Using this equation σ=nqµ
h and the data from Table 12.3: (q is the magnitude of electron h
d h d
f
bl
(
h
d f l
charge which equals 0.16 x 10‐18 C)
σ = nqµh
= (1.30 x 1021 m‐3)(0.16 x 10‐18 C) (0.05 m‐2/V‐s)
24
= 10.4 Ω‐1 m‐1
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Compound Semiconductors
Group III‐V and II‐V compounds nominally have the inc lend structure and are intrinsic
the Zinc Blend structure and are intrinsic semiconductors. Can be doped, like Si, to change conduction (extrinsic) MX Compounds: Group III 3+ valence, Group V 5+ valence – avg. of 4+ valence per atom // Group II 2+ valence, Group VI 6+ valence – avg. 4+ valence per atom
Applications:
• Solar cells
• Light emitting diodes (occurs with electron‐hole recombination)
• Higher operation speeds, etc.
25
IC DEVICES: P‐N RECTIFYING JUNCTION
• Allows flow of electrons in one direction only (e.g., useful
to convert alternating current to direct current).
• Results:
p-type
type
+p
+ +
+ +
‐ 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
p‐n junction; current flows.
‐ Reverse bias: carriers
flow away from p‐n junction;
carrier conc. greatly reduced
at junction; little current flow.
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+
p-type
+
n-type
n
type
-
-
-
-
+ - n-type
++- - +-
p-type
- ++ +
+ +
n-type
-
-
-
-
+
14
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P‐N Rectifying Junction
27
Light Emitting Diode (LED)
http://electronics.howstuffworks.com/led.htm/printable
Band gap determines wavelength (color) of light emitted
http://spie.org/Images/Graphics/Newsroom/Importe
d/0695/0695_fig4.jpg
28
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Compare three light bulbs.
Conventional incandescent (tungsten filament)
Bulb is hot to the touch, most of the electricity is lost as heat.
Short life (few months?)
Compact fluorescent (CFL’s)
Bulb is warm, but not hot, less heat loss
Longer life (many months – 2 years)
LED’s
E t
Extremely
l efficient,
ffi i t littl
little or no conversion
i off electricity
l t i it to
t heat.
h t
Very long life – decades. Many LED’s made in the 70’s & 80’s are still working!
29
The Transistor
• Invented by Shockley, Bardeen, and Brattain in 1948. Nobel prize in 1956.
• A three terminal device that acts like a simple “on‐off” switch (logic control). – The basis of Integrated Circuits (IC) The basis of Integrated Circuits (IC)
technology
– Computers, cell phones, automotive control, etc.
Circa 1948
today
• When voltage (potential) is applied to the “gate”, current flows between the “source” and the “drain”. On/off switch – logic switch, go/no go ~ tens of nanometers (1000X smaller than diameter of your hair)
30
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SUMMARY
• Electrical conductivity and resistivity
31
are:
‐ material parameters, i.e. properties.
‐ independent of geometry.
• Electrical resistance is:
‐ a geometry and material dependent parameter.
• Conductors, semiconductors, and insulators...
‐ each is different, depending on whether there are accessible energy states for conducting electrons.
• For metals, conductivity is increased by
‐ reducing deformation
‐ reducing imperfections
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).
 Transistors are logic based devices
Metals: Influence of Temperature and Impurities on Resistivity
• Presence of imperfections increases resistivity
• Resistivity
5
increases with:
4
3
d
2
i
1
0
32
These act to scatter
electrons so that they
t k a less
take
l
di
directt path.
th
6
(10
0 -8 Ohm-m)
Re
esistivity, 
-- grain boundaries
-- dislocations
-- impurity atoms
-- vacancies
-- temperature
-- wt% impurity
-- %CW
t
-200
-100
0
T (°C)
Adapted from Fig. 12.8, Callister & Rethwisch 4e. (Fig. 12.8
adapted from J.O. Linde, Ann. Physik 5, p. 219 (1932); and C.A.
Wert and R.M. Thomson, Physics of Solids, 2nd ed., McGraw-Hill
Book Company, New York, 1970.)
 = thermal
+ impurity
+ deformation
32
16