Download Chapter 18. Electrical Properties (2)

Introduction to Materials Science, Chapter 19, Electrical properties
Temperature variation of conductivity (I)
 = n|e|e + p|e|h
Strong exponential dependence of
concentration in intrinsic semiconductors
carrier
Temperature dependence of mobilities is weaker.
n = p  A exp (- Eg /2 kT)
  C exp (- Eg /2 kT)
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Introduction to Materials Science, Chapter 19, Electrical properties
Temperature variation of conductivity (II)
n = p  A exp (- Eg /2 kT)
  C exp (- Eg /2 kT)
Plotting log of  , p, or n vs. 1/T produces a
straight line. Slope is Eg/2k; gives band gap energy.
ln(n) = ln(p)  ln(A) - Eg /2 kT
Eg
 ln p

1 T 
2k
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Introduction to Materials Science, Chapter 19, Electrical properties
Temperature variation of conductivity (III)
Extrinsic semiconductors
• low T: all carriers due to extrinsic excitations
• mid T: most dopants ionized (saturation
region)
• high T: intrinsic generation of carriers
dominates
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Introduction to Materials Science, Chapter 19, Electrical properties
Semiconductor Devices. Diode (I)
Diode allows current flow in one direction only
p-n junction diode: adjacent p- and n-doped
semiconductor regions
Positive side of a battery is connected to p-side
(forward bias): large amount of current flows.
Holes and electrons pushed into junction region,
where they recombine (annihilate).
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Introduction to Materials Science, Chapter 19, Electrical properties
Semiconductor Devices. Diode (II)
If the polarity of the voltage is flipped, the diode
operates under reverse bias. Holes and electrons
are removed from the region of the junction, which
therefore becomes depleted of carriers and behaves
like an insulator.
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Introduction to Materials Science, Chapter 19, Electrical properties
Semiconductor Devices. Diode (III)
Reverse bias: holes and electrons are drawn away
from junction.
Junction region depleted of free carriers 
current is small.
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Introduction to Materials Science, Chapter 19, Electrical properties
Semiconductor Devices. Diode (IV)
Asymmetric current-voltage characteristics of
diode converts alternating current to direct current
(rectification).
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Introduction to Materials Science, Chapter 19, Electrical properties
Transistors.
Used to amplify electric signal and
Switching devices in computers.
Two major types
Junction (or bimodal) transistor
MOSFET transistor.
p-n-p (or n-p-n) junction transistor
contains two diodes back-to-back. The
Central region (base) is thin (~ 1 micron or
less) and is sandwiched in between emitter
and collector
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Introduction to Materials Science, Chapter 19, Electrical properties
Junction transistor
Emitter-base junction is forward biased: holes are
pushed across junction. Some recombine with
electrons in the base, but most cross the base as it
is thin. They are then swept into the collector.
A small change in base-emitter voltage causes a
relatively large change in emitter-base-collector
current. Hence a large voltage change across
output (“load”) resistor - voltage amplification
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Introduction to Materials Science, Chapter 19, Electrical properties
Junction transistor
Emitter-base junction is forward biased, basecollector junction is reverse biased.
Thus, the base of the PNP transistor must be
negative with respect to the emitter, and the
collector must be more negative than the base.
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Introduction to Materials Science, Chapter 19, Electrical properties
PNP Forward-biased junction
Forward biased emitter-base junction,
positive terminal of battery repels emitter
holes toward base, while negative terminal
drives base electrons toward emitter
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Introduction to Materials Science, Chapter 19, Electrical properties
PNP junction interaction
In reverse-biased junction: negative voltage on
collector and positive voltage on base blocks
majority current carriers from crossing junction.
Increasing forward-bias voltage of transistor
reduces emitter-base junction barrier. This allows
more carriers to reach the collector, causing an
increase in current flow from emitter to collector
and through external circuit.
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Introduction to Materials Science, Chapter 19, Electrical properties
MOSFET
(Metal-Oxide-Semiconductor Field Effect Transistor)
MOSFET transistor: two small islands of p-type
semiconductor created within n-type silicon
substrate. Islands connected by narrow p-type
channel.
Metal contacts are made to islands (source and
drain), one more contact (gate) is separated from
channel by a thin (< 10 nm) insulating oxide layer.
Gate serves the function of the base in a junction
transistor (electric field induced by gate controls
current through the transistor)
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Introduction to Materials Science, Chapter 19, Electrical properties
MOSFET
(Metal-Oxide-Semiconductor Field Effect Transistor)
Voltage applied from source encourages carriers (holes
in the case shown below) to flow from the source to the
drain through the narrow channel.
Width (and hence resistance) of channel is controlled by
intermediate gate voltage. For example, if positive
voltage is applied to the gate, most of the holes are
repelled from the channel and conductivity is
decreasing.
Current flowing from the source to the drain is
therefore modulated by the gate voltage (amplification
and switching)
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Introduction to Materials Science, Chapter 19, Electrical properties
Transistors and microelectronic devices
 MOSFET dominates microelectronic industry
(memories, microcomputers, amplifiers, etc.)
 Large Si single crystals are grown and purified.
Thin circular wafers (“chips”) are cut from
crystals
 Circuit elements are constructed by selective
introduction of specific impurities (diffusion or
ion implantation)
 A single 8” diameter wafer of silicon can contain
as many as 1010 - 1011 transistors in total
 Cost to consumer ~ 0.00001c each.
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Introduction to Materials Science, Chapter 19, Electrical properties
Conduction in Polymers and Ionic
Materials
Ionic Materials
 The band gap is large and only very few
electrons can be promoted to the valence band
by thermal fluctuations
 Cation and anion diffusion can be directed by
the electric field and can contribute to total
conductivity: total = electronic + ionic
 High temperatures produce Frenkel and
Schottky defects which result in higher ionic
conductivity.
Polymers
 Polymers are typically good insulators but can
be made to conduct by doping.
 A few polymers have very high electrical
conductivity - about one quarter that of copper,
or about twice that of copper per unit weight.
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Introduction to Materials Science, Chapter 19, Electrical properties
Capacitance
Voltage V applied to parallel conducting plates
 plates charged by +Q, –Q
electric field E develops between plates
+++++
Charge can remain even after
voltage removed.
----- -
Ability to store charge  capacitance
C = Q / V [Farads]
C depends on geometry of plates and material
between plates
C = r o A / L =  A / L
A is area of plates, L is distance between plates,  is
permittivity of dielectric medium, o is permittivity of a
vacuum (8.85x10-12 F/m2), and  r is relative permittivity
(dielectric constant) of material, r =  / o = C / Cvac
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Introduction to Materials Science, Chapter 19, Electrical properties
Dielectric Materials
Dielectric constant of vacuum is 1 and is close to 1
for air and many other gases. When piece of
dielectric material is placed between two plates
capacitance can increase significantly.
C = r o A / L with r = 81 for water, 20 for acetone,
12 for silicon, 3 for ice, etc.
Dielectric is insulator in which electric
dipoles are induced by electric field
d
+ _
+
_
_
+
_
+
Magnitude of electric dipole moment is p = q d
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Introduction to Materials Science, Chapter 19, Electrical properties
Dielectric Materials
Dipole orientation along electric field in the
capacitor causes charge redistribution.
Surface nearest to the positive capacitor plate is
negatively charged and vice versa.
Q0 + Q’
+ + + + + + + +
P
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
net negative charge
at the surface, -Q’
region of no
net charge
- - - - - - - - -
-Q0 - Q’
net negative charge at
the surface, Q’ = PA
Dipole alignment  extra charge Q’ on
plates:
Qt = |Q+Q’|
now C = Qt / V
Increased capacitance r = C / Cvac > 1
Dipole formation/alignment in electric field is called
polarization  P = Q’/A
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Introduction to Materials Science, Chapter 19, Electrical properties
Dielectric Materials
Surface charge
displacement) is
density
(also
called
dielectric
D = Q/A = r oE = oE + P
Polarization is responsible for the increase in charge
density above that for vacuum
Mechanisms:dipole formation/orientation
 electronic (induced) polarization: Electric field
displaces negative electron “clouds” with
respect to positive nucleus.
 Ionic materials (induced) polarization: Applied
electric field displaces cations and anions in
opposite directions
 molecular (orientation) polarization:
Some
materials possess permanent electric dipoles
(e.g. H2O). In absence of electric field, dipoles
are randomly oriented. Applying electric field
aligns these dipoles, causing net (large) dipole
moment.
Ptotal = Pe + Pi + Po
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Introduction to Materials Science, Chapter 19, Electrical properties
Mechanisms of Polarization
electronic polarization
ionic polarization
molecular (orientation) polarization
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Introduction to Materials Science, Chapter 19, Electrical properties
Dielectric Strength
Breakdown: high electric fields (>108 V/m) excite
electrons to conduction band + accelerate them to
high energies  they collide with and ionize other
electrons
Avalanche process (or electrical discharge).
Field necessary is called dielectric strength or
breakdown strength.
Piezoelectricity (some ceramic materials)
Application of a force  electric field
(polarization) and vice-versa
Piezoelectric materials convert mechanical strain
into electricity (microphones, strain gauges, sonar
detectors)
Piezoelectric materials include barium titanate
BaTiO3, lead zirconate PbZrO3, quartz.
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Introduction to Materials Science, Chapter 19, Electrical properties
Nanoscopic materials design
The Center for Nanoscopic Materials Design at UVa
http://www.mrsec.virginia.edu/
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Introduction to Materials Science, Chapter 19, Electrical properties
Summary
Make sure you understand language and concepts:
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Acceptor state
Capacitance
Conduction band
Conductivity, electrical
Dielectric constant
Dielectric displacement
Dielectric strength
Diode
Dipole, electric
Donor state
Doping
Electrical resistance
Electron energy band
Energy band gap
Extrinsic semiconductor
Fermi energy
Forward bias
Free electron
Hole
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Insulator
Intrinsic semiconductor
Ionic conduction
Junction transistor
Matthiessen’s rule
Metal
Mobility
MOSFET
Ohm’s law
Permittivity
Piezoelectric
Polarization
Polarization, electronic
Polarization, ionic
Polarization, orientation
Rectifying junction
Resistivity, electrical
Reverse bias
Semiconductor
Valence band
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