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Tao Deng, [email protected] 1
1896 1920 1987 2006
Properties of Materials
Chapter 3
Electrical Properties of Materials
Tao Deng
Tao Deng, [email protected] 2
3. The electrical properties
• Electrical conductivity
• Dielectric property
• Thermoelectric
• Pyroelectric
• Piezoelectric
• Ferroelectric
• Photoelectric
Tao Deng, [email protected] 3
3.1 Electrical conductivity
3.1.1 Introduction
3.1.1.1 Characterization of electrical conductivity
Electrical conduction: when a voltage is applied between two
ends of a material , there is a current flowing through the
material.
S
LR Resistance:
L
SRResistivity: 1μ·cm=10-9·m=10-6·cm=10-2·mm2/m
R
VI Ohm's Law
Tao Deng, [email protected] 4
I=SJ(J is electrical current density )
V=LE(E is electric al field intensity )
1J E
1Electrical conductivity (-1·m-1 or S/m):
J E
Relative electrical conductivity (IACS%):
If the conductivity of the international standard soft copper (resistivity at 20
0C: 0.01724·mm2/m) is 100%, a material’s relative conductivity is defined as the
percentage of its’ conductivity divided by soft copper's conductivity. For example, the
IACS% of iron is 17%; The IACS% of aluminum is 65%.
3.1 Electrical conductivity
Tao Deng, [email protected] 5
3.1.1 The electrical conductivity of typical materials at
room temperature
Silver 6.8 x 107
Copper 6.0 x 107
Iron 1.0 x 107
METALS conductors
Silicon 4 x 10-4
Germanium 2 x 100
GaAs 10-6
SEMICONDUCTORS
semiconductors
Polystyrene <10-14
Polyethylene 10-15 -10-17
Soda-lime glass 10-10
Concrete 10-9
Aluminum oxide <10-13
CERAMICS
POLYMERS
insulators
- 10-11
• Room temperature values (Ohm-m)-1 = ( - m)-1
Tao Deng, [email protected] 6
3.1.1.2 Materials’ electrical conductivity
Conductor: ρ<10-5 Ω.m;
Semiconductor: ρ=10-5~ 1010 Ω.m;
Insulator: ρ>1010 Ω.m;
Tao Deng, [email protected] 7
3.1.1.3 Mechanism of electrical conduction
(1) Carriers
Current is the directional flow of electrical charge in space. In any
matter, as long as there are free particles with charges (carriers), there will be
current under electric field
• In metals, the carriers are free electrons (electronic conduction)
• In inorganic materials, there are two types of carriers:
– Ions, including positive/negative ions and vacancies (ionic conduction)
– Electrons, including negative electrons and holes (electronic conduction)
• In polymers, the carriers are solitons
• In superconducting materials, the carriers are two-electron Cooper pairs
Tao Deng, [email protected] 8
(2)Mobility of carriers
In the conductor with a cross-sectional area of the unit area, n is the number of
carriers in the unit volume and q is the charge carried by each carrier. If the external
electric field (E) is applied along the longitudinal direction, there is a force of qE acting
on each carrier . Under the action of this force, each carrier moves along the direction of
E, and its average speed is v.
J nqv
J nqv
E E
v
E
Mobility of carrier is
defined as :
It is the average drift velocity of the carriers under the action of a unit
electric field.
E
3.1.1.3 Mechanism of electrical conduction
Tao Deng, [email protected] 9
nq
If there are several carriers that contribute to the conductivity in the
material, then the total conductivity is the sum of all individual carriers:
i i i i
i i
n q
Two key factors for material‘s conductivity:
• The concentration of carriers
• Carrier mobility.
External conditions (such as temperature and pressure), bonding,
composition, and other factors have an impact on the carrier concentration
and carrier mobility.
3.1.1.3 Mechanism of electrical conduction
Tao Deng, [email protected] 10
3.1.1.4 Band theory
(1)Basic concept
-The potential field from positive ions has a
periodicity and it makes the movement of free
electrons not completely free.
-Study the energy distribution of electrons in the
periodic potential field in metals.
Tao Deng, [email protected] 11
3.1.1.4 Band theory
x1
When the distance between
atoms is large (x1),
electrons in atoms are
mutually independent.
Arrangement of metallic atoms
Tao Deng, [email protected] 12
3.1.1.4 Band theory
Arrangement of metallic atoms within Bulk Metals
x3
When the spacing is less than x2,
the originally independent energy
levels of an atom spread into a
band consisting of a discrete
series of energy levels; the energy
difference between these levels is
small (about 10-23eV.)
Tao Deng, [email protected] 13
3.1.1.4 Band theory
Arrangement of metallic atoms within Bulk Metals
x4
When the atomic spacing
is further reduced (x4) ,
the band is broadening.
Tao Deng, [email protected] 14
Energy band
• The highest energy band partialy occupied by some
electrons is called the valence band
• Core band – band energy is lower than that of the valence
band
• Conduction band – band energy is higher than that of the
valence band
• Band gap ( Eg)- the forbidden energy gap between the
valence band and the conduction band
Tao Deng, [email protected] 15
The energy band of three typical materials
Empty band Valence band
Metallic conductor
Overlapping of Valence
band and the empty band
Valence band is
half full
Ov
erlap
regio
n
Co
nd
uctio
n B
an
d
con
du
ction
ba
nd
For example
Si: Eg=1.1eV
Ge:Eg=0.71eV
Semiconductor
Eg ≈ 0.2~2.5eV
Insulator
For example :
diamond
Eg=6.0eV
Eg>2.5eV
Tao Deng, [email protected] 16
3.1.1.5 Theory of the electrical conductivity
(1)The classical electron theory
•Free electrons are considered as "electron gas” - - analyze with
classic gas molecules kinetic theory.
• The interaction within the free electrons and between them and
the positive ions are treated as the mechanical collision.
tm
ne
mv
lne
22
22
l -mean free path of the electron;m -mass of the electron;v -average
speed of the electron;e - charge of the electron ;t - the average time
between twice collisions;n -the number of free electrons per unit volume;
Tao Deng, [email protected] 17
The influence of the temperature and the point
defects on electron movement
The influence of temperature
6 collisions
The model of an electron moving in the lattice
3 collisions
The influence of point defects
8 collisions
Tao Deng, [email protected] 18
(2)Quantum theory of free electrons
Basic assumptions:
• In metals, the electric field formed by the positive ions is
uniform;
• The electrons in the valence band belong to the entire metal;
they have no interaction with ions, and can move freely;
• The electrons in the inner bands of each atom have the same
energy states with those in the original single atoms, while the
electrons in the valence band have different energy states that are
quantalized to different energy levels.
3.1.1.5 Theory of the electrical conductivity
Tao Deng, [email protected] 19
(2)Quantum theory of free electrons
p
h
mv
h
22
2
82
1K
m
hmvE
2K
Wave-Particle Duality:
For monovalent metal, the kinetic
energy of free-electron:
Where, wave frequency (wave number or wave vector)
h
p
h
mv
222
Tao Deng, [email protected] 20
The relationship between electronic energy and wave
vector
-K +K O
E
E - K curve of free electrons
+K -K O
E
+K -K O
E
e
E
The effect of the electric field on the E-K curve
Tao Deng, [email protected] 21
The interference of electronic wave
The electrical resistance is caused by the
scattering of electronic waves through:
• Ion lattice;
• Static lattice distortion generated by defects or
impurities;
• Dynamic lattice distortion generated by thermal
vibration.
Tao Deng, [email protected] 22
3.1.1.6 Ionic conduction
(1) Conductive mechanism of ionic crystals
a) Conduction through intrinsic ions
Due to the increase of thermal vibration, ions leave the lattice site to
form interstitial ions and vacancies (thermal defects). Such thermal defects
can move under the electric field to generate current. Concentration of
thermal defects increases with in temperature, so the ionic intrinsic
conductivity increases with temperature as well:
Where Es - The activation energy of ions.
2) Conduction through impurity ions
kT
EA s
ss exp
T
BAim exp
k
EB s
Tao Deng, [email protected] 23
(2)The conduction mechanism in glass
• Glass is usually an insulator -- at high temperature,
some glasses can become a conductor.
• Glass is also a conductor of the electrolyte. Its
conductivity comes from the movability of ions in the
structure. For example, in the silica network of a soda
glass, a sodium ion jumps from one structural gap to
another to generate the current. This conduction is
similar to the conduction from interstitial ions in the
ionic crystals.
• The composition of the glass has a great impact to the
resistance.
Tao Deng, [email protected] 24
3.1.1.7 The conduction in polymers
• In 1977, Shirakawa from Japan and MacDiamid from the
United States found that the conductivity of polyacetylene,
doped with I2 or AsF5 , increases from 10-9 S / cm to 103 S/cm.
Tao Deng, [email protected] 25
3.1.1.7 The conduction in polymers
Tao Deng, [email protected] 26
Polyacetylene
• Carbon atoms are bonded with each other through double bond → single bond →
double bond to form a quasi-one-dimensional carbon chain,;every hydrogen atom
bonds with a carbon atom located on the carbon chain;
•Each carbon atom is adjacent to two carbon atoms and one hydrogen atom ;
• Each carbon atom has four valence electrons. In polyacetylene, neighboring carbon
atoms using their sp2 hybrid orbitals to form carbon - carbon σ bonds, and at the
same time, they also use their sp2 orbitals to interact with hydrogen’s s orbitals to
form carbon – hydrogen σ bonds;
• Each carbon atom has a valence electron (pz orbitals) and it becomes a π electron in
the molecular bond of polyacetylene.
H atoms on both sides of the double bond H atoms at the same side the double bond.
Trans-form Cis-form
Tao Deng, [email protected] 27
The band structure of one-dimensional carbon chain
of polyacetylene
The energy band of one-
dimensional equidistant
carbon chain
Should be like a metal??
The energy band of one-
dimensional dimerized
carbon chain
Like a semiconductor!
Tao Deng, [email protected] 28
The soliton model
In a certain range of the doping concentration, trans-polyacetylene has a high
electrical conductivity.
The Soliton model:
Trans-polyacetylene has two
lowest dimerization states: A-phase
and B-phase, with the same energy
and symmetrical structure. If the A-
phase and B-phase coexist in the same
molecular chain, there will be a
domain wall between them, which is
called soliton. The alternating single
bond-double bond structure is
destroyed at the soliton.
A phase, the soliton and B phase in trans-polyacetylene
The conductive carriers of polyacetylene carry charge without spinning.
Tao Deng, [email protected] 29
3.1.2 The electrical conductivity of the metal
3.1.2.1 The electrical conductivity of the elements
Tao Deng, [email protected] 30
Analysis of element conductive band theory
3s valence band is half-filled.
High electrical conductivity
The outermost s band is full, but the outermost s overlaps with the
outermost p to form the conduction band.
The conductivity is higher than IA family.
The outermost p is filled with a small amount of electrons. Most of it is empty, with some
overlapping with the main shell s.
Higher conductivity.
Sp hybrid orbital caused by covalent
bond; involving the 2s electrons(4
valence electron) to form two hybrid
bands, where one is filled, and the
other is empty, but there is a band
gap between the two hybrid band.
The conductivity is poor.
The outermost s band is full, partially overlapping with the
half-filled d-band to form a conduction band with less
empty level .
Conductivity is relatively poor.
Similar to the alkali metal, there is non-overlapping band and valence band is half-filled. Higher conductivity
.
Tao Deng, [email protected] 31
3.1.2.2 Matthiessen Law
The resistance of ideal metals are based on only two scatterings- phononic
scattering and electronic scattering. This resistance is reduced to zero at absolute
zero. The third scattering (electrons scattered by impurities and defects) can be
observed in the non-ideal crystal with defects, which still exists even at absolute
zero. The scattering coefficient is composed of two parts:
T
Where, the scattering coefficient vT is proportional to the temperature T, ν is proportional
to the concentration of impurities and independent of temperature.
T
Where, (T) is the basic resistance of pure metals; is the residual
resistance determined by chemical and physical defects, regardless of the
temperature.
Matthiessen law
Tao Deng, [email protected] 32
3.1.2.3 The relationship between electrical resistivity
and temperature in metals
Usually, in the case of temperature
higher than the room temperature: T 10
where,ρ0 - electrical resistivity at 0℃;α-Temperature coefficient of resistance;β、γ-High-order coefficient;
32
0 1 TTTT
5T
T
2T
Generally, ρ increases as T increases.
In the very low temperature:
Electron - electron scattering;
In the higher Temperature:
Electron - phonon scattering
-T<ΘD时,ρ∝T5;
-T> ΘD时,ρ∝T
Tao Deng, [email protected] 33
Temperature coefficient
The average temperature
coefficient of resistance: T
T
0
0
True temperature coefficient
of resistance: dT
d
T
T
1
• Except the transition metals, for all other pure metals α≈4×10-3。
• Transition metals, especially ferromagnetic metals, have a high α. For
example, iron has a α= 6 ×10-3.
Tao Deng, [email protected] 34
3.1.2.4 The impact of stress and deformation
caused by cold processing
Cold processing will increase
the lattice distortion, thus
increase the resistivity:
• Fe、Cu、Al、Mg .etc. ,
may increase by 2~6%;
• W、Mo、Sn .etc., may
increase by 15~90%.
Recrystallization annealing
may cancel the increase of the
resistance
99.8%
97.8%
93.5%
80%
44%
Th
e am
ou
nt o
f defo
rma
tion
du
ring
cold
pro
cessing
Annealing temperature/oC
Tao Deng, [email protected] 35
3.1.2.5 The conductive property of the alloys
(1) The resistivity of the solid solution
Generally, with the increase of the concentration
of the solute, the resistivity also increases because of
the lattice distortion. When solute concentration is
small, the resistivity follows Matthiessen's law:
rT • ρT- Base resistance of pure base metal
•ρr -The additional resistance caused by the
concentration of solute (impurity) 、 point defects,
dislocations, etc., independent of temperature.
Tao Deng, [email protected] 36
(2)The resistivity of ordered alloys
With the increase of order in the solid
solution
• The chemical interaction among the
alloy components is strengthened, and
number of conductive electrons decreases,
so the residual resistance increases;
• The ionic potential field become more
symmetrical, so that the probability of the
electron scattering is greatly reduced and
the residual resistivity decreases;
The second factor is usually dominant, so
the resistivity of the alloy is normally
reduced with increased structural order
Quenching state
Annealed
state
Au, % (atom)
Tao Deng, [email protected] 37
3.1.2.6 The influence of pressure on the metal conductivity
• Normal metal :
The resistivity decreases as
the pressure increases:
iron, cobalt, nickel, copper,
silver, gold, niobium,
vanadium, lead, etc.
• Abnormal metal :
The resistivity doesnot
follow the normal trend as
the pressure increases:
alkali metal, alkaline earth
metal and rare earth metals;
Tao Deng, [email protected] 38
The effect of pressure on the conductivity of non-
conductive materials High pressure can often lead to the metallization of the substance, causing
the changes of the conductivity type, enabling the transform of insulator→
semiconductor → metal → superconductors.
Element PC /MPa ρ/(μΩ.cm) Element PC /MPa ρ/(μΩ.cm)
S 40,000 - H 200,000 -
Se 12,500 - Diamond 60,000 -
Si 16,000 - P 20,000 60±20
Ge 12,000 - AgO 20,000 70±20
I 22,000 500 - - -
The critical pressure required for certain semiconductor and
dielectric materials’ transformation into the metallic state
Tao Deng, [email protected] 39
3.1.2.7 The influence of geometric dimensions on
the electronic resistivity
When the size of material is reduced to the same
order of magnitude of the free path of the
conduction electron, the scattering of electrons in
the surface of the sample creates a new additional
resistance. In this case, the effective scattering
coefficient Leff is
Where, L、Ld , respectively, is the free path of the
electrons scattered in the bulk sample and the surface .
deff LLL
111
The resistivity of thin film is:
d
Ld 10
where,ρ0 -The resistivity of bulk sample ;
d - The thickness of film;
Tao Deng, [email protected] 40
3.1.3 The electrical properties of the semiconductors
Tao Deng, [email protected] 41
3.1.3 The electrical properties of the semiconductors
• Crystalline semiconductor
– Elemental semiconductor:Si, Ge, Se, Te and so on
– solid solution semiconductor:Ge-Si, Bi-Sb, GaAs-GaP
and so on ;
– compound semiconductor :GaAs, CdS, SiC, GeS, AsSe3
and so on ;
• Noncrystalline semiconductor
– noncrystalline silicon(α –Si)、polycrystalline silicon ;
– chalcogenide glass ;
• Organic semiconductor
– Polymer semiconductor
Tao Deng, [email protected] 42
The electronic energy states in semiconductor
1s 2s 2p
3s
3p
n=1
n=2
n=3 Forbidden band
Empty band
(conduction band)
Energy
The distance between atoms
The evolutional process of silicon covalent crystals
The sharing of valence electrons in semiconductor crystals splits the
original atomic electron energy states into a series of levels with very
small difference of energy between them to form a energy band.
single atom
The distance between atoms
in Covalent Crystals
Filled band
(valence band)
Tao Deng, [email protected] 43
3.1.3.1 Intrinsic semiconductor
Intrinsic semiconductor: pure, single crystal, no structural defects.
Stimulated by the electric field,
temperature, or light
The process of intrinsic excitation
The number of free electrons in the
conduction band=the number of holes in
the valence band
Tao Deng, [email protected] 44
(1) The concentration of the intrinsic carrier
kT
ETKpn
g
ii2
exp23
1
Where ni - the concentration of free electrons; Pi - The concentration of
holes; T-The absolute temperature; k - Boltzmann constant;K1 =
4.82×1015K-3/2;
•The concentration of the carriers increases with increasing temperature;
•The concentration of carriers decreases when the forbidden band becomes
wider.
For example:when T =300K,EgSi =1.1eV, ni
Si =1.5×1010 cm-3;
EgGe =0.72eV, ni
Ge =2.4×1013 cm-3;
Based on the probability of the intrinsic carrier occupying the energy level:
Tao Deng, [email protected] 45
(2)The mobility and the electrical resistivity of
intrinsic semiconductors
Under the external electric field, the average speed of the directional
drifting of carriers is a constant value that is proportional to the electric
field strength ε:
nnv ppv where,μn and μp , respectively, are the average drifting velocities (cm / s) of free
electrons and holes under the unit field strength (V / cm); they are called the mobility
The resistivity of intrinsic semiconductor is:
pnipini
iqnqnqnj
1
where,q -The absolute value of the electronic charge.
For Ge:μn =3900 cm2/Vs;μp =1900 cm2/Vs
For Si: μn =1400 cm2/Vs;μp =500 cm2/Vs
Tao Deng, [email protected] 46
3.1.3.2 The electrical properties of the semiconductor
containing impurities
(1)N-type semiconductor (extra electrons)
N-type semiconductor – doping the intrinsic semiconductor (with 4 valence
electrons) with the pentavalent elements, such as P, As, Sb, etc.
EC-ED<<Eg,So, it is easy to excite the free electron.
ni>>np
nD
nqN
1
where,ND -The dopant concentration
The energy band and the Fermi distribution
of the N-type semiconductor
Tao Deng, [email protected] 47
(2)The P-type semiconductor (extra holes)
P-type semiconductor – doping the intrinsic semiconductor (with 4 valence
electrons) with the trivalent elements, such as Al, Ga, etc.
ni<<np
EA-EV<<Eg,Electrons in the valence band can enter the EA level at room
temperature, as a result of some vacancy generated in the valence band.
The structure of the P-type semiconductor The energy band and the Fermi distribution
of the N-type semiconductor
+3
Tao Deng, [email protected] 48
3.1.3.3 The impact of the temperature on the
resistance of semiconductor
The influence of temperature depends on the competition of the
resulting change in concentration of carriers and the mobility of carriers.
The dependence of the resistivity of N-type
semiconductor on temperature
Phonon scattering is
weak, but number
of the ionic
impurity donors
increases with
temperature, and
therefore the
resistivity decreases.
All Impurities are ionized. The intrinsic excitation has not yet
started, the concentration of carriers almost remains constant,
and the phonon scattering dominates, so the resistivity increases.
The intrinsic
excitation starts with
a temperature rise,
the carrier
concentration
increases dramatically,
far more than the
phonon scattering,
and therefore the
resistivity decreases.
Tao Deng, [email protected] 49
3.1.3.4 Conduction in semiconductor
T
B
e
0 T
B
e0
Under the normal circumstances, the dependence of the electrical
conductivity (resistivity) of temperature is
Where, B - The conductive activation energy of material. The
higher B, the greater the change of resistivity with temperature.
(1)The effect of temperature
Tao Deng, [email protected] 50
(2) The effect of light
Photoconduction: The irradiation of the light makes the
resistance of some semiconductors decrease.
The energy of photons is transferred to the electrons in
valence band, and the excited electrons jump to the empty
band.
Application of photosensitive effect :
Photosensitizing effects: automatic control systems, lighting
automation.
Tao Deng, [email protected] 51
(3)The effect of voltage
The relationship between the current and voltage of some
semiconductors (such as the ceramic semiconductor of zinc
oxide ) is not linear, i.e. the resistance varies with the change
of voltage . This effect can be used to make varistors, which
can be applied for voltage absorption, high-pressure
regulator, and surge arresters.
Tao Deng, [email protected] 52
(4)The effect of pressure
– In addition to generating the structural deformation, some
semiconductors under pressure have a change of the
energy band structure., which results in the change of
electrical resistivity. The relationship of semiconductor’
piezoresistive effect with stress is:
T
0
where,ρ0- the resistivity without stress;Δρ-The change of
resistivity when stress is added; β-Piezoresistive coefficient;T-the applied stress (the tension is positive; the compress is negative).
Tao Deng, [email protected] 53
(5)Magnetic effect
Hall Effect
When a semiconductor
with current is placed in the
uniform magnetic field, a
lateral electric field
perpendicular to the direction
of the external electric field
and magnetic field will be
generated.
The magnetoresistant effect
The current density is reduced as a magnetic field, perpendicular to
the current inside the semiconductor, is applied. Due to the presence of the
magnetic field, the resistance of the semiconductor increases.
Tao Deng, [email protected] 54
3.1.4 Superconductivity
• Phenomenon
At a temperature below a certain critical
temperature Tc, the specific resistance of a
material suddenly drops to very low (<10-25
Ω. cm).
• Potential applications
Superconducting thermonuclear reaction
Lossless superconducting transmission
Super electromagnet
Superconducting maglev train
Magnetic resonance imaging
The dependence of the resistivity of
mercury on temperature(1911-Onnes)
Tao Deng, [email protected] 55
3.1.4.3 The physics of the superconductivity
e2 e1
Positive ion
• In the superconducting state, there are attractive force between the electrons near
the Fermi surface (rather than the electrostatic repulsion in the normal state), the
electrons with opposite momentum and spin are paired together to generate Cooper
pairs . It is the result of the interaction between the electrons and crystal lattice.
• The total momentum and the average speed of Cooper pairs remain constant
during their movement. They don't consume energy and can move through the
lattice with no resistance.
Tao Deng, [email protected] 56
3.1.4.4 The superconducting tunneling effect
(Josephson effect)
In the 1960s, Josephson effect in weakly
connected superconductors is one of the
significant breakthroughs in the research of
superconductivity.
Weakly connected superconductors have a
sandwich structure of superconducting -
insulator - superconductor (SIS) with a
nanometer insulating film in the middle of the
two superconductors.
Josephson effect:For the S-I-S structure with current < IC,there is no
voltage through the dielectric layer. The weakly connected superconductors
have a zero resistance, i.e. the insulating (vacuum, normal) layer between
two superconductors can also pass the superconducting current.
Josephson junction
Tao Deng, [email protected] 57
Josephson junctions
Possible Josephson junctions:
(1) Superconductor- insulator -
Superconductor;
(2) Superconductor - normal metal -
Superconductor;
(3) Superconductor - vacuum -
Superconductor (STM);
(4) two superconductors contacted
by point;
(5) Two superconductor contacted
by microbridge;
(a) Tunnel junction (b) Proximity effect bridge (c)
One-dimensional micro-bridge (d) Two-
dimensional micro-bridge (e) Three-dimensional
micro-bridge (f) the micro-bridge with thickness
changing (g) Point contact
Tao Deng, [email protected] 58
3.1.5 Measurement of electrical resistance
3.1.5.1
(1) Measurement of resistance in
metals
Adjusting the current and four variable resistors,
so that the electric potentials of point f and point c in
the bridge circuit are equal. The bridge is in
equilibrium:
4221
3211
RIRI
RIRIRR nx
2
1
R
RRR nx
If R1 = R3, then R2 and R4 can be adjusted with R2 = R4 in the double bridge
measurement. In other words, the equilibrium of the bridge can be achieved by
adjusting R3 and R4 only:
Measurement through double bridge
Tao Deng, [email protected] 59
(2)The resistance measurements of semiconductors
V
I
S
l
322131
1111
2 llllllV
I
lV
I
2
The two-probe method
The four-probe method
Tao Deng, [email protected] 60
(3) The resistance measurements of insulators
x
UtR
Q
b mQ C
x
b m
UtR
C
Ballistic galvanometer can be used in
the measurement of the resistance of an
insulator. When the switch K is switched to 1
and after a time of t:
Where U is the voltage of DC supply ; t is the charging time; Q is the electric charge on the
capacitor after a charging time t, which can be measured by ballistic galvanometer. When
the switch K is switched to 2, we have
where Cb is the impact constant of ballistic galvanometer; αm is the maximum offset
of the galvanometer (direct readout). Therefore :
Tao Deng, [email protected] 61
3.1.5.2 The application of resistance measurement
Measuring the solubility curve of the solid
solution
Studying of alloy aging
Studying the order - disorder transition in
alloys
Investigating material fatigue process