2. Electrical ConductionROhms lawV = IRIlArea, A Vwhere I is
current (Ampere), V is voltage (Volts) and R is theresistance (Ohms
or ) of the conductorResistivityResistivity, = RA/l ( -m), where A
is the area and l is thelength of the conductor.Electrical
conductivityConductivity,= 1/ = l/RA ( -m)-1 3. Band
TheoryElectrons occupy energy states in atomic orbitalsWhen several
atoms are brought close to each other in asolid these energy states
split in to a series of energy states(molecular orbitals).The
spacing between these states are so small that theyoverlap to form
an energy band. 4. Band TheoryThe furthest band from the nucleus is
filled with valenceelectrons and is called the valence band.The
empty band is called the conduction band.The energy of the highest
filled state is called Fermi energy.There is a certain energy gap,
called band gap, betweenvalence and conduction bands. Primarily
four types of band structure exist in solids. 5. Band TheoryIn
metals the valence band is either partially filled (Cu) or
thevalence and conduction bands overlap (Mg).Insulators and
semiconductors have completely filledvalence band and empty
conduction band.It is the magnitude of band gap which separates
metals,semiconductors and insulators in terms of their
electricalconductivity.The band gap is relatively smaller in
semiconductors while itis very large in insulators. 6. Conduction
MechanismAn electron has to be excited from the filled to the
emptystates above Fermi level (Ef) for it to become free and a
chargecarrier.In metals large number of free valence electrons
areavailable and they can be easily excited to the empty statesdue
to their band structure.On the other hand a large excitation energy
is needed toexcite electrons in Insulators and semiconductors due
the largeband gap. Empty statesEf Conduction in Metals Filled
states 7. Intrinsic SemiconductorsSemiconductors like Si and Ge
have relatively narrow bandgap generally below 2 eV.Therefore, it
is possible to excite electrons from the valence tothe conduction
band. This is called intrinsic semi conductivity.Every electron
that is excited to the conduction band leavesbehind a hole in the
valence band.An electron can move in to a hole under an electrical
potentialand thus holes are also charge carriers.Conduction band
Band gap Hole Valence band 8. Intrinsic conductivityElectrical
conductivity of a conductor primarily depends on twoparameters
charge carrier concentration, n, and carriermobility, .
Conductivity, = n e e is absolute charge (1.6 x 10-19 C).Intrinsic
semiconductors have two types charge carriers,namely electrons and
holes =n e e+p e hwhere, n and p are concentration of electron and
hole chargecarriers respectively and e and h are their
mobility.Since each electron excited to conduction band leaves
behinda hole in the valence band, n = p = ni and = n e ( e + h) = p
e ( e + h) = ni e ( e + h) 9. Extrinsic SemiconductorsThe
conductivity is enhanced by adding impurity atoms(dopant) in
extrinsic semi conductors . All semi conductors forpractical
purposes are extrinsic.A higher valence dopant e.g. P (5+) in Si
(4+) creates an extraelectron (n-type) while a lower valence dopant
like B (3+) createsa hole (p-type) as shown in the atomic bonding
model below.This increases the charge carrier concentration and
hence theenhancement in conductivity. Si Si Si SiSi SiSi
SiFreeHoleelectron Si PSi SiSi B Si Si Si Si Si SiSi SiSi Si
n-typep-type 10. Extrinsic SemiconductorsThe band theory model of
n-type and p-type extrinsicsemiconductors are shown below.In
n-type, for each impurity atom one energy state (known asDonor
state) is introduced in the band gap just below theconduction
band.In p-type, for each impurity atom one energy state (known
asacceptor state) is introduced in the band gap just above
thevalence band. Conduction band Donor stateBand gapAcceptorstate
Valence bandn-type p-type 11. Extrinsic conductivityLarge number of
electrons can be excited from the donor stateby thermal energy in
n-type extrinsic semiconductors.Hence, number of electrons in the
conduction band is fargreater than number of holes in the valence
band, i.e. n >> pand =n e eIn p-type conductors, on the other
hand, number of holes ismuch greater than electrons (p >> n)
due to the presence of theacceptor states. =p e h 12. Effect of
TemperatureMetalsIncreasing temperature causes greater electron
scattering dueto increased thermal vibrations of atoms and hence,
resistivity, , (reciprocal of conductivity) of metals increases
(conductivitydecreases) linearly with temperature. 13. Effect of
Temperature Metals contdThe resistivity of metals depends on two
other factors namely,impurity level and plastic deformation as
these generatescattering centers for electrons.Increase in impurity
level results in more scattering centersand decreases the
conductivity.Similarly plastic deformation introduces more
dislocationswhich act as scattering centers and increase the
resistivity. total = t + i + d 14. Effect of Temperature Intrinsic
SemiconductorsIn intrinsic semiconductors the carrier concentration
increaseswith temperature as more and more electrons are excited
due tothe thermal energy. 15. Effect of TemperatureExtrinsic
SemiconductorsTemperature dependence of extrinsic semiconductors,
on theother hand is totally different.For example, an n-type
conductor exhibits three regions in thetemperature vs. carrier
concentration curve. 16. Effect of TemperatureExtrinsic
Semiconductors contd..In the low temperature region known as
Freeze-out region,the charge carriers cannot be excited from the
donor level toconduction band due to insufficient thermal energy.In
the intermediate temperature range ( 150 450 K) almostall the donor
atoms are ionized and electron concentration isapproximately equal
to donor content. This region is known asExtrinsic region.In the
high temperature region sufficient thermal energy isavailable for
electrons to get excited from the valence to theconduction band and
hence it behaves like an intrinsic semiconductor. 17. Electrical
properties of some metals at RTMetal Conductivity Resistivity(
-1-m-1)( -m)Silver6.8 x 1071.59 x 10-8 Copper 6.0 x 1071.68 x 10-8
Gold 4.3 x 1072.44 x 10-8Aluminum3.8 x 1072.82 x 10-8Nickel 1.43 x
1076.99 x 10-8 Iron1.0 x 107 9.0 x 10-8Platinum 0.94 x 1071.06 x
10-7 18. Electrical properties of some semi conductorsMaterial Band
gap Conductivity np (eV) ( -1-m-1)(m2/V-s) (m2/V-s)Si1.114 x
10-40.140.05Ge0.672.2 0.380.18 GaP2.25- 0.03 0.015 GaAs 1.421 x
10-60.85 0.04 InSb 0.172 x 104 7.70.07 CdS2.40- 0.03 - ZnTe 2.26-
0.03 0.01 19. Dielectric PropertyA dielectric material is an
insulating material which canseparate positive and negatively
charged entities.Dielectric materials are used in capacitors to
store theelectrical energy.CapacitanceCapacitance, C, is related to
charge stored, Q, between twooppositely charged layers subjected to
a voltage V. C = Q/VIf two parallel plates of area, A, are
separated by a distance lin vacuum, then C = o A/l. o, permittivity
of vacuum = 8.85 x10-12 F/m.If a dielectric material is present
between the plates,C = A/l, is the permittivity of the dielectric
medium.Relative permittivity r = / o, also known as
dielectricconstant. 20. Capacitance and PolarizationThe orientation
of a dipole along the applied electric field iscalled polarization
(P).It causes charge density to increase over that of a vacuumdue
to the presence of the dielectric material so thatD= o + P. is the
electric field.D is surface charge density of a capacitor, also
calleddielectric displacement. 21. Types of PolarizationFour types
of polarization: Electronic, Ionic, Orientation, andSpace charge
(interfacial).Electronic polarization is due to displacement of the
centre ofthe electron cloud around the nucleus under the applied
field.Ionic polarization occurs in ionic material as the
appliedelectric filed displaces the cations and anions in
oppositedirections resulting in a net dipole moment.Orientation
polarization can only occur in materials havingpermanent dipole
moments. The rotation of the permanentmoment in the direction of
the applied field causes thepolarization in this case.Space charges
polarization arises from accumulation ofcharge at interfaces in a
heterogeneous material consisting ofmore than one phase having
different resistivity. 22. Ferro-electricityFerro-electricity is
defined as the spontaneous alignmentof electric dipoles in the
absence of an external field.The spontaneous polarization results
from relativedisplacement of cations and anions from their
symmetricalpositions. Therefore, ferroelectric materials must
possespermanent dipoles.Examples of ferroelectric materials:
BaTiO3, Rochelle salt(NaKC4H4O6.4H2O), potassium dihydrogen
phosphate(KH2PO4), potassium niobate (KNbO3), lead
zirconatetitanate [Pb (ZrO3, TiO3)].These materials have extremely
high dielectric constantsat relatively low applied field
frequencies. Hence,capacitors made from ferroelectric materials are
smallerthan those made from other dielectric materials. 23.
PiezoelectricityPiezo-electricity is defined as conversion of
electricalenergy into mechanical strain and vice versa.It arises
due to polarization induced by an external force.Thus by reversing
the direction of external force, direction ofthe established field
can be reversed i.e. the application of anexternal electric field
alters the net dipole length causing adimensional
change.Application for these materials includes
microphones,ultrasonic generators, sonar detectors, and mechanical
straingauges.Examples: Barium titanate, lead titanate, lead
zirconate(PbZrO3),ammonium dihydrogen phosphate (NH4H2PO4),and
quartz. 24. EvaluationAt the end of this chapter one should be able
to understandThe source of electrical conductivityBand theory,
energy bands and band gapReasons for high conductivity of
metalsSemi conductivity Intrinsic and ExtrinsicEffect of
temperature on conductivityDielectric behaviorFerro and
Piezo-electricityKey words: Electrical conductivity; Band theory;
Band gap;Metallic conductors; Semi conductors;
Dielectric;Ferroelectricity; Piezoelectricity. 25. Web
Referenceshttp://hyperphysics.phy-astr.gsu.edu/hbase/solids/band.html#c3http://hyperphysics.phy-astr.gsu.edu/hbase/solids/intrin.htmlhttp://en.wikipedia.org/wiki/Electronic_band_structurehttp://www.youtube.com/watch?v=03j4ZvQCKWY&feature=relatedhttp://www.youtube.com/watch?v=AgkQrCeJF1Y&feature=relmfuhttp://www.virginia.edu/bohr/mse209/chapter19.htmhttp://simple-semiconductors.com/1.htmlwww.exo.net/~jillj/activities/semiconductors.ppthttp://free-zg.t-com.hr/Julijan-Sribar/preview/semicond.pdf
26. Quiz1. What is Ohms Law?2. What is resistivity?3. Briefly
explain the band theory of electrical conduction.4. What is Fermi
energy?5. Why are metals highly conductive?6. Briefly explain the
conduction mechanism in metals?7. What is the difference between
band structure of Cu andMg?8. How is the conductivity of metals
affected by impurity level?9. What is the role of dislocations on
conductivity of metals?10. Why does the metallic conductivity
decrease withincreasing temperature?11. What is the typical band
gap in semiconductors?12. What is intrinsic semi conductivity? 27.
Quiz13. Show that the conductivity in intrinsic semi conductors, =
ni e ( e + h)14. What is extrinsic semi conductivity? Which factors
controlthe conductivity in these semi conductors?15. What are
acceptor and donor levels?16. Explain the atomic and band theory
models of extrinsicsemi conductivity.17. What is the effect of
temperature on extrinsic semiconductivity?18. How does the carrier
concentration in intrinsic semiconductors depend on temperature?19.
Name some compound semi conductors.20. Calculate the electrical
conductivity of intrinsic Si at 150 C.The carries concentration in
Si at 150 C is 4 x 1019 m-3 and2 2e = 0.06 m /V-s and h = 0.022 m
/V-s. 28. Quiz21. If the electrical conductivity = oe-Eg/2kT then
calculate theconductivity of GaAs at Room temp (27 C) and 70 C.ni =
1.4 x 1012 m-3, e = 0.72 m2/V-s and h = 0.02 m2/V-s forGaAs at RT.
Eg of GaAs is 1.47 eV. k = 8.62 x 10-5 eV/K22. Find the electrical
conductivity of pure Si at 200 C.Electrical resistivity of Si at RT
is 2.3 x 103 -m and Eg = 1.1 eV.23. Find the electrical
conductivity of pure Ge (Eg = 0.67 eV) at250 C. Electrical
resistivity of Ge at RT is 45 x 10-2 -m24. What is dielectric
constant?25. What is polarization? How many types are there?26.
What is ferro-electricity? Give some examples of ferro-electric
materials.27. What is piezoelectricity?
