conductors
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CONDUCTORS. M V V K Srinivas Prasad K L University. Electrical Conduction in Metals. Ohm’s Law At constant temperature the current flowing through a conductor is directly proportional to the potential difference across the ends of the conductor. Ohm’s Law: Macroscopic form. Resistance. - PowerPoint PPT PresentationTRANSCRIPT
CONDUCTORS
M V V K Srinivas PrasadK L University
Ohm’s Law◦ At constant temperature the current flowing
through a conductor is directly proportional to the potential difference across the ends of the conductor.
Ohm’s Law: Macroscopic form
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Electrical Conduction in Metals
(ohms) wire,of resistance = R
(volts) V ,difference potential = V
(amperes) A current, electrical = i
:where
R
V = i
The opposing force offered by the material to the flow of current.
Depends on◦ Nature of the material (ρ).◦ Temperature.◦ Geometry/ dimensions (length L, area of cross
section A)
R = r (L/A)
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Resistance
It is a material property. It defines how difficult is it for current to
flow. Geometry independent. Temperature dependent.
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Resistivity
RA
ρ
surface area of current flow
current flow path length
Examples of Resistivity (ρ)
Ag (Silver): 1.59×10-8 Ω·m Cu (Copper): 1.68×10-8 Ω·m Graphite (C): (3 to 60)×10-5 Ω·m Diamond (C): ~1014 Ω·m Glass: ~1010 - 1014 Ω·m Pure Germanium: ~ 0.5 Ω·m Pure Silicon: ~ 2300 Ω·m
M V V K Srinivas Prasad, K L University
It is the current flowing through unit area of cross section.
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Current Density (J)
m section, cross of Area =
Amp conductor, he through tflowingcurrent = ImA / density,current = J
where
I = J
2
2
A
A
)m (ty conductivielectrical =
m y,resistivit electrical =
m / V field, electric = EmA / density,current = J
where
E = E
= J
1-
2
Ohm's Law -- Microscopic Form
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Experimental verification of ohm’s law
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Electrical conductivity varies between different materials by over
27 orders of magnitude, the greatest variation of any physical property
Metals: > 107 (.m)-1
Semiconductors: 10-6 < < 105 (.m)-1
Insulators: < 10-6 (.m)-1
(.cm)-1
Energy Band Structures in
Solids
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In most of solids conduction is by electrons.
σ depend on no. of electrons available for conduction.
The no. of electrons available for conduction depends on◦Arrangement of electrons states or levels with respect to energy.
◦The manner in which these states are occupied by electrons.
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Isolated Atom
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f02_02_pg18
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WHY ENERGY BANDS ARE FORMED?
Electrons of one atom are perturbed by the electrons and nuclei of the adjacent atoms.
Results in splitting of atomic states into a series of closely spaced electron states to from what are called ELECTRON ENERGY BAND.
Extent of splitting depends on interatomic separation.
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Electronic Band Structures
From Fig. 17.2Callister’s Materials Science and Engineering, Adapted Version.
Valence band – filled – highest occupied energy levels Conduction band – empty – lowest unoccupied energy levels
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Band Structure
valence band
Conduction band
from Fig. 17.3Callister’s Materials Science and Engineering, Adapted Version.
With in each band the energy states are discrete.
No. of states with in each band will equal the total of all states contributed by the N atoms.◦ s band consists of N states◦ p band consists of 3N states
Electrical properties of a solid depends on its electron band structure.
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Energy Band Structure
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Energy Band Structure
Conductors
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Conductors
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Conduction & Electron Transport• Metals (Conductors):
-- for metals, empty energy states are adjacent to filled states.
• two types of band structures for metals
• thermal energy excites electrons into empty higher energy states.
- partially filled band - empty band that overlaps filled band
filled band
Energy
partly filled band
empty band
GAP
fille
d st
ates
Partially filled bandEnergy
filled band
filled band
empty band
fille
d st
ates
Overlapping bands
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Energy Band Structures
Semiconductors and Insulators
Metals
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Electron movement
An electron moves about randomly in a metal being frequently and randomly scattered by thermal vibrations of the atoms. In the absence of an applied field there is no net drift in any direction.
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Applied Field – net drift
• In the presence of an applied field, there is a net drift along the x-direction.
• After many scattering events the electron has been displaced by a net distance, Δx, from its initial position toward the positive terminal.
• The electrons scatter by collisions with atoms and vacancies that lose the KE and drastically change their direction of motion.
• Electrons move randomly but with a net drift in the direction opposite to the electric field.
Imperfections
Impurity atoms
Vacancies
Interstitial atoms
Dislocations
Thermal vibrationsM V V K Srinivas Prasad, K L
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Scattering of electrons is because of
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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 = eEe – electron mobility [m2/V-s]. 1 / Friction
Transfers part of energy supplied by electric field into lattice as heat.
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Electron Mobility
Electrical conductivity proportional to number of free electrons per unit volume, Ne, and electron mobility, e
= Nee e
(m) = Metal (s) = Semicon
Mobility (RT) (m2V-1s-1)
Carrier Density Ne (m
-3) Na (m) 0.0053 2.6 x 1028
Ag (m) 0.0057 5.9 x 1028 Al (m) 0.0013 1.8 x 1029 Si (s) 0.15 1.5 x 1010
GaAs (s) 0.85 1.8 x 106
InSb (s) 8.00
metal >> semi
metal < semiNmetal >> Nsemi
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Electrical resistivity of metals
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Total resistivity tot (Matthiessen rule)
total = thermal+impurity+deformationIncreases with T, with deformation, and with alloying.
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