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CONDUCTORS M V V K Srinivas Prasad K L University

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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 Presentation

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Page 1: CONDUCTORS

CONDUCTORS

M V V K Srinivas PrasadK L University

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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

M V V K Srinivas Prasad, K L University 2

Electrical Conduction in Metals

(ohms) wire,of resistance = R

(volts) V ,difference potential = V

(amperes) A current, electrical = i

:where

R

V = i

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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)

M V V K Srinivas Prasad, K L University 3

Resistance

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It is a material property. It defines how difficult is it for current to

flow. Geometry independent. Temperature dependent.

M V V K Srinivas Prasad, K L University 4

Resistivity

RA

ρ

surface area of current flow

current flow path length

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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

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It is the current flowing through unit area of cross section.

M V V K Srinivas Prasad, K L University 6

Current Density (J)

m section, cross of Area =

Amp conductor, he through tflowingcurrent = ImA / density,current = J

where

I = J

2

2

A

A

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)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

M V V K Srinivas Prasad, K L University 7

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Experimental verification of ohm’s law

M V V K Srinivas Prasad, K L University 8

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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

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Energy Band Structures in

Solids

M V V K Srinivas Prasad, K L University 10

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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.

M V V K Srinivas Prasad, K L University 11

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M V V K Srinivas Prasad, K L University 12

Isolated Atom

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f02_02_pg18

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WHY ENERGY BANDS ARE FORMED?

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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.

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Valence band – filled – highest occupied energy levels Conduction band – empty – lowest unoccupied energy levels

M V V K Srinivas Prasad, K L University 18

Band Structure

valence band

Conduction band

from Fig. 17.3Callister’s Materials Science and Engineering, Adapted Version.

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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

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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

M V V K Srinivas Prasad, K L University

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Energy Band Structures

Semiconductors and Insulators

Metals

M V V K Srinivas Prasad, K L University

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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.

M V V K Srinivas Prasad, K L University

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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.

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Imperfections

Impurity atoms

Vacancies

Interstitial atoms

Dislocations

Thermal vibrationsM V V K Srinivas Prasad, K L

University 30

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.

M V V K Srinivas Prasad, K L University

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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

M V V K Srinivas Prasad, K L University

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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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