M V V K Srinivas Prasad K L University. Ohm’s Law ◦ At constant temperature the current flowing...

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

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

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)


Resistance

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

flow. Geometry independent. Temperature dependent.


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.


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


Experimental verification of ohm’s law


M V V K Srinivas Prasad, K L University9

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


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.



Isolated Atom


f02_02_pg18


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.



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


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.


Energy Band Structure


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.



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

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.


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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



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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M V V K Srinivas Prasad K L University. Ohm’s Law ◦ At constant temperature the current flowing...

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