Electrical Conductance Conductivity of Metal Semiconductor and Insulator | Band Theory

What is Conductance?

When we apply same potential difference across different conductors, we will see different currents flow through them. Actually how much current will flow through a specific conductor for certain applied potential difference across it, depends upon a specific property of the conductor, called electrical conductance.

This property determines how easily a current can flow through a conductor. As we know resistance is such a property of a conductor which resists the flow of current through it. That means, electrical conductance is reciprocal property of resistance. Generally conductance is denoted as,

Definition of Electrical Conductance

Electrical conductance is defined as a special property of a conductor which determines how easily an current can flow through it.

Equation or Formula of Electrical Conductance

Let us take a piece of conductor of length l and cross sectional area A. If length of the conductor is increased, the electrons have to drift more paths. Hence more chance of inter atomic collision. That means current gets much harder path to travel, means electrical conductance of the conductor is reduced.

Thus conductance is inversely proportional to length of the conductor.

If cross sectional area of conductor is increased then current gets more drift electrons. Hence, conductance of the conductor is increased.

From equation (1) and (2),

Where, σ = constant of proportional known as conductivity or specific conductance.

Specific Conductance or Conductivity

In the equation of the conductance we have already mentioned the term σ or Sigma as conductivity. Now in that equation if we put l = 1m and A = 1m2 then G = σ. That indicates σ is the conductance of a conductor whose length is 1 m and cross sectional area is 1 m2. That mean specific conductance or conductivity is the conductance of a conductor whose volume is 1 m × 1 m2 = 1 m3.

Definition of Electrical Conductivity

Conductivity is a material of per unit volume.
Electrical conductivity is a basic property of material. Due to this property one material can conduct electricity. Some materials are good conductor of electricity that means current can pass through them very easily; again some materials do not allow current to flow through them. The material through which current passes easily, called good conductor of electricity in other words, the electrical conductivity of these materials is high. On the other hand the materials do not allow the current to flow through them are called electrical insulators. There are some materials whose electrical conductivity is not as high as conductor and also not as poor as insulator, they have an intermediate conductivity and these type of materials are known as semiconductors.

Unit of Conductance

As we mentioned earlier conductance is reciprocal of resistance of resistance. That is,

Unit of resistance is ohm and that is why unit of conductance is generally written as mho – the reverse spelling of ohm. A modern electrical engineering, mho is named by Siemens.

Unit of Conductivity

The equation of conductivity, we have already deducted as,

Hence, unit of conductivity is,

Here, S is Siemens.

Table of Resistivity and Conductivity of Different Materials at 20oC

MaterialResistivity at 20oCConductivity 20oC
Air1.3 × 1016 to 3.3 × 10163 × 10-15 to 8 × 10-15
Aluminum2.82 × 10-83.5 × 107
Annealed copper1.72 × 10-85.80 × 107
Calcium3.36 × 10-82.98 × 107
Carbon (amorphous)5 × 10-4 to 8 × 10-41.25 to 2 × 103
Carbon (diamond)1 × 1012~10-13
Carbon (graphite)2.5 × 10-6 to 5.0 × 10-6 //basal plane2 to 3 × 105 //basal plane
Carbon steel-10101.43 × 10-7
Constantan4.9 × 10-72.04 × 106
Copper1.68 × 10-85.96 × 107
Deionized water1.8 × 1055.5 × 10-6
Drinking water2 × 101 to 2 × 1035 × 10-4 to 5 × 10-2
Fused quartz7.5 × 10171.3 × 10-18
GaAs5 × 10-7 to 10 × 10-35 × 10-8 to 103
Germanium4.6 × 10-12.17
Glass10 × 1010 to 10 × 101410-11 to 10-15
Gold2.44 × 10-84.10 × 107
Grain oriented electrical steel4.60 × 10-72.17 × 106
Hard rubber1 × 101310-14
Iron1.0 × 10-71.00 × 107
Lead2.2 × 10-74.55 × 106
Lithium9.28 × 10-81.08 × 107
Manganin4.82 × 10-72.07 × 106
Mercury9.8 × 10-71.02 × 106
Nichrome1.10 × 10-69.09 × 105
Nickel6.99 × 10-81.43 × 107
Paraffin wax1 × 101710-18
PET10 × 102010-21
Platinum1.06 × 10-79.43 × 106
Sea water2 × 10-14.8
Silicon6.40 × 1021.56 × 10-3
Silver1.59 × 10-86.30 × 107
Stainless steel6.9 × 10-71.45 × 106
Sulfur1 × 101510-16
Teflon10 × 1022 to 10 × 102410-25 to 10-23
Tin1.09 × 10-79.17 × 106
Titanium4.20 × 10-72.38 × 106
Tungsten5.60 × 10-81.79 × 107
Wood (damp)1 × 103 to 410-4 to 10-3
Wood (oven dry)1 × 1014 to 1610-16 to 10-14
Zinc5.90 × 10-81.69 × 107

Band Theory for Electrical Conductivity

The electrons in the outer most orbit of an atom experiences least attraction force. So the outermost atom can easily be detached from the parent atom. Let’s explain the details with band theory.
When a number of atoms are brought together, the electrons of one atom experience forces of other atoms. This effect is most pronounced in outer most orbits. Due to this force, the energy levels, which were sharply defined in an isolated atom, are now broadened into energy bands. Due to this phenomenon generally two bands result, namely valance band and conduction band.

Valance Band

The outermost orbital of an atom, where electrons are so tightly bounded that; they cannot be removed as free electron.

Conduction Band

This is the highest energy level or orbital in outer most shell, in which electrons are free enough to move.

Band Gap

There is one energy gap that separates these two bands, the valance band and conduction band. This gap is called forbidden energy gap.

Electrical Conductivity of Metal

In metals, the atoms are so tightly packed that electron of one atom experience sufficiently significant force of other closed atoms. The result, the valance band and conduction band in metals come very closer to each other and may even overlap. Consequently, by receiving very small amount of energy from external heat or electrical energy source, the electrons readily ascend to higher levels in the metal. Such electrons are known as free electrons. These free electrons are responsible for current that flows through a metal. When external electric source is connected to a piece of metal, these free electrons start flowing towards higher potential terminal of the source, causing current to flow in the metal. In metal, density of free electrons in conduction band is much higher than other materials, hence metal is referred as very good electrical conductor. In other words electrical conductivity of metal is very good.
Conduction Band

Table for Conductivity of Different Metals

MetalsConductivity in Siemens/meter at 20oC
Silver6.30 × 107
Copper5.96 × 107
Aluminium3.5 × 107
Annealed copper5.80 × 107
Calcium2.98 × 107
Carbon steel (1010)6.99×106
Constantan2.04 ×106
GaAs5 × 10−8 to 103
Gold4.10 × 107
Grain oriented electrical steel2.17×106
Lead4.55 × 106
Lithium1.08 × 107
Manganin2.07 × 106
Mercury1.02 × 106
Nichrome9.09 × 105
Nickel1.43 × 107
Platinum9.43 × 106
Stainless steel1.45 × 106
Tin9.17 × 106
Titanium2.38 × 106
Tungsten1.79 × 107
Zinc1.69 × 107

Electrical Conductivity of Semiconductor

In semiconductor the valance band and conduction band are separated by a forbidden gap of sufficient width. At low temperature, no electron possesses sufficient energy to occupy the conduction band and thus no movement of charge is possible. But at room temperature it is possible for some electrons to give sufficient energy and make the transitions in conduction band. The density of electrons in conduction band at room temperature is not as high as in metals, thus cannot conduct current as good as metal. The electrical conductivity of semiconductor is not as high as metal but also not as poor as electrical insulator. That is why, this type of material is called semiconductor – means half conductor.

Table for Conductivity of Different Semiconductors

SemiconductorConductivity in Siemens/meter at 20oC
Silicon1.56 × 10− 3

Electrical Conductivity of Insulator

Ideally electrical conductivity of an electrical insulator is nil. The atoms in the insulator molecules are electrically stable enough. The outer most shells of these atoms are completely filled with electrons. In such material where forbidden gap is very large and as a result the energy required by the electron to cross over to the conduction band is practically large enough. Insulators do not conduct electricity easily. That means the electrical conductivity of insulator is very poor.

Table for Conductivity of Different Insulators

InsulatorConductivity in Siemens per meter at 20oC
Air3 × 10-15to 8 × 10−15
Fused quartz1.3 × 10-18
Glass10-11 to 10-15
Hard rubber10-14
Paraffin wax10-18
Teflon10-25 to 10-23
Wood10-16 to 10 -14
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