Electrical Properties of Materials

For Structural Materials we looked at the atomic bonding to determine mechanical properties. For Electronic Materials we will look at the electronic structure to determine electrical properties. This means looking at the electrons in the atoms of the material and examining their electron configurations. Specifically, we will look at the energy levels of these electrons, and how these levels fit into concepts of energy bands, valance bands, conduction bands.

Catagories of Electrical Materials
Broadly speaking, electrical materials can be broken up into 3 catagories according to the value of their electrical conductivities.

                                     
The Material Property of Electrical Conductivity

The material property of electrical conductivity has the widest range of values of any material property. Copper, one of the most conducting of all materials has an electrical conductivity of 58 x 106 ohm-1m-1 whereas polyethylene, a polymeric insulator has an electrical conductivity on the order of 10-14 ohm-1m-1.

Electrical conductivity is designated by the letter sigma and is calculated from this equation:
sigma = n q m
where
                 
The Material Property of Resistivity

Resistivity is another material property. It is the reciprocal of conductivity. Whereas conductivity measures the ability of a material to allow charge carriers to move through it, resisitivity measures the ability of a material to prevent charge carriers from moving through it.
         
Resistivity is designated by the greek letter rho. Hence:
sigma = 1/rho

                                     
Ohms Law on macroscopic level and microscopic level

You are probably familiar with Ohm’s Law:

V = IR
where
This relationship is considered to be on a macroscopic level because it considers a physical device. If the device is made from some material with a cross sectional area, A, and a length, l, then its resistance is given by:
 R = (rho x l) /A
where rho is the resistivity of the material.

Note: The relationship between resistance and resistivity is analogus to weight and density. Weight is a property of an object whereas density is a material property. Similarily, reisitance is a property of an object, or a device whereas resisistivity is a material property.

Substituting this expression for resistance into Ohm's Law above we can get a relationship on a microscopic level:
V = IR
V = I (rho x l) /A
V/l = (rho) ( I/A )
Rearranging gives:
I/A  V/l (1/rho)
J = E (sigma)
where
This equation is considered to be Ohm's Law on a microscopic level.

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