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.
- Conductors - high values of electrical conductivity
- Insulators - low values of electrical conductivity
- Semiconductors - intermediate values of electrical conductivity
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
- n is the charge carrier density (usually electrons)
- q is the charge on each carrier
- m (actually the greek letter mu) is the mobility of each carrier given by: m = v/E
where - v is the drift velocity of the carrier
This
means how fast the carrier is moving through the solid from one end to
another. It is not the same thing as its absoute velocity. The drift
accounts for the collisions with the crystal lattice and the fact that
the carrier will travel a random and chaotic path. In the absense of an
electric field there will be no net motion through the solid and the
drift velocity will be zero. - E is the applied electric field strength
This is just the voltage divided by the distance between the points where this voltage is measured, V/d
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
- V is the voltage across some device
- I is the current through it
- R is the resistance of the device
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
- J = current density or current flux
- E = electric field strength
- sigma is the electrical conductivity
This equation is considered to be Ohm's Law on a microscopic level.