# 9. Conductivity and Resistivity

#### by George Sephton on October 3, 2014 at 10:28 am | 0 comments.

## Current

In tutorial 2, we briefly looked at how current flows and the difference between Alternating Current and Direct Current; in this tutorial we will look closely at current flow in a semiconductor and at the definition of electrical conductivity and resistivity.

Electrical current is the flow of charge: it is essentially how many charged particles pass a certain point over a certain time. It is dependent on several things:

- How fast the particles are moving
- The cross sectional area of the conducting material
- How much charge is carried by the particle
- The density of these mobile charges

With this in mind we can define current as:

- is the current
- is total charge
- is time

Or when thinking about the number of charger carriers:

- is the density of charge carriers
- is the charge per charge carrier
- is the velocity of the charge carriers
- is the cross sectional area of the material

Note the dot product ().

## Current Density

In the diagram above, we can see 2 types of current flow: uniform and non-uniform. In both cases the current is the same and this is due to Current Density ().

**Uniform Current Flow**, the current density threading a cross sectional area is defined by:

**Non-Uniform Current Flow**, the current density must be integrated with respect to the cross sectional area:

## Drift Current Density

The drift current density is the current density within an electric field. We calculate this differently depending on negative (electrons) or positive (holes) charges:

- For electrons:

- For holes:

The total current density in a semiconductor can then be calculated as:

### Electrical Conductivity

Electrical conductivity () is a measure of a materials ability to conduct a current, it measured in Siemens per metre () and can be defined as:

Similarly the Electrical Resistivity () is a measure of how a material opposes current. It is calculated by examining the resistance of a material along with its volume and it is measured in Ohm metres (). It is defined as:

- is the resistance of the material
- is the cross sectional area of the material
- is the length of the material

That’s it! You have reached the end of the physics tutorial. As we mentioned in tutorial 1, we can apply all of this knowledge to a variety of Semiconductor devices; and all of those tutorials can be found in the Semiconductor Devices category.