# Controlling Conductivity and Simple Band Theory

All solids can be broadly grouped into one of three categories:

• Metals and metallic conductors – this includes all metals and carbon.  ρ (resistivity) is low and increases as temperature increases.
• Insulators – most of them are non-metals, plastics and much are organic materials if dry.
• Semi-conductors – this includes Silicon, germanium, Gallium arsenide etc…With these, ρ (resistivity) decreases as temperature rises.
Simple Band Theory
The simple band theory is the theory of which explains conductance and resistance amongst insulators, metals and semi-conductors.

Insulator

The Valence band is where the electrons are in the material. If it is easy (or doesn’t take much energy) for the electrons to move from the valence band to the conduction band, you can say it is has a high conductivity. For insulators, there is a gap between the Valence and Conduction band which means the electrons need more energy to get to Conduction band.
Metals

As you can see with the metals simple band theory, the Conduction (grey lines) and Valence (black lines) band overlap each other. This means a tiny amount of energy is needed to move the electrons from the Valence band to the Conduction band making them have a high conductivity.
Semi-Conductor

With semi-conductors, as you increase the temperature, more electrons jump/move to the Conduction band.
If a pure semi-conductor is doped with a few atoms (1 per 100 or 1 per 1000) that have either an extra electron to go in the conduction band or they absorb an electron from the Valence band, they will leave more positive holes to conduct in the Valence band.
A hole is caused by the electrons jumping to and from the Valence band:
• The electrons strictly are not moving but jumping from hole to hole.
• As an electron moves from the Valence band to the Conduction band, it will leave a hole.
• As an electron moves to the Conduction band or Valence band, it will land on a hole and then jump from hole to hole.