In 1900, Paul Drude formed a theory of conduction in metals using the newly discovered concept of the electron. The theory states:
- Metals have a high density of free electrons.
- Electrons in metals move according to Newton’s laws
- Electrons in metals scatter when encountering defects, ions and the momentum of the electron is random after this scattering event.
In short, the Drude Model explains how electrons can be expected to move in metals, which is fundamental to the operation of many devices.
Applied Electric Field
In the presence of an electric field, electron motion on average can be described with the following momentum p(t), when tau is the scattering time and 1/tau is the scattering rate:
Now consider several cases for electron motion in metals.
No applied electric field, E(t) = 0
In this case, electrons move randomly and the electron path momentum averages zero.
Constant Uniform Electric Field
When a uniform electric field is present, electron movement averages in the opposite direction of the electric field.
Relating momentum to velocity, we can find the electron drift velocity which is the rate at which the electron travels in an average direction caused by the field. The electron mobility is the relationship between drift velocity and the electric field.
Electron current density is related to the number of electrons, an electron’s charge, the mobility, and the electric field. The factor between electron current density and electric field is the conductivity.