Drude model
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The Drude model of electrical conduction was developed in the 1900s by Paul Drude to explain the transport properties of electrons in materials. The Drude model is the application of kinetic theory to electrons in a solid. It assumes that the material contains immobile positive ions and an "electron gas" of classical, non-interacting electrons of density n, each of whose motion is damped by a frictional force, due to collisions of the electrons with the ions, characterized by a relaxation time τ. Under an applied electric field E, the current density j is
- <math>j = \frac{ne^2 \tau}{m}E<math>
where e is the charge of the electron. The conductivity σ is then
- <math>\sigma = \frac{ne^2 \tau}{m}<math>.
This simple classical model does a surprisingly good job of explaining DC and AC conductivity in metals, the Hall effect, and thermal conductivity (due to electrons) in metals.