Drude model

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'.

Related Topics:
Electrical conduction - 1900s - Paul Drude - Electron - Kinetic theory

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

In its simplest form, the Drude model describes the electrical current density J under an applied electric field E,

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

:J = rac{ne^2 au E}{m}

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

where e is the charge of the electron, and m its effective mass. The conductivity is defined as sigma=J/E, or

Related Topics:
Charge - Conductivity

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

:sigma = rac{ne^2 au}{m}.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

The Drude model can also predict the current as a response to a time-dependent electric field with an angular frequency ω, in which case

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

:sigma(omega) = rac{ne^2 au/m}{1 - iomega au}.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Here it is assumed that

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

:E(t) = Re(E_0 e^{iomega t})

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

:J(t) = Re(sigma(omega) E_0 e^{iomega t}).

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

The imaginary part indicates that the current lags behind the electrical field, which happen because the electrons need roughly a time τ to accellerate in response to a change in the electrical field. Here the Drude model is applied to electrons; it can be applied both to electrons and holes, i.e. positive charge carriers in semiconductors.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

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.

Related Topics:
Metal - Hall effect - Thermal conductivity

~ ~ ~ ~ ~ ~ ~ ~ ~ ~