Drude model

The Drude theory (also Drude model, according to Paul Drude ) is a classic description of the charge transport through an external electric field in metals or generalized by free electrons in solids. Looking at electric fields ( hence light) is also the name Drude Zener theory or model used ( by Clarence Melvin Zener ).

It was extended in 1905 by Hendrik Antoon Lorentz and 1933 by Arnold Sommerfeld and Hans Bethe supplemented by the results of quantum mechanics.

Description

In the model, an electrical conductor is considered as an ion crystal, in which the electrons can move freely. Responsible for the current conduction are therefore electrons forming an electron gas. The term electron gas is due to the similarity of this theory to the kinetic theory of gases: prevails in the interior of the conductor that is no electric field, the electrons behave like gas molecules in a container. This behavior is described by the kinetic gas theory.

By an external electric field, the free electrons in the conductor experience a force and are accelerated. The electrons are accelerated in the conductor material, however, when voltage is applied not continuous. If this were so, the resistance and the current should not be constant and Ohm's Law would therefore not apply. It is after a short time an equilibrium, in which the average velocity of the electrons is proportional to the field strength.

The Drude model explains this fact as follows: The electron collides with a lattice ion and is decelerated. This process is described phenomenologically by a mean collision time between two collisions. With increasing temperature, the mean collision time decreases, explaining the decreasing conductivity of the metals.

The equation of motion for this is:

The mass of the electron, the electron speed, the drift speed (s - speed minus the thermal velocity ), and the collision time

For the steady state () holds:

The charge carrier density, the current density is thus

The conductivity is therefore

This equation is referred to as Drude formula or Drude conductivity.

Areas of application

With this model for the first time could be explained by Ohm's Law, if the calculated with this model resistance value is about six times larger than the true ( measured ) is resistance of each material. But it also has another significant weaknesses.

Confines

The Drude model is consistent with its assumption that all electrons would contribute to the current, seen in contradiction to the statements of the Pauli principle, and also classic, this assumption creates a contradiction: From statistical thermodynamics it follows that all degrees of freedom of a system ( here: solids) contribute funds to its internal energy. Each electron would have to deliver. However, measurements have shown that the electronic contribution to the total energy is about a thousand times smaller. So it can not be part of all the electrons of the electron gas, and even more so the motion of the electron gas is less free than it describes the kinetic theory of gases.

The model predicts a proportionality of resistance and electron velocity to the root from the temperature. This is not the case in reality. Furthermore, no statement can be made ​​as to whether a material is a conductor, semiconductor or insulator. The latter can be considered an advantage in so far as one can apply the theory on the free electrons in the conduction band of a semiconductor.

Remedy the quantum mechanical description of the model, respectively, outgoing sommerfeld between the band model, in which the band gaps are predicted correctly.

A generalization of the Drude model represents the Lorentz oscillator model (also Drude Lorentz model) dar. This additional absorption peaks are described which are caused for example by band transitions. With the Lorentz oscillator model, it is possible to describe the dielectric function of a variety of materials (including semi- conductors and insulators ).