Ballistic Transport

BALLISTIC TRANSPORT

The conductivity is a bulk parameter. It is derived by assuming a large number of electrons (the electron gas model) and a large number of collisions between electrons and phonons, impurities, imperfections, etc.

In particular, if conduction path L is reduced to become much less than the mean free path L_m we expect that no collisions will take place.

Definition

When the dimension of the conductor (L) is smaller than the mean free path of the electron (L) then the transport of electron is called ballistic transport.

Explanation

When the length 'L' of the conductor becomes much smaller than the mean free path 'L' the transport is termed 'ballistic'. It means that the electrons do not scatter during the time, it travels through the conductor.

For example, ballistic transport can be observed in a metal nano wire.

Condition of Ballistic transport

The mean free path can be increased by reducing the number of impurities in a crystal or by lowering its temperature

Ballistic transport conditions are

(i) L << L_m and

(ii) L << L ϕ

where L → Length of the conductor.

L_m → Mean free path [length that the electron can travel before having an elastic collision]

Lϕ → Length over which an electron can travel before having an inelastic collision. This is also called the phase-coherence length, since it is the length over which an electron wave function retains its coherence.

Ballistic transport occurs over very small length scales and is obviously coherent.

The electron doesn't hit anything as it travels through the material and therefore, there is no momentum or phase relaxation. Thus, in Ballistic material, the electron's wave function can be obtained from Schroedinger's equation.

Application

One practical application of ballistic transport is to ultra-short-channel semiconducting FETS or carbon nano tube transistors.

That is in a very small length scales, electron transport occurs ballistically. It can be seen that ballistic transport will be important in many future nanoscopic devices.