Mesoscopic Structure

MESOSCOPIC STRUCTURE

Mesoscopic structure deals with materials of an intermediate length. The scale of these materials can be described as being between the size of a quantity of atoms (such as a molecule) and of materials measuring micrometers.

The lower limit can also be defined as being the size of individual atoms. Both mesoscopic and macroscopic objects contain a large number of atoms.

The average properties derived from derived from its constituent materials describe macroscopic objects. They usually obey the laws of classical mechanics. The mesoscopic object, by contrast, is affected by fluctuations around the average. It is subject to quantum mechanics.

Definition

The structures which have a which have a size between the macroscopic world and the microscopic or atomic one are called mesoscopic structure. These structures have size usually range from a few nanometres to about 100 nm.

The electrons in such mesoscopic systems show their wavelike properties. Therefore, their behaviour is markedly dependent on the geometry of the samples.

For the description of behaviour of electrons in solids it is convenient to define a series of characteristic lengths. If the dimensions (size) of the solid is of the order of, or smaller than these characteristic lengths, the material might show new properties

In fact, the physics needed to explain these new properties is based on quantum mechanics. On the contrary, a mesoscopic system approaches its macroscopic limit if its size is several time its characteristics length.

Let us study some of the most commonly used characteristic lengths in mesoscopic systems.

(i) de Broglie wavelength

It is well known from quantum mechanics that for an electron of momentum p, there corresponds a wave of wavelength given by the de-Broglie wavelength:

In eqn. (1) we substituted p by mv in a semiclassical description, where m is the electron mass.

It is relatively easy to construct semiconductor nanostructures with one or two of their dimensions of the order of, or smaller than λB.

(ii) Mean free path

As the electron moves inside a solid, it is usually scattered by crystal imperfections like impurities, defects, lattice vibrations (phonons), etc.

The distance travelled by the electron between two inelastic collisions is called the mean free path le of the electron. If v is the speed of the electron, then

where τe is known as the relaxation time.

(iii) Diffusion length

In a mesoscopic system of typical size L, the electrons can move either in the ballistic regime or in the diffusive regime. If the mean free path le is much larger than L, the particle moves throughout the structure without scattering.

This is the so-called ballistic transport regime in which the surfaces usually are the main scattering entities.

On the other hand, if le << L, transport can be explained as a diffusion process. In this case, the system is characterized by a diffusion coefficient D. In terms of D, the diffusion length Le is defined by

where τe is the relaxation time.