Dear Ramchandra,

The following is a short article which illustrates the use of quantum Hall effect in the technology of semiconductors:

A current-carrying body placed in a magnetic field with the current direction unaligned with the field experiences a force leading to a transient sidewise drift of the charge carriers of the current. This drift continues until the force is balanced by an electric field produced by the charge accumulating at points on the body's surface in the direction of the drift. At points on the body's surface opposite the direction of the drift, there will clearly be an equal depletion of charge, which is equivalent to an accumulation of charge of opposite sign. The electric field created by this transient behavior is called the Hall field and results in a potential difference between corresponding points on the two oppositely charged surfaces. Which of the two surfaces is at the higher potential is determined by the sign of the charge carriers. If the carriers are positive, the surface in the direction of their drift will be at the higher potential; if the carriers are negative, the surface in the direction of their drift will be at the lower potential. The phenomenon thus described is called the Hall effect after E. H. Hall, who discovered it in 1879. A little over a century later, it was discovered by Klaus von Klitzingthat the Hall potential in a semiconducting material experiences quantum jumps as the magnetic field is increased when subjected to temperatures far below room temperature. This remarkable discovery has made it possible to measure an important constant of physics, called the fine structure constant, to a heretofore unattainable accuracy. Also, it provides scientists with a readily achieved standard for making accurate determinations of conductivity. For this discovery, von Klitzing was awarded the Nobel prize in 1985.

Of monumental importance to today's technology is a class of materials whose ability to conduct electric current increases with temperature and whose charge carriers can be either positive or negative, depending on the impurity introduced into them. These materials are called semiconductors, prime examples of which are the elements silicon and germanium. When these elements are given traces of the appropriate impurity element, they can be made into either p-type (containing positive carriers called holes) or n-type (containing negative carriers called electrons). The Hall effect is then used to confirm which type of material one is dealing with. Furthermore, by measuring the Hall potential, the current, the magnetic field, and the sample geometry, it is easy to calculate the number of charge carriers per unit volume in the material tested. In the 1940s, it was found that junctions could be formed with these two different types of semiconductors across which current could flow only in one direction. Devices of this kind are called rectifiers or diodes and are vital for converting alternating current to direct current, adding or removing audio and video signals from their carrier waves, and many other applications. It was also found that more than two junctions could be formed in one device, and these were called transistors. These devices were capable of being employed in amplifier and oscillator circuits in radios and TVs. Previously, rectifiers, amplifiers, and oscillators used vacuum tubes as their essential components, which were generally bulky, used lots of power, and burned out frequently. The new semiconductor devices had none of these problems. In the 1950s and 1960s, it was learned how to create many transistor circuits on a small chip using integrated circuitry. Without this new technology, the powerful computers that were used in our space program and are now found universally in the form of compact personal computers would not have been possible. Even more importantly, without the discovery of the Hall effect and its use in the scientific investigation of semiconducting materials, this sequence of developments could not have even begun. Finally, with the discovery of its large-scale quantum behavior, the future role of the Hall effect in the advancement of science and technology may eventually prove to be even greater than its past role.

http://science.jrank.org/pages/3194/Hall-Effect.html

Hoping this will be helpful,

Rafik

Very briefly, the quantum Hall effect has provided us with a means of measuring the ratio e/ħ (the ratio of the electron charge to the reduced constant of Planck) to an unprecedented accuracy, thereby enabling us to determine the physical constants of nature to a higher accuracy than was feasible previously (this determination involves a fitting procedure so that barring those natural constants that are by definition exact -- like the permeability of vacuum in the SI system of units, inaccuracy in one constant affects the accuracy with which we know other constants of nature). One of the major problems in determining these constants to high accuracy lied in the problem of measuring the electric current to sufficiently high accuracy. To appreciate this, one will have to consider the definition of the unit of electric current (Ampère in the SI system of units), which involves measuring the force between two infinitely-long conducting wires carrying electric current.

A classical Hall effect is the following: When electric current flows through a conductor electrons move in the opposite direction. Now if the conductor is placed in a magnetic field in a direction (say Z) perpendicular to the electron flow (say X) field due to the presence of Lorentz force electrons move sideways and a Hall voltage develops between the two sides of the conductor. That is the Hall voltage develops along the Y direction.

In the quantum version of Hall effect  we need a two dimensional electron system to replace the conductor, magnetic field has to be very high and the sample must be kept in a very low temperature. Then the ratio of the Hall voltage (along Y direction)  and the applied current (along X direction, also called Ichannel) is a fundamental constant which is independent of the macroscopic properties of the sample (such as it's mass, shape etc.).  It is a truly remarkable fact that this ratio can be expressed in terms of only two fundamental constants of nature (i) electron charge (ii) Planck's constant.