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Hall effect and its applications in semiconductors

What is the Hall effect?

“An effect when occurring when a current carrying conductor is placed in a magnetic field and orientated so that the field is at right angles to the direction of the current.”An electric field is produced in the conductor at right angles to both the current and the magnetic field.The field produced is related to the vector product of the current density J and magnetic flux density B by the relation.

EH =-RH (J×B)

The constant RH is the Hall coefficient.The electric field results in a small transverse potential difference,the Hall voltage,VH,being set up across the conductor.

In metals and degenerate semiconductors RH is independent of B and is given by 1/ne ,where n=carrier density and e=electronic charge.In non-degenerate semiconductors additional factors are introduced due to the energy distribution of the current carriers.

The hall effect is a consequence of the Lorentz force acting on the charge carrying electrons.A sideways drift is imposed on the motion of the electrons by their passage through the magnetic field.For materials in which current is carried by positive charge carriers (Holes) ,the direction of the Hall field ,EH, is reversed.

Under certain conditions the quantum Hall effect is observed.The motion of the electrons must be constrained so that they can only move in a two dimensional “flat land”:this can be achieved by confining the electrons to an extremely thin layer of semiconductor.In addition ,the temperature must be very low and a very strong magnetic flux density must be used.The magnetic field applied normal to the semiconductor layer produces the transverse Hall voltage as in the ordinary Hall effect.The ratio of the  Hall voltage to the current is the Hall resistance.At certain values of flux density,both the conductivity and the resistivity of the solid become zero,rather like in a superconductors.A graph of Hall resistance against flux density shows step like regions,which correspond to the values at which the conductivity is zero.At these points ,then,the Hall resistance is quantized;calculations shows that

(VH/I)n =h/e2

Where n is an integer ,h is the Planck constant,and e is the electron charge.The Hall resistance can be measured very accurately.It is equal to 25.8128 kΩ.Hence the quantum Hall effect can be used to calibrate a conventional resistance standard ,and can also be used in determination of h and e.

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