The Hall Effect

The Hall effect is a phenomenon that arises when an electric current and magnetic field are simultaneously

imposed on a conducting material. Specifically, in a flat plate conductor, if a current density, J

, is applied in

the x direction and (a component of) a magnetic field, B

, in the z direction, then the resulting electric field,

E

, transverse to J

and B

is known as the Hall electric field E

(see Figure 27.1) and is given by

where R is known as the Hall coefficient. The Hall coefficient can be related to the electronic structure and

properties of the conduction bands in metals and semiconductors and historically has probably been the most

important single parameter in the characterization of the latter. Some authors choose to discuss the Hall effect

in terms of the Hall angle, f, shown in Figure 27.1, which is the angle between the net electric field and the

imposed current. Thus,

For the vast majority of Hall effect studies that have been carried out, the origin of E

is the Lorentz force, F

,

that is exerted on a charged particle as it moves in a magnetic field. For an electron of charge e with velocity v,

F

is proportional to the vector product of v and B; that is:

In these circumstances a semiclassical description of the phenomenon is usually adequate. This description

combines the classical Boltzmann transport equation with the Fermi-Dirac distribution function for the

charge carriers (electrons or holes) (Ziman, 1960), and this is the point of view that will be taken in this

chapter. Examples of Hall effect that cannot be treated semiclassically are the spontaneous (or extraordinary)

Hall effect that occurs in ferromagnetic conductors (Berger and Bergmann, 1980), the quantum Hall effect

(Prange and Girvin, 1990), and the Hall effect that arises in conjuction with hopping conductivity

(Emin, 1977).