Hall Effect

The Hall Effect and Hall Probes

Figure 4: Diagrams of (a) a Hall bar and (b) the circuit for a Hall probe

There are a number of methods of measuring B, but the most

convenient is probably the Hall probe. Hall probes make use of the

Hall e_ect which was discovered in 1879 by Edwin Hall. When a

conducting plate (usually made of a semiconductor in practical

applications) carrying a current IH is placed in a _eld B (Fig. 4(a)),

a voltage is produced not only along the current direction, say VR

(this is the usual resistive part), but also in a ransverse direction, say

VH (this is the Hall voltage). The magnitude of VH depends on the

product of IH, the magnitude of B, and cos o, where o is the angle

between the plate normal and B. It also depends on the
thickness and type of the material. Thus

where k is a constant which we refer to as the probe constant. Notice
VH reverses when B is reversed (i.e. cos _ changes sign). Because

it is di_cult to align the Hall voltage contacts exactly opposite each

other, a part of the measured voltage is due to VR. This is the o_set

voltage V0, which may depend on the magnitude B, but does not

reverse when B is reversed. This means that V0 can be eliminated by

measuring the probe output for _B. In this experiment the probe is

powered by a constant current supply which is contained in a box.

There are two output terminals on the front of the box for the Hall

probe output voltage. There are also two output terminals on the

rear with which the Hall probe current may be checked. In order to

translate measurements of the Hall voltage into values of B, IH and

k must be recorded. The value of k is written on the power supply.

A schematic of the circuit is shown in Fig. 4(b).


Source ( pdf )
http://physics.queensu.ca/~phys250/magcirc.pdf


The Hall Effect

This subchapter introduces two important topics: The Hall effect

as an important observation in materials science and at the same

time another irrefutable proof that classical physics just can't hack

it when it comes to electrons in crystals.

- The Hall effect describes what happens to current flowing through

a conducting material - a metal, a semiconductor - if it is exposed

to a magnetic field B.

- We will look at this in classical terms; again we will encounter a

fundamental problem.

The standard geometry for doing an experiment in its most simple

form is as follows:

1.A magnetic field B is employed perpendicular to the current

direction j, as a consequence a potential difference (i.e. a voltage)

develops at right angles to both vectors.

2 In other words: A Hall voltage UHall will be measured perpendicular

to B and j.

3In yet other words: An electrical field EHall develops in y-direction

4 That is already the essence of the Hall effect.

more
http://www.tf.uni-kiel.de/matwis/amat/mw2_ge/kap_2/

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