# Relationship of conductivity and the hall voltage to temperature

The Hall coefficient of the given sample falls with rise in temperature. Hall coefficient is the ratio of mobility to conductivity tensor and relaxation time for. This subchapter introduces two important topics: The Hall effect as an important material - a metal, a semiconductor - if it is exposed to a magnetic field B. a potential difference (i.e. a voltage) develops at right angles to both vectors. In other . Measurements of the Hall coefficient of materials with a known conductivity. One may consider the Hall effect to result from the force on a charge moving in . so you are measuring the temperature difference between the.

We fit the temperature dependence above about 4 K to thermal activation, and extract the energy gap and the effective g-factor. Introduction The quantum Hall effect was discovered by von Klitzing, Dorda, and Pepper in [ 1 ]. Von Klitzing et al.

While the quantization was shown to be independent of the material properties of the sample [ 4 — 6 ], and the precision of quantum Hall measurements continually improved, it was found that finite temperature and current could both lead to deviations from the zero temperature value of the Hall resistance.

Several investigations [ 37 — 18 ] measured the temperature dependence of the Hall resistance across the device, and the longitudinal resistance Rx along the device, over the following years. It is clear that since any measurement must necessarily be made at finite temperature, understanding the temperature dependence of the quantum Hall resistance is critical if we wish to establish a resistance standard based on this value.

In practice, one can typically cool the sample to temperatures where no temperature dependence is measurable to the precision of the measurement. Only then can we be confident that we are approaching the zero-temperature limit. In this article, we present the results of a set of experiments investigating the temperature dependence of the device, known as GaAs 7in the integer quantum Hall regime.

Although remarkable progress has been made [ 19 — 22 ], a complete theory of the quantum Hall effect is still missing.

**EDC/MOBILITY /EFFECT OF TEMPERATURE**

Nonetheless, there have been serious attempts to explain the physics behind many of the key features of the quantum Hall effect. Plausible explanations for the temperature dependence of the Hall and longitudinal resistances have been proposed for different temperature regimes.

In particular, at high temperatures typically several kelvin thermal activation across an energy gap generally explains the experimental data satisfactorily.

However, early results on GaAs 7 and other devices by Cage et al. The vector product assures that FL is perpendicular to vD and B.

Note that instead the usual word "electron" the neutral term carrier is used, because in principle an electrical current could also be carried by charged particles other than electrons, e.

Remember a simple but important picture given before! For the geometry above, the Lorentz force FL has only a component in y - direction and we can use a scalar equation for it.

### The Hall Effect

We know that the force is in y-direction, but we do no longer know the sign. It changes if either q, vD, or Bz changes direction and we have to be aware of that. In other words, there is a component of the velocity in y-direction and the surfaces perpendicular to the y-direction will become charged as soon as the current or the magnetic field is switched on.

The flow-lines of the carriers will look like this: The charging of the surfaces is unavoidable, because some of the carriers eventually will end up at the surface where they are "stuck". Notice that the sign of the charge for a given surface depends on the sign of the charge of the carriers.