Model in equations and electrical conductivity:

Electrical conductivity is a variable that is highly dependent on the nature of the material. It is therefore common to classify materials according to their electrical conductivity. Semiconductors are solid bodies that exhibit measurable electrical conductivity only at elevated temperatures. This temperature dependence is due to the band structure of the electronic energy levels, comprising a valence band, a conduction band and an intermediate region which, in the case of pure undoped semiconductors, cannot be occupied by electrons. In the initial state, the valence band is the band most heavily occupied by electrons and the conduction band is the band immediately above it that is unoccupied.

where τ is the collision relaxation time. For t ≫ τ, we have

FondamentalEffect of temperature

If T increases, collisions are more frequent, τ decreases and σ decreases. As a result, the resistivity ρ increases with T.

As the temperature rises, more and more electrons are thermally excited from the valence band to the conduction band, creating "holes" in the valence band. Under the effect of a magnetic field, holes behave like positively charged particles and, like electrons, contribute to current density.

Exemple

To determine the conductivity of pure, undoped germanium, the experiment involves sending a constant current through the crystal and measuring the voltage drop as a function of temperature. To a first approximation, the measurement data can be considered as an exponential function in which the gap energy appears as a parameter.