# Introduction to the Physics of Semiconductor Devices

## Statistics of free charge carriers

- The concentration of free electrons and holes in a semiconductor can be
be calculated from the density of electronic states, DOS, (number of states
per unit volume and unit energy interval) and their occupation probability.

Electronic states in k-space for electrons in a two-dimensional infinite quantum
well. The points are the allowed k-vectors and the grey square indicates the volume
of one state in k-space. The differential change in the number of states
within the sphere with increasing radius is the density of states, DOS.

DOS in one, two and three dimensional infinite quantum wells.

- Electrons and holes are Fermions: the occupation probability of the electronic
states in the band extrema is therefore given by Fermi statistics.

Fermi distribution function.

- The concentration of free charge carriers in the bands can then be
calculated using the Fermi integral. If the Fermi level is more than
4kT distant from the band edges, Boltzmann statistics can be applied.