Quantum transport in semiconductors

Abstract

A review is made of the quantum effects which are observed in the transport coefficients of semiconductors. Quantization of the free carriers in semiconductors is produced whenever an external potential acts on an otherwise uniform and perfect crystal. Typical examples are a magnetic field, an electric field or the physical boundaries of the sample. A magnetic field quantizes the electron and hole states into a ladder of equally spaced Landau levels. This gives rise to the Shubnikov–de Haas, magnetophonon and magneto-impurity effects, where the positions of the Landau levels resonate with the Fermi, phonon, or impurity energies present in the sample. A series of oscillations in the magneto-resistance of many different types of materials results. Electric fields applied to the surface of metal oxide semiconductor (MOS) devices result in a set of quantum levels for motion perpendicular to the surface. At low temperatures the charge carriers are bound to the surface and behave as if they were two-dimensional. This is shown to give rise to very dramatic oscillatory metal–insulator behaviour in high magnetic fields. Quantization is also shown to occur in very thin layers of semiconductors which act like a simple square well potential, the energy levels of which can be studied as a function of layer thickness. The carriers are confined within the layers, and also show two-dimensional behaviour.