The general field of how semiconductor properties are modified in the presence of a magnetic field is a very wide one. To do justice to the field, one would need to devote several chapters to this area as we have done for electric field effects. However, it can be argued that from a technology point of view the response of electrons in semiconductors to electric fields and optical fields is more important. Magnetic field effects are primarily used for material characterization, although there is growing interest in magnetic semiconductors for device applications. In view of this fact we will provide an overview of how electrons in semiconductors respond to magnetic fields in just one chapter. In addition to a magnetic field, many important characterization techniques are carried out in the presence of an electric field or an optical field. We will therefore also discuss magneto-transport and magneto-optic properties. The general category of problems we will examine are sketched in Fig. 11.1.

In Fig. 11.1 we broadly differentiate between the “free” or Bloch states in semiconductors and the electron-hole coupled states like excitons or bound states. The magnetic field greatly alters the nature of the electronic states which then manifests itself in magneto-optic or magneto-transport phenomenon. It is important to realize that in many cases the physical phenomenon can qualitatively alter, depending upon the strength of the magnetic field. We will address the problem of electrons in the presence of a magnetic field in two steps.