In a crystalline material atoms vibrate about the rigid lattice sites and one of the most important scattering mechanisms for mobile carriers in semiconductors is due to these vibrations. In our discussions for the bandstructure we assumed that the background potential is periodic, and does not have any time dependence. In actual materials the background ions forming the crystal are not fixed rigidly but vibrate. The vibration increases as the temperature is increased. To understand the properties of electrons in a vibrating structure we use an approach shown schematically in Fig. 6.1. Scattering will occur due to the potential disturbances by the lattice vibration. Before we can answer the question regarding how lattice vibrations cause scattering, we must understand some basic properties of these vibrations. Once we understand the nature of the lattice vibrations we can begin to examine how the potential fluctuations arising from these vibrations cause scattering.

LATTICE VIBRATIONS

In Chapter 1 we have discussed how atoms are arranged in a crystalline material. The reason a particular crystal structure is chosen by a material has to do with the minimum energy of the system. As atoms are brought together to form a crystal, there is an attractive potential that tends to bring the atoms closer and a repulsive potential which tends to keep them apart. The attractive interaction is due to a variety of different causes including Van der Waals forces (resulting from the dipole moment created when an atoms' electron cloud is disturbed by the presence of another atom), ionic bonding where electrons are transferred from one atom to another and covalent bonding where electrons are shared between atoms.