Lattice vibrations in semiconudctors

S. S. MITRA; N: E. MASSA

Handbook on semiconductors

North Holland Publishing Co.

Lugar: New York; Año: 1982; p. 81 - 194

This chapter deals with lattice vibrations in semiconducting crystals and their effects on mechanical, optical, and thermal properties of these materials. We have purposely not included any discussion on effects of lattice vibrations on transport properties, both thermal and electrical, and the fundamental edge absorption. These are subjects of fuller discussions elsewhere in the volume.. We start with a crystal regarded as a mechanical system of nM particles, where n is the number of particles per unit cell and N is the number of unit cells. Such a crustal will have 3nM degrees of freedom, of which 3nN-3 are linearly independent normal modes and three are pure translations. They very large number (about 1014) of modes of a macroscopic piece of a crustal necessitates the description of the frequency spectrum in terms of a frequency distribution function. The frequency spectrum on the nuclear motions in the solid can be determined by constructing the classical equations of motion of the lattice points and obtaining the solutions of the normal modes as plane waves. The vibration frequencies occur as the 3n roots of the secular equation, involving the wave vector, which may take N values. The energy of each of the 3Mn modes is quantized and the term phonon is used to describe a quantized lattice vibration. Throughout the rest of this chapter we have considered lattice vibrations as phonons or quantized excitations rather than waves of vibrating ions, thus in their interactions with neutrons, photons, electrons or other phonons the requirements of the conservation of energy and momentum are tacitly implied.This chapter deals mainly with experimental phenomena listed in the table of contents. The role of phonon on the understanding of these phenomena is discussed in a relatively qualitative manner. Whenever possible. Examples are given from well known families of semiconducting material, viz., the group IV, II-V, II-VI, and IV-VI compounds. With few exceptions, the semiconductors have essentially been treated as insulators, and the effect of charge carriers on a particular property has been introduced only if relevant.