Multi-phonon absorption

Multi-phonon absorption occurs when two or more phonons simultaneously interact to produce electric dipole moments with which the incident radiation may couple. These dipoles can absorb energy from the incident radiation, reaching a maximum coupling with the radiation when the frequency is equal to the vibrational mode of the dipole in the far-infrared. The different vibration modes are complex, comprising several different types of vibrations. There are two modes of vibrations of atoms in crystals, longitudinal and transverse. In the longitudinal mode the displacement of atoms from their positions of equilibrium coincides with the propagation direction of the wave, for transverse modes, atoms move perpendicular to the propagation of the wave.

Where there is only one atom per unit cell, the phonon dispersion curves are represented only by acoustic branches. If there is more than one atom per unit cell both acoustic and optical branches appear. The difference between acoustic and optical branches being the greater number of vibration modes available. In a diatomic cell the acoustic branch is formed when both atoms move together in-phase, the optical branch being formed by out-of-phase vibrations. Generally, for N atoms per unit cell there will be 3 acoustic branches (1 longitudinal and 2 transverse) and 3N-3 optical branches

(N-1 longitudinal and 2N-2 transverse).

Compound semiconductors have two transverse optical modes(TO), two transverse acoustic modes(TA), one longitudinal optical mode(LO), and a longitudinal acoustic mode(LA). The two transverse modes can exhibit similar dispersion characteristics on the energy / wave vector diagrams. As phonon emission is quantized, selectivity forbids certain combinations of phonon absorption modes, however the varied combination of all the modes available produces a highly complex absorption structure. In single compound (homopolar) covalently bonded semiconductors such as Silicon and Germanium where there is no bonding dipole, the incident radiation induces a dipole moment with a stronger couple, producing more phonons (usually <4).

Multi-phonon absorption also occurs in ionic crystals in a form similar to that in homopolar crystals. Its strength is usually greater than in the homopolar case but is substantially weaker than one-phonon reststrahl absorption.

Infrared material absorption theory

• Introduction
• Electronic absorption
• Lattice absorption
• Single phonon absorption
• Multi-phonon absorption
• Dielectric dispersion
• Thermal vibrations