CALCULATION OF THE LINE-SHAPE OF ONE-PHONON REPLICAS IN POLAR SEMICONDUCTORS HAVING DIRECT FORBIDDEN BAND-GAPS

Analytical calculations of one-phonon replica emission and absorption of Is excitons in direct forbidden band-gap polar semiconductors are presented. It is assumed that the Frohlich exciton-lattice interaction is dominant for the optical-phonon modes involved in the scattering processes. Numerical calculations are carried out for the highest-frequency longitudinal-optical phonon modes of Gamma(5)' symmetry in TiO2 and SnO2. The scattering probability of the intraband processes is found to be much larger than that of the interband processes in both materials. The emission intensity of the one-phonon replica in SnO, can be approximated by I similar to epsilon(1/2)exp(-epsilon/k(B)T) with epsilon similar or equal to <(h)over bar omega> - (E(g) - E(B) - <(h)over bar Omega>) and the absorption coefficient by alpha(<(h)over bar omega>) similar to (<(h)over bar omega> + <(h)over bar Omega> + E(B) - E(G))(1/2) with <(h)over bar omega> less than or equal to 4387 meV, because the scattering probability amplitude can be taken to be constant. In TiO2, the emission intensity of the one-phonon replica is derived for temperatures up to 100 K.