Revisiting the Theory of Vibronic Transitions of Optical Ions in Solids

Abstract

In order to improve the performance of phosphors in lighting and display devices, one needs to understand the temperature dependence of the radiative and nonradiative processes of optical ions in solids. In this presentation, we have revisited the theory of radiative transitions from an excited state of a polyatomic system within the framework of the proper adiabatic theory. First the transition rate for spontaneous emission from an excited state to the ground state has been derived rigorously using the methods of molecular quantum electrodynamics. It is assumed that this transition is associated with a loss of energy through the creation of p phonons in the system. It will be shown for the first time in a rigorous manner that only limited number of vibrational modes for which the Huang-Rhys parameter, s, is nonzero will participate. These modes will be identified as the active modes. Other modes will be completely passive during the relaxation process. It is speculated that these active modes are the local vibrational modes, and can be identified from the vibronic spectra of rare earth ions, particularly at low temperature. Based on the present formulation of the problem, the band shape function, W(p,T), will be derived. This band shape function will be used to interpret available vibronic spectra for some optical ions at low temperature.