Temperature Dependence of Nonradiative Transitions of an Excited Optical Ion in Solids

Abstract

We have investigated the temperature dependence of nonradiative transitions of an optical ion in a solid from the excited electronic state to the ground electronic state within the framework of proper adiabatic approximation for a single configuration coordinate, q . The Hamiltonian based on the nonadiabaticity operator has been used to calculate the temperature dependence of nonradiative transition rates. This perturbing Hamiltonian, H na = − ℏ 2 ∂ ∂ q e ∂ ∂ q v − ℏ 2 2 ∂ 2 ∂ q 2 e I v consists of two terms. In the literature, the first term is usually used to explain nonradiative transitions of an optical ion in a solid. We have shown that the first term alone leads to a zero of the nonradiative transition rates when s = z for low temperature, where s represents the Huang-Rhys parameter and z relates to the energy gap between the excited state and ground state in terms of vibrational quantum of energy, ℏ ω . This zero cannot be removed unless the second term is included for calculating the transition rates. We have defined three auxiliary functions, U 1 , U 2 and U 3 to describe the temperature dependence of the nonradiative transition rates in a physically meaningful way.