The General Non-Radiative Energy Transfer Master Equations for Crystalline Materials, the Exact Solution and Current Modeling

The general non-radiative energy transfer coupled equations are solved for the case of doped crystalline materials. In this work the exact solution is reported and the microscopic and macroscopic dopant, donor and acceptor, emissions are calculated. Our calculations are compared to major models such as the Forster-Dexter, Yokota-Tanimoto and Burshtein. It is shown that our modeling unifies and extends the predictions obtained by those authors. Our calculations consider the discreteness of the crystalline materials, and more than one interaction can be assumed to drive each of the processes that are taking place among pair of dopants.