Emission Redshift in DCM2-Doped Alq$_{3}$ Caused by Non-Linear Stark Shifts and F\"orster-Mediated Exciton Diffusion

Organic light-emitting diodes (OLEDs) devices in the archetype small molecule fluorescent guest-host system tris(8-hydroxyquinolinato) aluminum (Alq$_{3}$) doped with 4-(dicyanomethylene)-2-methyl-6-julolidyl-9-enyl-4H-pyran (DCM2) displays a redshift in light-emission frequency which is extremely sensitive to the dopant concentration. This effect can be used to tune the emission frequency in this particular class of OLEDs. In this work, a model is proposed to describe this effect using a combination of density functional theory (DFT) quantum-chemical calculations and stochastic simulations of exciton diffusion via a F\"orster mechanism. The results show that the permanent dipole moments of the Alq$_{3}$ molecules generate random electric fields that are large enough to cause a non-linear Stark shift in the band gap of neighboring DCM2 molecules. As a consequence of these non-linear shifts, a non-Gaussian probability distribution of highest-occupied molecular orbital to lowest-unoccupied molecular orbital (HOMO-LUMO) gaps for the DCM2 molecules in the Alq$_{3}$ matrix is observed, with long exponential tails to the low-energy side. Surprisingly, this probability distribution of DCM2 HOMO-LUMO gaps is virtually independent of DCM2 concentration into Alq$_{3}$ matrix, at least up to a fraction of 10%. This study shows that this distribution of gaps, combined with out-of-equilibrium exciton diffusion among DCM2 molecules, are sufficient to explain the experimentally observed emission redshift.