Challenges for the Accurate Simulation of Anisotropic Charge Mobilities through Organic Molecular Crystals: The β Phase of mer-Tris(8-hydroxyquinolinato)aluminum(III) (Alq3) Crystal

Abstract

Quantitative agreement has been found between observed and calculated charge mobilities through organic conductors, despite the use of many assumptions in the calculations, including: the relative strength of the intermolecular electronic coupling to the reorganization energy driving charge localization, the treatment of site variability in the material, the involvement of tunneling processes during charge hopping between sites, the use of weak-coupling-based perturbation theory to determine hopping rates, the residence times for charges on sites, the effect of the large field strengths used in experimental studies, the general appropriateness of simple one-dimensional diffusion modeling approaches, and the involvement of molecular excited states of the ions. We investigate the impact of these assumptions, concluding that all may be very significant. In some cases, methodological options are considered, and optimum procedures are determined, showing that (i) the use of Koopmans' theorem to estimate intermolecular couplings in solids is problematic and (ii) the correct expression for the residence lifetime of a charge on a crystal site. These conclusions are drawn from simulations of anisotropic charge mobilities through the β phase of mer-tris(8-hydroxyquinolinato)aluminum(III) (Alq3) crystal, a material commonly used in OLED applications. Calculations are compared that determine mobilities at finite applied field from drift velocities through either semianalytical solutions of the master equation or else kinetic Monte Carlo simulations, as well as those that determine mobilities from multidimensional diffusion coefficients at zero field by Monte Carlo and those that analytically solve simplified one-dimensional diffusion models. For crystalline Alq3 itself, the calculations predict electron mobilities that are 4–6 orders of magnitude larger than those predicted by similar methods for amorphous Alq3, in agreement with experimental findings. This work vindicates recent theories describing the poor mobilities of the amorphous material, forming a complete basic picture for Alq3 conductivity.