The dynamic disorder and electric field effects on charge transport in triphenylamine-benzimidazole based molecular solids have been investigated using electronic structure calculations, molecular dynamics and Monte-Carlo simulations. During the charge propagation, the energy loss of the carrier in each hopping step is monitored by Monte-Carlo simulation. We derive a survival probability correlated momentum-energy distribution for drift-diffusion analysis and we demonstrate the dispersion initiated charge trapping mechanism which is indeed ideal for light emission efficiency via recombination. In the present model, the proposed carrier drift energy-current density expression and Shockley diode current density equation are used to study the current density-voltage characteristics; accordingly the ideality factor (∼1.8-2.0) dictates the deviation of Einstein's classical diffusion-mobility relation (where the ideality factor is unity). The dual mechanism of electric field assisted site energy gap on coherent-like transport and the electric field stretched dispersion on recombination are observed in tris(3'-(1-phenyl-1H-benzimidazole-2-yl)biphenyl-4-yl)amine (TBBI) and tris(4'-(1-phenyl-1H-benzimidazole-2-yl)biphenyl-4-yl)amine (TIBN) molecular systems, which can be used as host materials in organic light emitting diodes (OLEDs). We find the transport going from coherent to incoherent, due to the conversion mechanism of dynamic to static disorder. This can also be a controlled by applied electric field. By adjusting the applied electric field, film thickness and changing the π-stacked molecular aggregation via substitutions, one can fix the dispersive parameter and accordingly calculate the charge transport properties to design efficient host-materials for photovoltaic and light emitting diode devices.
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