Continuum time-delayed electron hopping and entropy-ruled Einstein relation for molecular solids.

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This work mainly elucidates ‘dispersion weighted charge transfer delay’ at each hopping step, which can be modified by electric field assisted site-energy difference and molecular vibrations. Here, the structural dynamics - charge transport correlation has been analyzed (for different external electric field values) in three thiazolothiazole based derivatives (TZTZ1, TZTZ2 and TZTZ3) with the aid of tight-binding Hamiltonian method and kinetic Monte-Carlo simulations. The field response degeneracy strength and its consequences on polaron transport have been studied by our proposed differential entropy-dependent carrier density and diffusion coefficient equations, with dispersion correction (i.e., time delay effect by dispersion). This theoretical study convincingly concludes four important corollaries: 1) The diode ideality factor for the three molecular solids considered (e.g., TZTZ1, TZTZ2 and TZTZ3) is close to unity, which suggests Langevin transport (trap-free diffusion) mechanism in them; and hence these molecular solids are suitable for charge transporting devices like, photovoltaics and field effect transistors. 2) For large site energy fluctuations, a significant loss in charge transfer rate at every hopping site leads to incoherent transport. 3) The traversing chemical potential along the extended molecular units decides whether the Einstein relation is valid or take the deviation from the original value of kT/q , which strongly depends on degenerate weightage. 4) By our continuum time delayed CT (or dispersion corrected CT) model, we can easily switch over the dynamic to static disordered transport or vice-versa or intermediate transport in molecular semiconductors with the help of two descriptors, bias voltage (or electric field) and molecular vibrational frequency.

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