Generalized Charge Energy Rate for Organic Solids and Biomolecular Aggregates Through Drift-Diffusion and Hopping Transport Equations: A Unified Theory

TL;DR

This paper develops a unified theoretical framework for charge and energy transport in complex organic and biomolecular systems, incorporating disorder, field effects, and nonlinear dynamics, supported by analytical and numerical results.

Contribution

It introduces a generalized drift-diffusion model connecting band and hopping transport, and proposes a donor-acceptor reaction state model for charge transfer analysis.

Findings

Transport depends on both drift and diffusion in disordered systems.

Charge and energy transport can be tuned via chemical potential.

Non-equilibrium drift-diffusion occurs in 2D and 3D devices.

Abstract

We derive generalized charge energy rate equations for organic solids and biomolecular aggregates, even when these are dynamically disordered. These equations suggest that the transport in such cases rely on both drift and diffusion phenomena. The presence of disorder and field effects makes the equations nonlinear and together with cooperativity, these enhance the charge and energy transport. The generalized drift diffusion expression connects the adiabatic band and nonadiabatic hopping transport mechanisms, well suited for any complex organic semiconductors or assemblies of bio molecular systems. Here we have proposed donor-acceptor (DA) reaction state model, which examines the probability of charge transfer and the rate between two distinct transition state identities. From our analytical equations, we suggest that charge and energy transport property in DA states can be tuned by only a single parameter, i.e., the chemical potential. Importantly, we find the non-equilibrium assisted drift-diffusion transport at non- steady state regime in 2D and 3D semiconducting devices. The numerical results clearly support our unified analytical equations, which goes beyond Einstein's diffusion law even in quasi- equilibrium cases.