Unified Entropy-Ruled Einstein’s Relation for Bulk and Low-Dimensional Molecular-Material Systems: A Hopping-to-Band Shift Paradigm

What is it about?

This work provides a new version of entropy-ruled diffusion-mobility relation for quantum systems/devices, which is the alternative form of Einstein's D/μ ratio. This proposed method is appropriate for both hopping and band transport systems at wide thermodynamical conditions. Here, the time-delayed hopping factor is accompanied in our entropy-ruled D/μ relation, which gives well-approximated results for localization transport in the molecular systems. Our proposed method was verified by some molecular as well as by graphene systems.

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Why is it important?

The conventional Einstein’s classical relation fails to explain the quantum features of organic semiconductors, including nonequilibrium and degenerate transport systems; also it does not depend on the dimension of the system (1, 2 and 3D), i.e., same expression for the all systems D/μ = kT/q. To overcome this issue, a unified version of entropy-ruled D/μ relation proposed by me (J. Phys. Chem. Lett., 2024, 15, 2519-2528) to study both the hopping and band transport systems. This relation has dimension-dependent, importantly here the dimension-dependent-density of states (DOS) play a crucial role for this relation. This method works well from the equilibrium to non-equilibrium cases in both the quantum and classical systems with wide temperature ranges for all dimensions. Here, the key descriptor for the fundamental transport is the variation of effective entropy with respect to the chemical potential, or vice-versa. The entropy is quantified using nonequilibrium fluctuation theorem-based entropy production rule. Importantly, the field-response transport property (FET characteristic study) of the given systems can be studied by our new entropy-ruled method. Here, we made quantum correction in the Shockley diode current density equation (known as "Navamani-Shockley diode equation"). Specifically, in this work, I introduce the imperfect Fermi-Dirac (IFD) distribution function to study the electron distribution in correlated electron systems.

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