Abstract
A simple model of charge transfer by loss-less quantum-mechanical tunneling between two solids is proposed. The model is applicable to electron transport and contact electrification between e.g. a metal and a dielectric solid. Based on a one-dimensional effective-mass Hamiltonian, the tunneling transmission coefficient of electrons through a barrier from one solid to another solid is calculated analytically. The transport rate (current) of electrons is found using the Tsu-Esaki equation and accounting for different Fermi functions of the two solids. We show that the tunneling dynamics is very sensitive to the vacuum potential versus the two solids conduction-band edges and the thickness of the vacuum gap. The relevant time constants for tunneling and contact electrification, relevant for triboelectricity, can vary over several orders of magnitude when the vacuum gap changes by one order of magnitude, say, 1 Å to 10 Å. Coulomb repulsion between electrons on the left and right material surfaces is accounted for in the tunneling dynamics.
Highlights
Contact electrification has been known since ancient times but the underlying fundamental mechanism is still not known [1,2,3,4,5,6,7,8,9,10]
The role of electron transport versus ion transport for the charge transfer has been under dispute [3, 7, 11,12,13,14], and only recently did work in the group of Zhong Lin Wang [15] assert that electron transport is the dominant triboelectricity mechanism for metal-metal, metalsemiconductor, and metal-insulator systems in contact
We describe a simple loss-less electron transfer mechanism based on the Tsu-Esaki tunneling theory [39, 40] between dissimilar solids and show that the tunneling rate and contact electrification are strongly sensitive to the conduction-band edges of the two materials, the vacuum potential and the vacuum-gap thickness, and the Fermi levels
Summary
Contact electrification has been known since ancient times but the underlying fundamental mechanism is still not known [1,2,3,4,5,6,7,8,9,10]. While a classic macroscopic understanding of energy generation due to relative motion of systems of dielectric materials, through the concept of Maxwell’s electric displacement, exists to a certain extent, the physical mechanisms and properties that play a role for the electron transfer processes in nanosystems are much less explored. We describe a simple loss-less electron transfer mechanism based on the Tsu-Esaki tunneling theory [39, 40] between dissimilar solids and show that the tunneling rate and contact electrification are strongly sensitive to the conduction-band edges of the two materials, the vacuum potential and the vacuum-gap thickness, and the Fermi levels. Environment, or inside triboelectric materials, which are nonideal insulators, are neglected
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