Skip to main page content
Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 2019 Aug 4;2019:6528689.
doi: 10.34133/2019/6528689. eCollection 2019.

Contact Electrification by Quantum-Mechanical Tunneling

Affiliations
Free PMC article

Contact Electrification by Quantum-Mechanical Tunneling

Morten Willatzen et al. Research (Wash D C). .
Free PMC article

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.

Conflict of interest statement

Authors declare no conflicts of interest with regard to the publishing of this paper.

Figures

Figure 1
Figure 1
Band diagram for tunneling of electrons through a vacuum gap in the absence of a Coulomb repulsion potential. (a) Left-to-right tunneling and (b) right-to-left tunneling.
Figure 2
Figure 2
Band diagram for tunneling of electrons through a vacuum gap in the presence of a Coulomb repulsion potential. (a) Left-to-right tunneling and (b) right-to-left tunneling.
Figure 3
Figure 3
Case 1: Time dependence of the electron number in the left material N1 as a function of time t for a set of vacuum gap thicknesses 2a. The vacuum potential V is fixed to 2 eV. Other parameters are given in the main text.
Figure 4
Figure 4
Case 2: Time dependence of the electron number in the left material N1 as a function of time t for a set of potential values V. The upper (lower) plot is with (without) the effect of Coulomb repulsion due to electron transfer and effective charging of the two materials. The distance between the materials 2a is fixed to 10 Å. Other parameters are given in the main text.
Figure 5
Figure 5
Case 3: Time dependence of the electron number in the left material N1 as a function of time t for a set of vacuum potential values V. The distance between the materials 2a is fixed to 20 Å. Other parameters are given in the main text.

Similar articles

See all similar articles

References

    1. Henniker J. Triboelectricity in polymers. Nature. 1962;196(474)
    1. Harper W. R. Contact and Frictional Dissipation. Oxford, UK: Clarendon Press; 1967.
    1. Shaw P. Experiments on tribo-electricity. I.—The tribo-electric series. Proceedings of the Royal Society A. 1917;94(656):p. 16. doi: 10.1098/rspa.1917.0046. - DOI
    1. Shaw P. E. The electrical charges from like solids. Nature. 1926;118(2975):659–660.
    1. Henry P. S. H. Survey of generation and dissipation of static electricity. British Journal of Applied Physics. 1953;4(supplement 2):p. S6.

LinkOut - more resources

Feedback