The main discharge products in Li-oxygen and Li-sulfur batteries, as evidenced by x-ray microscopy, are predominantly crystalline lithium peroxide, lithium superoxide, and lithium sulfide [1, 2]. These products have a high electric resistivity and, practically, the only conduction mechanism in these materials is electron and hole tunneling. In this presentation we develop a mathematical model to describe the tunneling current density in Li-oxygen and Li-sulfur batteries. The model is based on the WKB approximation, which is used to model the electron and hole tunneling probability through the insulating layer. The derivation of the tunneling current is relatively similar to the derivation by Simmons [3], which analyzed metal-insulator-metal systems (MIM) but, in our case, the mathematical derivation is carefully modified to describe metal-insulating-electrolyte systems (instead of MIM systems). More importantly, we derive closed-form equations for the tunneling current density that can be readily used in finite element simulations or in the mathematical modeling of the ohmic losses across the discharge layer in Li-oxygen and Li-sulfur batteries. As we expect the tunneling current density depends on the shape of the conduction and valence bands, applied voltage, and permittivity (because of the image charges created in the carbon). At normal applied voltages (below 0.5 V) the tunneling currents are negligibly small, however, they can become large enough to affect the discharge characteristics of the batteries for low discharge rates (e.g. below 0.1 C) if the barrier heights of the valance band in the case of holes and conduction band in the case of electrons are small. More details about the mathematical derivation, the approximations used in the derivation, the closed-form equations, and a comparison with current models in the literature will be presented at the meeting.

[1] N. Cañas, S. wolff, N. Wagner, K. Andreas Friedrich, In-situ X-ray diffraction studies of lithium-sulfur batteries, 2012.

[2] K.R. Ryan, L. Trahey, J.S. Okasinski, A.K. Burrell, B.J. Ingram, In situ synchrotron X-ray diffraction studies of lithium oxygen batteries, Journal of Materials Chemistry A, 1 (2013) 6915-6919.

[3] J.G. Simmons, Generalized Formula for the Electric Tunnel Effect between Similar Electrodes Separated by a Thin Insulating Film, Journal of Applied Physics, 34 (1963) 1793-1803.