Application of Space-Charge Model in Describing the Ionic Conductivity of Lithium-Borate Thin Films

Ionic conduction of lithium-borate thin films shows a nontrivial increase when the layer thickness is less than ۱۲۰ nanometers. In this research, the space-charge model is used to describe high conductivity in lithium-borate thin films. Regarding the amorphous structure of these layers, similar to the crystalline structure, we assume the Li+ ions and their counterparts as defects and the regions adjacent to electrode-electrolyte interfaces as space-charge regions. The electrochemical potential of defects arising from these regions leads to the well-known Poisson-Boltzmann equation. To solve this equation numerically, the fourth-order Rung-Kutta integration, together with a shooting method for two-point boundary value problems, is used. Since these two boundary conditions are at two different points, the shooting method is used to solve this problem. Finally, the calculated ionic conductivity is compared to the experimental one. A free parameter that is related to the size of the space-charge region is used to fit space-charge model data to the experimental results. Although the space charge model is used in this research to describe the ionic conductivity of lithium borate, it is expected that this model can be used for other ionic conductors by changing the model parameters.

Application of Space-Charge Model in Describing the Ionic Conductivity of Lithium-Borate Thin Films Keywords:

Ionic conduction , Lithium-borate , Thin film , Space-charge