Simulation of Ionic Conductivity of Lithium Borate Thin Films Using a Network of Electrical Resistors

Previous experiments show that the ionic conductivity of lithium borate thin films is strongly dependent on the thickness of the layers. A network of electrical resistors has been used as a model to describe the ionic conductivity of lithium borate films. This network consists of a large number of electrical resistors that have two different values. According to the percolation theory, the resistant network model describes the ion-conducting pathways inside the network of lithium borate glass. A MATLAB code has been written to calculate the equivalent network resistance, according to Kirchhoff's laws. The number of resistors in each direction of the network is proportional to the dimensions of the sample. The distribution of resistors in the network is random, but the relative probability of distribution for each of the two types of resistors is one of the parameters of this model. Experimental results show that the specific conductivity in thin films depends on the thickness of the layers, while it is constant in thicker layers. By examining various effective parameters in this model and according to the percolation theory, the non-trivial conductivity increase, observed in very thin layers, is simulated. The simulation performed by this model is satisfactory for both thin and thicker layers.