Numerical simulation of the current–voltage characteristic of a bipolar hafnium-oxide memristor

In this paper, we develop a finite element model that allows calculating the current-voltage characteristic of a bipolar memristor based on Pt/HfO$_2$/TiN hafnium oxide, which reflects both the high- and low-resistance states of the memristor. Maxwell’s equations for the stationary case served as the mathematical basis of the model. The model allows evaluating the relation between the properties of materials included in the structure of the memristor and its operating current.