Effect of the thickness of the TiO$_x$/TiO$_2$ layers on their memristor properties

The effect of the layer thickness of the TiO$_x$/TiO$_2$ heterostructure on its memristor properties is investigated. The dependence of the stoichiometry index of the prepared layers on their thickness is analyzed using Auger spectroscopy. The dependence of ratio $R_{\mathrm{off}}/R_{\mathrm{on}}$ of the resistances in the high- and low-resistance states of a memristor element on the thickness of its layers is nonmonotonic. The highest value of $R_{\mathrm{off}}/R_{\mathrm{on}}$ = 200 was attained for identical thickness of the TiO$_x$ and TiO$_2$ layers, equal to 30 nm.