Filamentary extension of the mem-con theory of memristance and its application to titanium dioxide sol-gel memristors

Titanium dioxide sol-gel memristors have two different modes of operation, believed to be dependent on whether there is bulk memristance, i.e. memristance throughout the whole volume, or a filamentary memristance, i.e. memristance caused by the connection of conducting filaments. The mem-con theory of memristance is based on the drift of oxygen vacancies rather than that of conducting electrons and has been previously used to describe bulk memristance in several devices. Here, the mem-con theory is extended to model memristance caused by small filaments of low resistance titanium dioxide and it compares favorably to experimental results for filamentary memristance in sol-gel devices.