Empirical Characterization of ReRAM Devices Using Memory Maps and a Dynamic Route Map

Memristors were proposed in the early 1970s by Leon Chua as a new electrical element linking charge to flux. Since that first introduction, these devices have positioned themselves to be considered as possible fundamental ones for the generations of electronic devices to come. In this paper, we propose a new way to investigate the effects of the electrical variables on the memristance of a device, and we successfully apply this technique to model the behavior of a TiN/Ti/HfO2/W ReRAM structure. To do so, we initially apply the Dynamic Route Map technique in the general case to obtain an approximation to the differential equation that determines the behaviour of the device. This is performed by choosing a variable of interest and observing the evolution of its own temporal derivative versus both its value and the applied voltage. Then, according to this technique, it is possible to obtain an approach to the governing equations with no need to make any assumption about the underlying physical mechanisms, by fitting a function to this. We have used a polynomial function, which allows accurate reproduction of the observed electrical behavior of the measured devices, by integrating the resulting differential equation system.