Memristive State Equation for Bipolar Resistive Switching Devices Based on a Dynamic Balance Model and Its Equivalent Circuit Representation

A memory state equation consistent with a number of experimental observations is presented and discussed within the framework of Chua's memristive systems theory. The proposed equation describes the evolution of the memory state corresponding to a bipolar resistive switching device subject to a variety of electrical stimuli. It is shown that the memory equation agrees with: i) the characteristic switching time associated with the ion/vacancy hopping mechanism within the dielectric film, ii) the SET/RESET voltage logarithmic dependence on the voltage sweep ramp rate, iii) the hysteretic behavior of the remnant conductance for cycled input signals, iv) the generation of self-similar conductance loops for arbitrary initial conditions, and v) the collapse of the resistive window with the increment of the input signal frequency. It is also shown that the proposed equation admits a circuital representation suitable for circuit simulations.