Analytic and SPICE modeling of stochastic ReRAM circuits

The modeling of conventional (deterministic) electronic circuits – ones consisting of transistors, resistors, capacitors, inductors, and other traditional electronic components – is a well established subject. The cycle-to-cycle variability of emerging electronic devices, in particular, certain ReRAM cells, has lead to the concept of stochastic circuits. Unfortunately, even in relatively simple cases, the direct transient analysis of stochastic circuits is computationally demanding and potentially impractical, if possible at all. An important development in this area has been the application of a master equation that is easily implemented in SPICE. In this conference paper, we briefly review the master equation approach and present an improved implementation of this approach in SPICE. Moreover, we find an attractor state in a periodically driven memristive circuit – a stochastic counterpart of deterministic memristor attractors.