  Resistance switching memory cells such as electrochemical metallization cells
and valence change mechanism cells have the potential to revolutionize
information processing and storage. However, the creation of deterministic
resistance switching devices is a challenging problem that is still open. At
present, the modeling of resistance switching cells is dominantly based on
deterministic models that fail to capture the cycle-to-cycle variability
intrinsic to these devices. Herewith we introduce a state probability
distribution function and associated integro-differential equation to describe
the switching process consisting of a set of stochastic jumps. Numerical and
analytical solutions of the equation have been found in two model cases. This
work expands the toolbox of models available for resistance switching cells and
related devices, and enables a rigorous description of intrinsic physical
behavior not available in other models.
