  We present a phenomenological theory of filamentary resistive random access
memory (RRAM) describing the commonly observed features of their
current-voltage characteristics. Our approach follows the approach of
thermodynamic theory developed earlier for chalcogenide memory and threshold
switches and largely independent of their microscopic details. It explains,
without adjustable parameters, such features as the domains of filament
formation and switching, voltage independent current in SET and current
independent voltage in RESET regimes, the relation between the set and reset
voltages, filament resistance independent of its length, etc. Furthermore, it
expresses the observed features through the material and circuitry parameters
thus paving a way to device improvements.
