Report on an Analytical Theory of the Filamentary RRAM Parameter Drift, Statistical Variations and Reliability Including Possible Quantum Effects
Our survey of the published data on statistical variations in RRAM structures leads to the conclusion that there exist two groups of observations representing correspondingly temporal (time and/or external action rate dependent) and non-temporal (statistical ensemble related) observations. We argue that the first group observations can be readily explained by the concept of two-state fluctuators (double well potentials). For the second group we provide a phenomenological description substantiating the general observation of the prevailing log-normal statistics. In addition, we provide simple physical analysis of the Quantum Point Contact model showing that its effect on applications is reducible to the tunneling current in a disordered system, and, in addition the presence of quantum constriction leads to significant thermodynamic consequences that have not been analyzed yet.