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Bipolar redox-based resistive random-access memory cells are intensively studied for new storage class memory and beyond von Neumann computing applications. However, the considerable variability of the resistance values in ON and OFF state as well as of the SET voltage remains challenging. In this paper, we discuss the physical origin of the significant reduction in the switching variability of HfO2-based devices achieved by the insertion of a thin TiOx layer between the HfO2 layer and the oxygen exchange metal layer. Typically, HfO2 single layer cells exhibit an abrupt SET process, which is difficult to control. In contrast, self-compliance effects in the HfO2/TiOx bilayer devices lead to an increased stability of SET voltages and OFF-state resistances. The SET process is gradual and the RESET becomes abrupt for higher switching currents. Comparison of the experimental data with simulation results achieved from a physics-based compact model for the full description of the switching behavior of the single layer and bilayer devices clearly reveal three major effects. The TiOx layer affects the temperature distribution during switching (by modifying the heat dissipation), forms an additional series resistance and changes the current conduction mechanism in the OFF state of the bilayer device compared to the single layer device. [ABSTRACT FROM AUTHOR]