The increasing demand for high-density data storage leads to an increasing interest in novel memory concepts with high scalability and the opportunity of storing multiple bits in one cell. A promising candidate is the redox-based resistive switch repositing the information in form of different resistance states. For reliable programming, the underlying physical parameters need to be understood. We reveal that the programmable resistance states are linked to internal series resistances and the fundamental nonlinear switching kinetics. The switching kinetics of Ta$_{2}$O$_{5}$-based cells was investigated in a wide range over 15 orders of magnitude from 250 ps to 10$^{5}$ s. We found strong evidence for a switching speed of 10 ps which is consistent with analog electronic circuit simulations. On all time scales, multi-bit data storage capabilities were demonstrated. The elucidated link between fundamental material properties and multi-bit data storage paves the way for designing resistive switches for memory and neuromorphic applications.
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