  The resistance state of filamentary memristors can be tuned by relocating
only a few atoms at interatomic distances in the active region of a conducting
filament. Thereby the technology holds promise not only in its ultimate
downscaling potential and energy efficiency but also in unprecedented speed.
Yet, the breakthrough in high-frequency applications still requires the
clarification of the dominant mechanisms and inherent limitations of ultra-fast
resistive switching. Here we investigate bipolar, multilevel resistive
switchings in tantalum pentoxide based memristors with picosecond time
resolution. We experimentally demonstrate cyclic resistive switching operation
due to 20 ps long voltage pulses of alternating polarity. Through the analysis
of the real-time response of the memristor we find that the set switching can
take place at the picosecond time-scale where it is only compromised by the
bandwidth limitations of the experimental setup. In contrast, the completion of
the reset transitions significantly exceeds the duration of the ultra-short
voltage bias, demonstrating the dominant role of thermal diffusion and
underlining the importance of dedicated thermal engineering for future
high-frequency memristor circuit applications.
