  The morphology and dimension of the conductive filament formed in a
memristive device are strongly influenced by the thickness of its switching
medium layer. Aggressive scaling of this active layer thickness is critical
towards reducing the operating current, voltage and energy consumption in
filamentary type memristors. Previously, the thickness of this filament layer
has been limited to above a few nanometers due to processing constraints,
making it challenging to further suppress the on-state current and the
switching voltage. Here, we study the formation of conductive filaments in a
material medium with sub-nanometer thickness, formed through the oxidation of
atomically-thin two-dimensional boron nitride. The resulting memristive device
exhibits sub-nanometer filamentary switching with sub-pA operation current and
femtojoule per bit energy consumption. Furthermore, by confining the filament
to the atomic scale, we observe current switching characteristics that are
distinct from that in thicker medium due to the profoundly different atomic
kinetics. The filament morphology in such an aggressively scaled memristive
device is also theoretically explored. These ultra-low energy devices are
promising for realizing femtojoule and sub-femtojoule electronic computation,
which can be attractive for applications in a wide range of electronics systems
that desire ultra-low power operation.
