  Memristors have demonstrated immense potential as building blocks in future
adaptive neuromorphic architectures. Recently, there has been focus on
emulating specific synaptic functions of the mammalian nervous system by either
tailoring the functional oxides or engineering the external programming
hardware. However, high device-to-device variability in memristors induced by
the electroforming process and complicated programming hardware are among the
key challenges that hinder achieving biomimetic neuromorphic networks. Here, an
electroforming-free and complementary metal oxide semiconductor
(CMOS)-compatible memristor based on oxygen-deficient SrTiO$_{3-x}$ (STO$_x$)
is reported to imitate synaptic learning rules. Through spectroscopic and
cross-sectional transmission electron microscopic analyses, electroforming-free
characteristics are attributed to the bandgap reduction of STO$_x$ by the
formation of oxygen vacancies. The potential of such memristors to behave as
artificial synapses is demonstrated by successfully implementing high order
time- and rate-dependent synaptic learning rules. Also, a simple hybrid
CMOS-memristor approach is presented to implement a variety of synaptic
learning rules. Results are benchmarked against biological measurements form
hippocampal and visual cortices with good agreement. This demonstration is a
step towards the realization of large scale adaptive neuromorphic computation
and networks.
