  Neuromorphic computing architectures enable the dense co-location of memory
and processing elements within a single circuit. This co-location removes the
communication bottleneck of transferring data between separate memory and
computing units as in standard von Neuman architectures for data-critical
applications including machine learning. The essential building blocks of
neuromorphic systems are non-volatile synaptic elements such as memristors. Key
memristor properties include a suitable non-volatile resistance range,
continuous linear resistance modulation and symmetric switching. In this work,
we demonstrate voltage-controlled, symmetric and analog potentiation and
depression of a ferroelectric Hf$_{57}$Zr$_{43}$O$_{2}$ (HZO) field effect
transistor (FeFET) with good linearity. Our FeFET operates with a low writing
energy (fJ) and fast programming time (40 ns). Retention measurements have been
done over 4-bits depth with low noise (1%) in the tungsten oxide (WO$_{x}$)
read out channel. By adjusting the channel thickness from 15nm to 8nm, the
on/off ratio of the FeFET can be engineered from 1% to 200% with an
on-resistance ideally >100 kOhm, depending on the channel geometry. The device
concept is using earth-abundant materials, and is compatible with a back end of
line (BEOL) integration into complementary metal-oxidesemiconductor (CMOS)
processes. It has therefore a great potential for the fabrication of high
density, large-scale integrated arrays of artificial analog synapses.
