  This study presents a comprehensive examination of the development of
TiN/SiO$_\mathrm{x}$/Cu/SiO$_\mathrm{x}$/TiN memristive devices, engineered for
neuromorphic applications using a wedge-type deposition technique and Monte
Carlo simulations. Identifying critical parameters for the desired device
characteristics can be challenging with conventional trial-and-error
approaches, which often obscure the effects of varying layer compositions. By
employing an \textit{off-center} thermal evaporation method, we created a
thickness gradient of SiO$_\mathrm{x}$ and Cu on a 4-inch wafer, facilitating
detailed resistance map analysis through semiautomatic measurements. This
allows to investigate in detail the influence of layer composition and
thickness on single wafers, thus keeping every other process condition
constant. Combining experimental data with simulations provides a precise
understanding of the layer thickness distribution and its impact on device
performance. Optimizing the SiO$_\mathrm{x}$ layers to be below 12.5 nm,
coupled with a discontinuous Cu layer with a nominal thickness lower than 0.6
nm, exhibits analog switching properties with an
R$_\mathrm{on}$/R$_\mathrm{off}$ ratio of $>$100, suitable for neuromorphic
applications, whereas R $\times$ A analysis shows no clear signs of filamentary
switching. Our findings highlight the significant role of carefully choosing
the SiO$_\mathrm{x}$ and Cu thickness in determining the switching behavior and
provide insights that could lead to the more systematic development of
high-performance analog switching components for bio-inspired computing
systems.
