From Processing to Functionality: Engineering Accessible Material States in Cu-Embedded SiO$_x$ Memristive Devices

Resistive switching in oxide-based devices is widely governed by stochastic defect processes, yet a predictive link between fabrication conditions and functional behavior remains elusive. Here, we establish a multiscale framework connecting plasma-defined deposition conditions to macroscopic device functionality in sputtered SiO$_x$/Cu/SiO$_x$-based systems. By combining large-scale statistical analysis of more than 50,000 experimentally characterized devices with physics-based plasma and atomistic simulations, we show that device behavior does not emerge from deterministic process-to-performance mappings, but from a probabilistic cascade spanning defect formation, defect-state evolution, and functional-regime emergence. Data-driven clustering reveals a continuous functional state space composed of operational switching types, while inverse modeling identifies the reconstructed oxygen-vacancy density as an effective latent descriptor capturing the combined influence of structural disorder and defect topology. This latent descriptor is strongly coupled to both Cu redistribution and electrical response, linking otherwise hidden material properties to observable device characteristics. Furthermore, macroscopic switching behavior is argued to arise from ensemble integration across spatially heterogeneous subdomains, providing a physical explanation for the pronounced variability of large-area devices. These findings shift the perspective from deterministic defect engineering toward probabilistic defect-state design and establish a physically grounded framework for understanding and controlling functional variability in such oxide-based systems, such as memristive or resistive-switching devices.