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

Tobias Gergs; Rouven Lamprecht; Sahitya Yarragolla; Ole Gronenberg; Luca Vialetto; Hermann Kohlstedt; Thomas Mussenbrock; Jan Trieschmann

cond-mat.mtrl-sciSep 24, 2026

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

Authors: Tobias Gergs, Rouven Lamprecht, Sahitya Yarragolla, Ole Gronenberg, Luca Vialetto, Hermann Kohlstedt, Thomas Mussenbrock, Jan Trieschmann

Organizations: Theoretical Electrical Engineering, Department of Electrical and Information Engineering, Kiel University, Kaiserstraße 2, 24143 Kiel, Germany · Chair of Applied Electrodynamics and Plasma Technology, Faculty of Electrical Engineering and Information Technology, Ruhr University Bochum, 44780 Bochum, Germany · Fraunhofer Institute for Electronic Nano Systems ENAS, 09126 Chemnitz, Germany · Nanoelectronics, Department of Electrical and Information Engineering, Kiel University, Kaiserstraße 2, 24143 Kiel, Germany · Kiel Nano, Surface and Interface Science KiNSIS, Kiel University, Christian-Albrechts-Platz 4, 24118 Kiel, Germany · Synthesis and Real Structure, Department of Materials Science, Kiel University, Kaiserstraße 2, 24143 Kiel, Germany · Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, Los Angeles, CA 90095, United States of America

Abstract

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.

Figures & tables

Figure 1: Schematic illustration of the deposition process. The target and substrate processes are depicted at mesoscopic and nanoscale resolution, highlighting their governing role. In addition to elastic momentum transfer collisions, dominant transport processes are highlighted, i.e., Ar electron impact ionization, O 2 electron impact ionization, and O 2 dissociative attachment.

Figure 2: Schematic illustration of wafer-scale device variability. Nominally identical devices distributed across the wafer can exhibit diverse electrical responses, represented by exemplary I – V characteristics. The TiN/SiO x /Cu/SiO x /TiN device architecture is shown at mesoscopic and nanoscale resolution, where red and yellow spheres indicates $V_{\mathrm{O}}$ and Cu, respectively.

Figure 3: Schematic illustration of the information flow underlying the forward and reverse engineering of defect-state formation in Cu-embedded SiO x memristive devices.

Figure 4: a) U-matrix predicted by SOM, superimposed with the I – V curves centroids of the respective $34\times 34$ clusters; b) Cluster aggregation based on I – V features; c) Per cluster: 200 randomly selected, experimental, and min-max normalized I – V curves (gray), superimposed with the results of the CIC device simulations (black) and with the centroids of all respective I – V curves (colored). An enlarged version of a) is included in the Supplementary Information for better readability. The color in b) and c) codes the key nanoelectrical characteristics.

Figure 5: Generalized manufacture yields $Y_{\mathrm{device}}$ as a function of the radial device site on the wafer $r_{\mathrm{wafer}}$ during the SiO x deposition. Power $P_{\mathrm{SiO}_{x}}$ and deposition time $t_{\mathrm{SiO}_{x}}$ are included in each top right corner.

Figure 6: a) In SiO x dissolved effective Cu density $n_{\mathrm{Cu}}$ as a function of the effective oxygen vacancy density $n_{\mathrm{V_{O}}}$ required by CIC device-level simulations. b) The expected value of the oxygen vacancy densities as a function of the radial device site on the wafer $r_{\mathrm{wafer}}$ and deposition time $t_{\mathrm{SiO}_{x}}$ . The power $P_{\mathrm{SiO}_{x}}$ is included in each top left corner.

Figure 7: Results of Ar/O 2 plasma simulations at 5 % O 2 , 0.5 Pa, 300 K, $V_{\mathrm{rf}}=250$ V, and $V_{\mathrm{SB}}=-110$ V. a) Chemical composition $x$ in SiO x , b) Ar + ion flux $\Gamma_{\mathrm{Ar^{+}}}$ , and c) average energy per Ar + ion $\bar{E}_{\mathrm{Ar^{+}}}$ at the substrate as a function of radial position.

Figure 8: Results of Ar ion-SiO x interaction simulations for $x\in[0,1]$ in SiO x and Ar + flux to Si flux ratio $\Gamma_{\mathrm{Ar^{+}}}/\Gamma_{\mathrm{Si}}\in[0,1]$ with mean ion energies of 35 eV. a) Intrinsic defect densities for DBs, NBOs, and V O . b) Ratio of Si-Si bond density to Si-O bond density $n_{\text{Si-Si}}/n_{\text{Si-O}}$ . c) Mass density $\rho$ .

HP	search range	selection
$n_{\mathrm{neurons}}$	[9,5776]	1156
$\eta$	[0.01,10]	0.01
$\sigma$	[1,100]	10
$t$	[ $10^{3}$ , $10^{5}$ ]	$10^{5}$
topology	{Rect,Hex}	Rect
distance	{Cos,Euclid}	Euclid

Table 1: Search ranges and selected values of the SOM HPs. The number of neurons, initial learning rate, initial spread of the Gaussian neighborhood function, and number of iterations are denoted by

n_{\mathrm{neurons}}

\eta

\sigma

, and

t

, respectively. Topology and distance metrics are abbreviated as rectangular (Rect), hexagonal (Hex), cosine (Cos), and Euclidean (Euclid).

HP	search range	selection
kernel function	{Gaus,Exp,Lin}	Exp
BW of $A_{\mathrm{device}}$	[ $10^{-5}$ , $10^{3}$ ]	0.26
BW of $F_{\mathrm{Ar}}/F_{\mathrm{O_{2}}}$	[ $10^{-5}$ , $10^{3}$ ]	5.11
BW of $P_{\mathrm{SiO}_{x}}$	[ $10^{-3}$ , $10^{1}$ ]	0.16
BW of $t_{\mathrm{SiO}_{x}}$	[ $10^{-5}$ , $10^{3}$ ]	0.10
BW of $r_{\mathrm{wafer}}$	[ $10^{-5}$ , $10^{3}$ ]	0.05

Table 2: Search range defined either by the respective interval or complete set, and finally selected HP for the KDE. The kernel functions are abbreviated as follows Gaussian (Gaus), Exponential (Exp), and Linear (Lin). Please note that the HP values have been normalized to a range of 0–1 using min/max normalization. Hence, all BWs are in arbitrary unit (a.u.).

Figure 9: Maximum change in device yield $(\Delta Y_{\mathrm{device}})_{\mathrm{max}}$ as a function of individual process parameters (marginalized accordingly). The markers’ centers and ranges indicate the mean and root mean square deviations across the seven clusters, respectively.

Figure 10: Schematic of the cylindrically symmetric simulation domain and the magnetic field structure of the Ar/O 2 sputter deposition. Magnets are indicated above the target.

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Abstract

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