2D Axisymmetric Continuum Model for RESET Kinetic Variations in Electrochemical Metallization Cells

Electrochemical metallization (ECM) cells operate on the principle of growing and dissolving a conducting filament (CF) in an insulator separating two metal electrodes. Typically, the thickness of the insulator is a few nanometres. The growth (SET) of the CF occurs by applying a positive voltage to the electrochemical active electrode (AE), which leads to oxidation of the electrode and migration by ion hopping within the oxide – also called switching layer (SL) – of the resulting metal ions. Reduction occurs preferentially on a critical nucleus at the inert electrode (IE), leading to growth of the CF. Reversal of the voltage leads to reversal of the above processes and dissolution (RESET) of the CF. A previously published 2D axisymmetric model ^[1] contains Butler-Volmer equations to describe ionic currents, Simmons tunnel equation for electronic tunnel current between the conducting filament (CF) and the active electrode, Fuchs-Sondheimer model for resistivity of the CF, mechanical stress, to limit the lateral CF growth and a moving mesh approach for growth of the CF. This model was extended with tunnel junction heating, an additional energy dissipation when electronic tunnel currents occur, the dissolution of the anode and the previously current limiting resistor was exchanged by an ideal current limitation. The model was then modified to simulate not only SET but also RESET kinetics. In this work the dissolution of the AE and the combined influence of heating, mechanical stress variations, dissolution of the active electrode, the length of the SET voltage pulse (programming time) and the maximum SET current on the RESET time was investigated. It is shown, that mechanical stress – which crucially affects the lateral size of the CF – and the dissolution of the active electrode have the largest impact on the RESET time and that only tunnel junction heating allows significant heating of the CF even at low currents in the low microampere range. The integration of this findings into compact models should lead to better descriptions of measurement results and thus improving and boosting the design of memristive devices and neuromorphic circuits.<br/><br/><b>References:</b><br/>[1] M. Buttberg, I. Valov, S. Menzel, <i>Neuromorphic Computing and Engineering</i> 2023, <i>3</i>, 024010.<br/><b>Acknowledgements</b><br/>This work was supported in part by the Deutsche Forschungsgemeinschaft under project SFB 917 and in part by the Federal Ministry of Education and Research (BMBF Germany) in the project NEUROTEC II under Grant 16ME0398K and Grant 16ME0399.