The effect of oxygen ions and vacancies generation and recombination processes on heat and mass transfer and electrophysical properties of metal oxide memristor

About the authors:

Baurzhan H. Gabdulin, Postgraduate Student, Department of Applied and Technical Physics, School of Natural Sciences, University of Tyumen, Tyumen, Russia; Junior Researcher, Memristive Materials Laboratory, Center for Nature-Inspired Engineering, University of Tyumen, Tyumen, Russia; baurzhan.gabdulin@gmail.com, https://orcid.org/0009-0000-2586-7469

Alexander N. Busygin, Cand. Sci. (Phys.-Math.), Senior Scientific Researcher, Nanomaterials and Nanoelectronics Laboratory, Center for Nature-Inspired Engineering, University of Tyumen, Tyumen, Russia; a.n.busygin@utmn.ru, https://orcid.org/0000-0002-3439-8067

Sergey Yu. Udovichenko, Dr. Sci. (Phys.-Math.), Professor, Department of Applied and Tech­nical Physics, School of Natural Sciences, University of Tyumen, Tyumen, Russia; Scientific Director of the Memristive Materials Laboratory, Center for Nature-Inspired Engineering, University of Tyumen, Tyumen, Russia; udotgu@mail.ru, https://orcid.org/0000-0003-3583-7081

Abstract:

A thermophysical model of metal oxide memristor based on the stationary continuity equation of electron current density is developed. The model considers the processes of generation and recombination of oxygen vacancies and ions. The oxygen ion-vacancy pairs recombination rate was introduced into the model, and a more precise expression was used for the rate of their generation. A non-stationary continuity equation of oxygen ion concentration was introduced, which is necessary

for determining the recombination rate of pairs. Changes were made in the formulas for the diffusion coefficient and vacancy drift rate related to the temperature and electric field of the memristor.

The processes of ion generation and recombination affect the redistribution of vacancy and oxygen ion concentrations, which leads, in addition to an increase in the electron current density, to a change in the electric field and, consequently, in the value of the Joule heat source. It is shown that the current-voltage curve at switching of the memristor into a highly conductive state, obtained by taking into account all the above processes, has the smallest mean-square deviation from the experimental curve.

As a result of numerical simulation on the basis of the developed thermophysical model of the memristor, it is shown that when the processes of generation and recombination of oxygen vacancies and ions are taken into consideration, the temperature profile along the film thickness and in time changes significantly when modeling the current-voltage characteristic of the memristor.

The presented model is in demand for numerical simulation of signal processing in large memristor arrays used in neuromorphic devices.

References:

Bao, K., Meng, J., Jonathan, D., Poplawsky, J. D., & Skowronski M. (2023). Electrical conductivity of TaOx as function of composition and temperature. Journal of Non-Crystalline Solids, 617(1), art. 122495. https://doi.org/10.1016/j.jnoncrysol.2023.122495

Basnet, P., Pahinkar, D. G., West M. P., Perini C. J., Graham S., Vogel E. M. (2020). Substrate dependent resistive switching in amorphous-HfOx memristors: an experimental and computational investigation. Journal of Materials Chemistry C, 8(15), 5092–5101. https://doi.org/10.1039/c9tc06736a

Brivio, S., Frascaroli, J., Covi, E., & Spiga, S. (2019). Stimulated ionic telegraph noise in filamentary memristive devices. Scientific Reports, 9(1), art. 6310. https://doi.org/10.1038/s41598-019-41497-3

Chernov, A. A., Islamov, D. R., Piknik, A. A., Perevalov, T. V., & Gritsenko, V. A. (2017). Three-dimensional non-linear complex model of dynamic memristor switching. ECS Transactions, 75(32), 95–104. https://doi.org/10.1149/07532.0095

Duenas, S., Castan, H., Barbolla, J., Kola, R. R., & Sullivan, P. A. (2000). Electrical characteristics of anodic tantalum pentoxide thin films under thermal stress. Microelectronics reliability, 40(4–5), 659–662. https://doi.org/10.1016/S0026-2714(99)00310-8

Gooran-Shoorakchaly, A., Sharif, S. S., & Banad, Y. M. (2025). Investigating the effect of electrical and thermal transport properties on oxide-based memristors performance and reliability. Scientific Reports, 15(1), 1–13. https://doi.org/10.1038/s41598-025-02909-9

Kim, S., Kim, S.-J., Kim, K. M., Lee, S. R., Chang, M., Cho, E., Kim, Y.-B., Kim, C. J., Chung, U. I.,
Yoo, In-K. (2013). Physical electro-thermal model of resistive switching in bi-layered resistance-change memory. Scientific Reports, 3(1), art. 1680. https://doi.org/10.1038/srep01680

Kruchinin, V. N., Volodin, V. A., Perevalov, T. V., Gerasimova, A. K., Aliev, V. Sh., & Gritsenko, V. A. (2018). Optical properties of nonstoichiometric tantalum oxide taox (x < 5/2) according to spectral-ellipsometry and Raman-scattering data. Optics and Spectroscopy, 124(6), 808–813. https://doi.org/10.1134/S0030400X18060140

Larentis, S., Nardi, F., Balatti, S., David, C. Gilmer, D. C., Ielmini, D. (2012). Resistive switching by voltage-driven ion migration in bipolar RRAM — part II: modeling. IEEE Transactions on electron devices, 59(9), 2468–2475. https://doi.org/10.1109/TED.2012.2202320

Li, R., Bai, Y., & Skowronski, M. (2025). Parametric study of “filament and gap” models of resistive switching in TaOx-based devices. Journal of Applied Physics, 137(11), art. 114501. https://doi.org/10.1063/5.0246985

Lin, J., Liu, H., Wang, S., & Zhang, S. (2021). Modeling and simulation of hafnium oxide RRAM based on oxygen vacancy conduction. Crystals, 11(12), art. 1462. https://doi.org/10.3390/cryst11121462

Liu, X., Nandi, S. K., Venkatachalam, D. K., Li, S., Belay, K., & Elliman, R. G. (December 14–17, 2014). Finite element modeling of resistive switching in Nb2O5-based memory device. 2014 Conference on Optoelectronic and Microelectronic Materials & Devices, Perth, WA, Australia, pp. 280–282. https://doi.org/10.1109/COMMAD.2014.7038711

Noman, M., Jiang, W., Salvador, P. A., Skowronski, M., & Bain, J. A. (2011). Computational investigations into the operating window for memristive devices based on homogeneous ionic motion. Applied Physics. A, 102(4), 877–883. https://doi.org/10.1007/s00339-011-6270-y

Pahinkar, D. G., Basnet, P., West, M. P., Zivasatienraj, B., Weidtnbach, A., Doolittle, W. A., Vogel, E. M., & Graham S. (2020). Experimental and computational analysis of thermal environment in the operationof HfO2 memristors. AIP Advances, 10(3), art. 035127. https://doi.org/10.1063/1.5141347

Parit, A. K., Yadav, M. S., Gupta, A. K., Mikhaylov, A., & Rawat, B. (2021). Design and modeling of niobium oxide-tantalum oxide based self-selective memristor for large-scale crossbar memory. Chaos, Solitons and Fractals, 145, art. 110818. https://doi.org/10.1016/j.chaos.2021.110818

Umnyagin, G. M., Degtyarov, V. E., & Obolenskiy, S. V. (2019). Numerical simulation of the current–voltage characteristics of bilayer resistive memory based on non-stoichiometric metal oxides. Semiconductors, 53, 1246–1248. https://doi.org/10.1134/S1063782619090252

Zeumault, A., Alam, S., Omar Faruk, M., Aziz, A. (2022). Memristor compact model with oxygen vacancy concentrations as state variables. Journal of Applied Physics, 131(12), art. 124502. https://doi.org/10.1063/5.0087038

Zhang, K., Ren, Y., Ganesh, P., & Cao, Y. (2022). Effect of electrode and oxide properties on the filament kinetics during electroforming in metal-oxide-based memories. npj Computational Materials, 8(1), art. 76. https://doi.org/10.1038/s41524-022-00770-2

Zhang, K., Wang, J., Huang, Y., Chen, L. Q., Ganesh, P., & Cao, Y. (2020). High-throughput phase-field simulations and machine learning of resistive switching in resistive random-access memory. npj Computational Materials, 6(1), art. 198. https://doi.org/10.1038/s41524-020-00455-8

Zhu, Y., Zhang, J., Sun, X., Zhao, Y., Zhu, Y., Wang, S., Wu, J., Xu, Z., Wu, Z., & Dai, Y. (2025). Effect of filament regimes in the resistive switching behavior of oxide-based complementary memristor. Journal of Computational Electronics, 24(2), 1–10. https://doi.org/10.1007/s10825-025-02306-5