Numerical Analysis and Innovative Simulation
Techniques for Designing Advanced MRAM

8.3 Conclusion

This thesis has demonstrated that the complex physics of ultra-scaled STT-MRAM devices, spanning spin transport across multiple interfaces, interlayer exchange coupling in composite stacks, and deterministic switching phenomena in sub-20 nm geometries, can be captured within a single, unified computational framework. The three-dimensional drift-diffusion approach developed here provides spatial resolution of torque densities, spin-accumulation profiles, and magnetization textures that are fundamentally inaccessible to macro-spin or one-dimensional models. This resolution reveals phenomena, including sequential switching, deterministic back-hopping, and the inherently non-additive coupling of spin-transfer torques in multi-segment stacks, that collectively reshape the design paradigm for next-generation devices.

From a practical standpoint, the results establish quantitative design guidelines across seven device configurations spanning four architecture families (ultra-scaled composite FL, SAF-enhanced, hybrid FL, and ds-MTJ). The identification of specific IEC windows for SAF stability, the demonstration of controlled MLC operation through intermediate magnetization states, and the optimization of double spin-torque and hybrid structures for sub-nanosecond switching provide an actionable roadmap for the development of higher-density, faster, and more reliable MRAM.

Looking ahead, the next leap in device performance will likely stem not only from new materials and advances in fabrication, but also from the mathematical capability to simulate them. The transition to higher-order finite elements, parallel-in-time integration, and fully coupled space-time solvers promises to reveal hidden dynamics at the quantum-classical boundary, enabling predictive simulation of phenomena that remain beyond the reach of current methods. This thesis provides both the physical foundation and the computational starting point for that pursuit.

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[215]  M. Bendra, R. L. de Orio, W. Goes, S. Selberherr, and V. Sverdlov, “Investigating Reliability Issues in Multi-Layered STT-MRAM with Synthetic Antiferromagnets,” in 2024 IEEE International Symposium on the Physical and Failure Analysis of Integrated Circuits (IPFA), 2024, pp. 1–5. doi: 10.1109/IPFA61654.2024.10690971.

[216]  M. Bendra, W. Goes, S. Selberherr, and V. Sverdlov, “Simulation of SAF-enhanced multilayered STT-MRAM structures,” Microelectronic Engineering, vol. 302, p. 112426, 2026. doi: 10.1016/j.mee.2025.112426.

[217]  M. Bendra, S. Selberherr, W. Goes, and V. Sverdlov, “Enhancing Sub-Nanosecond Magnetic Tunnel Junctions with Double Spin Torque and Synthetic Antiferromagnetic Layers,” in International Symposium on Hysteresis Modeling and Micromagnetics (HMM), 2025.

[218]  M. Bendra, B. Pruckner, R. L. de Orio, S. Selberherr, W. Goes et al., “Advancing Nonvolatile Memory Technologies: Enhancing Reliability and Performance through Double Spin Torque Magnetic Tunnel Junctions and Interlayer Exchange Coupling,” in 2024 Device Research Conference (DRC), 2024, pp. 1–2. doi: 10.1109/DRC61706.2024.10605512.

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List of Publications

Journal Articles

[1]  M. Bendra, W. Goes, S. Selberherr, and V. Sverdlov, “Simulation of SAF-Enhanced Multilayered STT-MRAM Structures,” Microelectronic Engineering, vol. 302, p. 112426, 2026. doi: 10.1016/j.mee.2025.112426.

[2]  M. Bendra, de Orio, Roberto Lacerda, S. Selberherr, W. Goes, and V. Sverdlov, “Interlayer Exchange Coupling for Enhanced Performance in Spin-Transfer Torque MRAM Devices,” Solid-State Electronics, vol. 229, p. 109179, 2025. doi: 10.1016/j.sse.2025.109179.

[3]  M. Bendra, de Orio, Roberto Lacerda, S. Selberherr, W. Goes, and V. Sverdlov, “A Multi-Level Cell for Ultra-Scaled STT-MRAM Realized by Back-Hopping,” Solid-State Electronics, vol. 223, p. 109027, 2025. doi: 10.1016/j.sse.2024.109027. Invited.

[4]  M. Bendra, de Orio, Roberto Lacerda, S. Selberherr, W. Goes, and V. Sverdlov, “Advanced Modeling and Simulation of Multilayer Spin-Transfer Torque Magnetoresistive Random Access Memory with Interface Exchange Coupling,” Micromachines, vol. 15, no. 5, 2024. doi: 10.3390/mi15050568. Invited.

[5]  M. Bendra, de Orio, Roberto Lacerda, S. Selberherr, W. Goes, and V. Sverdlov, “A Multi-Level Cell for Ultra-Scaled STT-MRAM Realized by Back-Hopping,” Solid-State Electronics, vol. 208, p. 108738, 2023. doi: 10.1016/j.sse.2023.108738.

[6]  S. Fiorentini, N. P. Jørstad, J. Ender, de Orio, Roberto Lacerda, S. Selberherr, M. Bendra, W. Goes, and V. Sverdlov, “Finite Element Approach for the Simulation of Modern MRAM Devices,” Micromachines, vol. 14, no. 5, 2023. doi: 10.3390/mi14050898. Invited.

[7]  M. Bendra, S. Fiorentini, W. Goes, S. Selberherr, and V. Sverdlov, “The Influence of Interface Effects on the Switching Behavior in Ultra-Scaled MRAM Cells,” Solid-State Electronics, vol. 201, p. 108590, 2023. doi: 10.1016/j.sse.2023.108590. Invited.

[8]  M. Bendra, S. Fiorentini, W. Goes, S. Selberherr, and V. Sverdlov, “Interface Effects in Ultra-Scaled MRAM Cells,” Solid-State Electronics, vol. 194, p. 108373, 2022. doi: 10.1016/j.sse.2022.108373.

[9]  T. Hadámek, S. Fiorentini, M. Bendra, J. Ender, de Orio, Roberto Lacerda, W. Goes, S. Selberherr, and V. Sverdlov, “Temperature Increase in STT-MRAM at Writing: A Fully Three-Dimensional Finite Element Approach,” Solid-State Electronics, vol. 193, p. 108269, 2022. doi: 10.1016/j.sse.2022.108269. Invited.

[10]  S. Fiorentini, M. Bendra, J. Ender, de Orio, Roberto Lacerda, T. Hadámek, W. Goes, S. Selberherr, and V. Sverdlov, “Spin and Charge Drift-Diffusion in Ultra-Scaled MRAM Cells,” Scientific Reports, vol. 12, p. 20958, 2022. doi: 10.1038/s41598-022-25586-4.

[11]  J. Ender, S. Fiorentini, de Orio, Roberto Lacerda, T. Hadámek, M. Bendra, W. Goes, S. Selberherr, and V. Sverdlov, “Advances in Modeling Emerging Magnetoresistive Random Access Memories: From Finite Element Methods to Machine Learning Approaches,” Proceedings of SPIE, vol. 12157, pp. 1 215 708–1–1 215 708–14, 2022. doi: 10.1117/12.2624595. Invited.

Conference Contributions

[12]  V. Sverdlov, N. P. Jørstad, B. Pruckner, M. Bendra, W. Goes, and S. Selberherr, “Emerging Magnetoresistive Memories,” in 2025 IEEE 16th International Conference on ASIC (ASICON), Kunming, China, 2025, pp. 1–4. doi: 10.1109/ASICON66040.2025.11326380.

[13]  V. Sverdlov, B. Pruckner, N. P. Jørstad, M. Bendra, S. Selberherr, and W. Goes, “Modeling Advanced Magnetoresistive Memories,” in 2025 IEEE European Solid-State Electronics Research Conference (ESSERC), Munich, Germany, 2025, pp. 365–368. doi: 10.1109/ESSERC66193.2025.11214099.

[14]  M. Bendra, S. Selberherr, W. Goes, and V. Sverdlov, “Enhancing Sub-Nanosecond Magnetic Tunnel Junctions with Double Spin Torque and Synthetic Antiferromagnetic Layers,” in International Symposium on Hysteresis Modeling and Micromagnetics (HMM), 2025.

[15]  M. Bendra, de Orio, Roberto Lacerda, S. Selberherr, W. Goes, and V. Sverdlov, “Influence of Interface Exchange Coupling in Multilayered Spintronic Structures,” in 2024 47th MIPRO ICT and Electronics Convention (MIPRO), 2024, pp. 1579–1583. doi: 10.1109/MIPRO60963.2024.10569798.

[16]  M. Bendra, B. Pruckner, de Orio, Roberto Lacerda, S. Selberherr, W. Goes, and V. Sverdlov, “Advancing Nonvolatile Memory Technologies: Enhancing Reliability and Performance through Double Spin Torque Magnetic Tunnel Junctions and Interlayer Exchange Coupling,” in 2024 Device Research Conference (DRC), 2024, pp. 1–2. doi: 10.1109/DRC61706.2024.10605512.

[17]  M. Bendra, W. Goes, S. Selberherr, and V. Sverdlov, “Simulation of SAF-Enhanced Multilayered STT-MRAM Structures,” in 2024 Austrochip Workshop on Microelectronics (Austrochip), 2024, pp. 1–4. doi: 10.1109/Austrochip62761.2024.10716241.

[18]  M. Bendra, de Orio, Roberto Lacerda, W. Goes, S. Selberherr, and V. Sverdlov, “Investigating Reliability Issues in Multi-Layered STT-MRAM with Synthetic Antiferromagnets,” in 2024 IEEE International Symposium on the Physical and Failure Analysis of Integrated Circuits (IPFA), 2024, pp. 1–5. doi: 10.1109/IPFA61654.2024.10690971.

[19]  B. Pruckner, N. P. Jørstad, M. Bendra, T. Hadámek, W. Goes, S. Selberherr, and V. Sverdlov, “Simulation of Advanced MRAM Devices for Sub-ns Switching,” in 2024 International Conference on Simulation of Semiconductor Processes and Devices (SISPAD), 2024, pp. 1–4. doi: 10.1109/SISPAD62626.2024.10733317.

[20]  M. Bendra, S. Fiorentini, J. Ender, de Orio, Roberto Lacerda, T. Hadámek, N. P. Jørstad, B. Pruckner, S. Selberherr, W. Goes, and V. Sverdlov, “Back-Hopping in Ultra-Scaled MRAM Cells,” in 46th MIPRO ICT and Electronics Convention (MIPRO), 2023, pp. 159–162. doi: 10.23919/MIPRO57284.2023.10159764.

[21]  M. Bendra, S. Fiorentini, S. Selberherr, W. Goes, and V. Sverdlov, “A Multi-Level Cell for Ultra-Scaled STT-MRAM Realized by Back-Hopping,” in 9th Joint International EuroSOI Workshop and International Conference on Ultimate Integration on Silicon (EuroSOI-ULIS), Tarragona, Spain, 2023.

[22]  M. Bendra, S. Fiorentini, S. Selberherr, W. Goes, and V. Sverdlov, “Simulation of Spin-Torque and Magnetization Dynamics in STT-MRAM Multi-Level Cells,” in International Symposium on Hysteresis Modeling and Micromagnetics (HMM), 2023.

[23]  M. Bendra, de Orio, Roberto Lacerda, W. Goes, V. Sverdlov, and S. Selberherr, “Modeling of Ultra-Scaled Magnetoresistive Random Access Memory,” in International Conference on Microelectronic Devices and Technologies (MicDAT), Funchal, Portugal, 2023, pp. 28–30. ISBN 978-84-09-53748-8

[24]  S. Fiorentini, de Orio, Roberto Lacerda, J. Ender, S. Selberherr, M. Bendra, N. P. Jørstad, W. Goes, and V. Sverdlov, “Finite Element Method for MRAM Switching Simulations,” in Proc. of the International Conference on Mathematical Models, Computational Techniques in Science, and Engineering (MMCTSE), Athens, Greece, 2023, invited.

[25]  N. P. Jørstad, T. Hadámek, M. Bendra, J. Ender, B. Pruckner, W. Goes, and V. Sverdlov, “Numerical Simulations of Spintronic Magnetoresistive Memories,” in Silvaco Users Global Event (SURGE), Santa Clara, USA, 2023, invited.

[26]  V. Sverdlov, S. Fiorentini, M. Bendra, J. Ender, de Orio, Roberto Lacerda, T. Hadámek, N. P. Jørstad, W. Goes, and S. Selberherr, “Comprehensive Modeling of Nanoscale Magnetoresistive Memory,” in 3rd Global Experts Conference on Materials Science & Nanotechnology (GECMSN23), Dubai, UAE, 2023, invited.

[27]  V. Sverdlov, M. Bendra, W. Goes, S. Fiorentini, A. Garcia-Barrientos, and S. Selberherr, “Multi-Level Operation in Ultra-Scaled MRAM,” in IEEE Latin American Electron Devices Conference (LAEDC), 2023, pp. 1–4. doi: 10.1109/LAEDC58183.2023.10209117.

[28]  V. Sverdlov, M. Bendra, B. Pruckner, S. Fiorentini, W. Goes, and S. Selberherr, “Comprehensive Modeling of Advanced Composite Magnetoresistive Devices,” in IEEE 53rd European Solid-State Device Research Conference (ESSDERC), 2023, pp. 93–96. doi: 10.1109/ESSDERC59256.2023.10268508.

[29]  M. Bendra, S. Fiorentini, J. Ender, de Orio, Roberto Lacerda, T. Hadámek, W. J. Loch, N. P. Jørstad, S. Selberherr, W. Goes, and V. Sverdlov, “Spin Transfer Torques in Ultra-Scaled MRAM Cells,” in 45th Jubilee International Convention on Information, Communication and Electronic Technology (MIPRO), 2022, pp. 129–132. doi: 10.23919/MIPRO55190.2022.9803736.

[30]  M. Bendra, S. Fiorentini, J. Ender, de Orio, Roberto Lacerda, T. Hadámek, W. J. Loch, N. P. Jørstad, W. Goes, S. Selberherr, and V. Sverdlov, “Interface Effects in Ultra-Scaled MRAM Cells,” in 8th Joint International EuroSOI Workshop and International Conference on Ultimate Integration on Silicon (EuroSOI-ULIS), Udine, Italy, 2022, pp. 1–2.

[31]  M. Bendra, W. J. Loch, N. P. Jørstad, S. Fiorentini, S. Selberherr, W. Goes, and V. Sverdlov, “Modeling Ultra-Scaled Multi-Layer STT-MRAM Cells: A Unified Spin and Charge Drift-Diffusion Approach,” in 2022 IEEE International Electron Devices Meeting (IEDM), 2022, poster.

[32]  S. Fiorentini, M. Bendra, J. Ender, W. Goes, V. Sverdlov, and S. Selberherr, “Evaluating Spin Transfer Torques in Multilayered Magnetic Tunnel Junctions and Spin Valves,” in Workshop on Innovative Nanoscale Devices and Systems (WINDS), Lihue, HI, USA, 2022.

[33]  S. Fiorentini, M. Bendra, J. Ender, T. Hadámek, W. J. Loch, N. P. Jørstad, de Orio, Roberto Lacerda, W. Goes, S. Selberherr, and V. Sverdlov, “Modeling Advanced Spintronic-Based Magnetoresistive Memory,” in International Conference on Microwave & THz Technologies, Wireless Communications and OptoElectronics (IRPhE 2022), 2022, pp. 49–52. doi: 10.1049/icp.2022.2795.

[34]  S. Fiorentini, M. Bendra, J. Ender, de Orio, Roberto Lacerda, T. Hadámek, W. J. Loch, N. P. Jørstad, W. Goes, S. Selberherr, and V. Sverdlov, “Spin Torques in ULTRA-Scaled MRAM Devices,” in IEEE 52nd European Solid-State Device Research Conference (ESSDERC), 2022, pp. 348–351. doi: 10.1109/ESSDERC55479.2022.9947196.

[35]  S. Fiorentini, W. J. Loch, M. Bendra, N. P. Jørstad, J. Ender, de Orio, Roberto Lacerda, T. Hadámek, W. Goes, V. Sverdlov, and S. Selberherr, “Design Analysis of Ultra-Scaled MRAM Cells,” in IEEE 16th International Conference on Solid-State & Integrated Circuit Technology (ICSICT), 2022, pp. 1–4. doi: 10.1109/ICSICT55466.2022.9963202.

[36]  T. Hadámek, M. Bendra, S. Fiorentini, J. Ender, de Orio, Roberto Lacerda, W. Goes, S. Selberherr, and V. Sverdlov, “Temperature Increase in MRAM at Writing: A Finite Element Approach,” in 7th Joint International EuroSOI Workshop and International Conference on Ultimate Integration on Silicon (EuroSOI-ULIS), 2021, pp. 1–4. doi: 10.1109/EuroSOI-ULIS53016.2021.9560669.

[37]  M. Bendra, J. Ender, S. Fiorentini, T. Hadámek, de Orio, Roberto Lacerda, W. Goes, V. Sverdlov, and S. Selberherr, “Finite Element Method Approach to MRAM Modeling,” in 44th International Convention on Information, Communication and Electronic Technology (MIPRO), 2021, pp. 70–73. doi: 10.23919/MIPRO52101.2021.9597194.

[38]  J. Ender, S. Fiorentini, de Orio, Roberto Lacerda, T. Hadámek, M. Bendra, W. Goes, S. Selberherr, and V. Sverdlov, “Advanced Modeling of Emerging MRAM: From Finite Element Methods to Machine Learning Approaches,” in Proc. of the International Conference Micro-and Nanoelectronics (ICMNE), 2021.

[39]  V. Sverdlov, M. Bendra, S. Fiorentini, J. Ender, de Orio, Roberto Lacerda, T. Hadámek, W. J. Loch, N. P. Jørstad, W. Goes, and S. Selberherr, “Advanced Modeling of Emerging Devices for Digital Spintronics,” in Proc. of the International Conference on Nanoscience and Nanotechnology, Dubai, UAE, 2022, invited.

[40]  V. Sverdlov, M. Bendra, S. Fiorentini, J. Ender, de Orio, Roberto Lacerda, T. Hadámek, W. J. Loch, N. P. Jørstad, W. Goes, and S. Selberherr, “Advanced Modeling of Emerging Magnetoresistive Memory,” in Proc. of the International Meet & Expo on Nanotechnology (NANOMEET), Edinburgh, UK, 2022, invited.

[41]  V. Sverdlov, M. Bendra, S. Fiorentini, J. Ender, de Orio, Roberto Lacerda, T. Hadámek, W. J. Loch, N. P. Jørstad, W. Goes, and S. Selberherr, “Emerging Devices for Digital Spintronics,” in 2nd Global Conference & Expo on Nanotechnology & Nanoscience, 2022, pp. 32–33, invited.

[42]  V. Sverdlov, M. Bendra, S. Fiorentini, J. Ender, de Orio, Roberto Lacerda, T. Hadámek, W. J. Loch, N. P. Jørstad, W. Goes, and S. Selberherr, “Modeling Advanced Magnetoresistive Memory: A Journey from Finite Element Methods to Machine Learning Approaches,” in 2nd Global Webinar on Nanoscience & Nanotechnology, 2022, invited.

[43]  V. Sverdlov, W. J. Loch, M. Bendra, S. Fiorentini, J. Ender, de Orio, Roberto Lacerda, T. Hadámek, N. P. Jørstad, W. Goes, and S. Selberherr, “Modeling Approach to Ultra-Scaled MRAM Cells,” in Book of Abstracts of the International Meet on Applied Science, Engineering and Technology (ASETMEET), 2022, pp. 7–8, invited.

[44]  W. J. Loch, S. Fiorentini, N. P. Jørstad, J. Ender, de Orio, Roberto Lacerda, T. Hadámek, M. Bendra, W. Goes, S. Selberherr, and V. Sverdlov, “Double Reference Layer STT-MRAM Structures with Improved Performance,” in 8th Joint International EuroSOI Workshop and International Conference on Ultimate Integration on Silicon (EuroSOI-ULIS), Udine, Italy, 2022, pp. 1–2.

[45]  N. P. Jørstad, S. Fiorentini, J. Ender, de Orio, Roberto Lacerda, T. Hadámek, W. J. Loch, M. Bendra, W. Goes, S. Selberherr, and V. Sverdlov, “Finite Element Modeling of Spin-Orbit Torques,” in Proc. of the 8th Joint International EuroSOI Workshop and International Conference on Ultimate Integration on Silicon (EuroSOI-ULIS), Udine, Italy, 2022.