Advanced Modeling and Simulation of Multilayer Spin-Transfer Torque Magnetoresistive Random Access Memory with Interface Exchange Coupling.

In advancing the study of magnetization dynamics in STT-MRAM devices, we employ the spin drift-diffusion model to address the back-hopping effect. This issue manifests as unwanted switching either in the composite free layer or in the reference layer in synthetic antiferromagnets-a challenge that becomes more pronounced with device miniaturization. Although this miniaturization aims to enhance memory density, it inadvertently compromises data integrity. Parallel to this examination, our investigation of the interface exchange coupling within multilayer structures unveils critical insights into the efficacy and dependability of spintronic devices. We particularly scrutinize how exchange coupling, mediated by non-magnetic layers, influences the magnetic interplay between adjacent ferromagnetic layers, thereby affecting their magnetic stability and domain wall movements. This investigation is crucial for understanding the switching behavior in multi-layered structures. Our integrated methodology, which uses both charge and spin currents, demonstrates a comprehensive understanding of MRAM dynamics. It emphasizes the strategic optimization of exchange coupling to improve the performance of multi-layered spintronic devices. Such enhancements are anticipated to encourage improvements in data retention and the write/read speeds of memory devices. This research, thus, marks a significant leap forward in the refinement of high-capacity, high-performance memory technologies.

Editorial for the Special Issue on Magnetic and Spin Devices, Volume II.

Although the miniaturization of metal-oxide-semiconductor field effect transistors (MOSFETs)-the main driver behind an outstanding increase in the speed, performance, density, and complexity of modern integrated circuits-is continuing, numerous outstanding technological challenges in complimentary metal-oxide-semiconductor (CMOS) device miniaturization are slowly bringing the downscaling to saturation [...].

A Comprehensive Study of Temperature and Its Effects in SOT-MRAM Devices.

We employ a fully three-dimensional model coupling magnetization, charge, spin, and temperature dynamics to study temperature effects in spin-orbit torque (SOT) magnetoresistive random access memory (MRAM). SOTs are included by considering spin currents generated through the spin Hall effect. We scale the magnetization parameters with the temperature. Numerical experiments show several time scales for temperature dynamics. The relatively slow temperature increase, after a rapid initial temperature rise, introduces an incubation time to the switching. Such a behavior cannot be reproduced with a constant temperature model. Furthermore, the critical SOT switching voltage is significantly reduced by the increased temperature. We demonstrate this phenomenon for switching of field-free SOT-MRAM. In addition, with an external-field-assisted switching, the critical SOT voltage shows a parabolic decrease with respect to the voltage applied across the magnetic tunnel junction (MTJ) of the SOT-MRAM cell, in agreement with recent experimental data.

Finite Element Approach for the Simulation of Modern MRAM Devices.

Because of their nonvolatile nature and simple structure, the interest in MRAM devices has been steadily growing in recent years. Reliable simulation tools, capable of handling complex geometries composed of multiple materials, provide valuable help in improving the design of MRAM cells. In this work, we describe a solver based on the finite element implementation of the Landau-Lifshitz-Gilbert equation coupled to the spin and charge drift-diffusion formalism. The torque acting in all layers from different contributions is computed from a unified expression. In consequence of the versatility of the finite element implementation, the solver is applied to switching simulations of recently proposed structures based on spin-transfer torque, with a double reference layer or an elongated and composite free layer, and of a structure combining spin-transfer and spin-orbit torques.

Spin and charge drift-diffusion in ultra-scaled MRAM cells.

Designing advanced single-digit shape-anisotropy MRAM cells requires an accurate evaluation of spin currents and torques in magnetic tunnel junctions (MTJs) with elongated free and reference layers. For this purpose, we extended the analysis approach successfully used in nanoscale metallic spin valves to MTJs by introducing proper boundary conditions for the spin currents at the tunnel barrier interfaces, and by employing a conductivity locally dependent on the angle between the magnetization vectors for the charge current. The experimentally measured voltage and angle dependencies of the torques acting on the free layer are thereby accurately reproduced. The switching behavior of ultra-scaled MRAM cells is in agreement with recent experiments on shape-anisotropy MTJs. Using our extended approach is absolutely essential to accurately capture the interplay of the Slonczewski and Zhang-Li torque contributions acting on a textured magnetization in composite free layers with the inclusion of several MgO barriers.

Editorial for the Special Issue on Magnetic and Spin Devices.

As scaling of semiconductor devices displays signs of saturation, the focus of research in microelectronics shifts towards finding new computing paradigms based on novel physical principles [...].

Optimization of a Spin-Orbit Torque Switching Scheme Based on Micromagnetic Simulations and Reinforcement Learning.

Spin-orbit torque memory is a suitable candidate for next generation nonvolatile magnetoresistive random access memory. It combines high-speed operation with excellent endurance, being particularly promising for application in caches. In this work, a two-current pulse magnetic field-free spin-orbit torque switching scheme is combined with reinforcement learning in order to determine current pulse parameters leading to the fastest magnetization switching for the scheme. Based on micromagnetic simulations, it is shown that the switching probability strongly depends on the configuration of the current pulses for cell operation with sub-nanosecond timing. We demonstrate that the implemented reinforcement learning setup is able to determine an optimal pulse configuration to achieve a switching time in the order of 150 ps, which is 50% shorter than the time obtained with non-optimized pulse parameters. Reinforcement learning is a promising tool to automate and further optimize the switching characteristics of the two-pulse scheme. An analysis of the impact of material parameter variations has shown that deterministic switching can be ensured for all cells within the variation space, provided that the current densities of the applied pulses are properly adjusted.

Subband engineering in n-type silicon nanowires using strain and confinement.

We present a model based on k · p theory which is able to capture the subband structure effects present in ultra-thin strained silicon nanowires. For electrons, the effective mass and valley minima are calculated for different crystal orientations, thicknesses, and strains. The actual enhancement of the transport properties depends highly on the crystal orientation of the nanowire axis; for certain orientations strain and confinement can play together to give a significant increase of the electron mobility. We also show that the effects of both strain and confinement on mobility are generally more pronounced in nanowires than in thin films. We show that optimal transport properties can be expected to be achieved through a mix of confinement and strain. Our results are in good agreement with recent experimental findings.

A numerical study of transport and shot noise in 2D hopping.

We have used modern supercomputer facilities to carry out extensive Monte Carlo simulations of 2D hopping (at negligible Coulomb interaction) in conductors with a completely random distribution of localized sites in both space and energy, within a broad range of the applied electric field E and temperature T, both within and beyond the variable-range hopping region. The calculated properties include not only dc current and statistics of localized site occupation and hop lengths, but also the current fluctuation spectrum. Within the calculation accuracy, the model does not exhibit 1/f noise, so that the low-frequency noise at low temperatures may be characterized by the Fano factor F. For sufficiently large samples, F scales with conductor length L as (L(c)/L)(α), where α = 0.76 ± 0.08<1, and parameter L(c) is interpreted as the average percolation cluster length. At relatively low E, the electric field dependence of parameter L(c) is compatible with the law [Formula: see text] which follows from directed percolation theory arguments.

A numerical study of Coulomb interaction effects on 2D hopping transport.

We have extended our supercomputer-enabled Monte Carlo simulations of hopping transport in completely disordered 2D conductors to the case of substantial electron-electron Coulomb interaction. Such interaction may not only suppress the average value of hopping current, but also affect its fluctuations rather substantially. In particular, the spectral density S(I)(f) of current fluctuations exhibits, at sufficiently low frequencies, a 1/f-like increase which approximately follows the Hooge scaling, even at vanishing temperature. At higher f, there is a crossover to a broad range of frequencies in which S(I)(f) is nearly constant, hence allowing characterization of the current noise by the effective Fano factor [Formula: see text]. For sufficiently large conductor samples and low temperatures, the Fano factor is suppressed below the Schottky value (F = 1), scaling with the length L of the conductor as F = (L(c)/L)(α). The exponent α is significantly affected by the Coulomb interaction effects, changing from α = 0.76 ± 0.08 when such effects are negligible to virtually unity when they are substantial. The scaling parameter L(c), interpreted as the average percolation cluster length along the electric field direction, scales as [Formula: see text] when Coulomb interaction effects are negligible and [Formula: see text] when such effects are substantial, in good agreement with estimates based on the theory of directed percolation.