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Magnetic tunnel junctions (MTJs) with low switching current, high thermal stability, and small device size are strongly preferred for low-power, high-reliability, and high-density spintronic memory and logic applications. The research of MTJs from shape in-plane magnetic anisotropy to interfacial perpendicular magnetic anisotropy (i-PMA) has successfully paved the way down to 20-nm scale, below which, however, the i-PMA approach reaches a physical limit in sustaining sufficient thermal stability while achieving low-power spin transfer torque switching. Recently, studies have been reported a new approach to pave the way toward sub-10-nm MTJs satisfying the requirements by revisiting shape perpendicular magnetic anisotropy (s-PMA). In this paper, we present a compact model of the sub-10-nm s-PMA MTJ device, which captures both the static and dynamic physical behaviors. This model is SPICE-compatible for hybrid MTJ/CMOS circuit designs. This paper is expected to push forward the development of sub-10-nm-scale MTJ-based spintronic memory and logic circuits. [ABSTRACT FROM AUTHOR]

Although spin transfer torque (STT)-based magnetic tunneling junction (MTJ) owns advantages of nonvolatility, nonlimited endurance, and fast write/read, its demand for high current density significantly casts a shadow over its future prospects. Recently, a novel three-terminal MTJ cell that combines voltage-controlled magnetic anisotropy (VCMA) effect and negative capacitance (NC) effect is proposed. Drawing support from the NC amplified VCMA effect and the three-step operation scenario, this novel MTJ cell can dramatically lower the energy consumption to fJ as well as keep high operation speed within nanoseconds. The feasibility of the proposed NC enhanced VCMA spintronics device for memory and logic application is proved by extensive physical simulation in our previous work. However, a SPICE compatible compact model of the proposed NC enhanced VCMA spintronics device is still demanded for circuit and system level evaluation. In this paper, we provide an accurate and fast compact model of NC enhanced VCMA device for both memory and logic applications. [ABSTRACT FROM AUTHOR]

The spin-transfer torque domain wall (DW) magnetic tunnel junction (MTJ) enables spintronic logic circuits that can be directly cascaded without deleterious signal conversion circuitry and is one of the only spintronic devices for which cascading has been demonstrated experimentally. However, experimental progress has been impeded by a cumbersome modeling technique that requires a combination of micromagnetic and SPICE simulations. This paper, therefore, presents a SPICE-only device model that efficiently determines the DW motion resulting from spin accumulation and calculates the corresponding MTJ resistance. This model has been validated through comparison to the authoritative micromagnetic-based model, enabling reliable prediction of circuit behavior as a function of device parameters with a 10 000 $\times $ reduction in the simulation time. This model thus enables deeper device and circuit investigation, advancing the prospects for nonvolatile spintronic computing systems that overcome the von Neumann bottleneck. [ABSTRACT FROM AUTHOR]

This paper describes a robust, modular, and physics-based circuit framework to model the conventional and emerging magnetic tunnel junction (MTJ) devices. Magnetization dynamics are described by the stochastic Landau–Lifshitz–Gilbert (sLLG) equation whose results are rigorously benchmarked with a Fokker–Planck equation description of the magnet dynamics. We then show how sLLG is coupled to the transport equations of MTJ-based devices in a unified circuit platform. Step by step, we illustrate how the physics-based MTJ model can be extended to include different spintronics phenomena, including spin-transfer torque, voltage-controlled magnetic anisotropy (VCMA), and spin–orbit torque phenomena by the experimentally benchmarked examples. To demonstrate how our approach can be used in the exploration of novel MTJ-based devices, we present a recently proposed MEMS resonator-driven spin-torque nano-oscillator (STNO) that can reduce the phase noise of STNOs. We briefly elaborate on the use of our framework beyond conventional devices. [ABSTRACT FROM AUTHOR]

Magnetic tunnel junction (MTJ) spin torque oscillators (STOs) have shown the potential to be used in a wide range of microwave and sensing applications. To evaluate the potential uses of MTJ STO technology in various applications, an analytical model that can capture MTJ STO’s characteristics, while enabling system- and circuit-level designs, is of great importance. An analytical model based on macrospin approximation is necessary for these designs since it allows implementation in hardware description languages. This paper presents a new macrospin-based, comprehensive, and compact MTJ STO model, which can be used for various MTJ STOs to estimate the performance of MTJ STOs together with their application-specific integrated circuits. To adequately present the complete model, this paper is divided into two parts. In Part I, the analytical model is introduced and verified by comparing it against measured data of three different MTJ STOs, varying the angle and magnitude of the magnetic field, as well as the DC biasing current. The proposed analytical model is suitable for being implemented in Verilog-A and used for efficient simulations at device, circuit, and system levels. In Part II, the full Verilog-A implementation of the analytical model with accurate phase noise generation is presented and verified by simulations. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce a compact model for perpendicular spin-transfer torque (STT)-magnetic tunnel junctions (MTJs) implemented in Verilog-A to assure easy integration with electrical circuit simulators. It takes into account the effects of voltage-dependent perpendicular magnetic anisotropy, temperature-dependent parameters, thermal heating/cooling, MTJ process variations, and the spin-torque asymmetry of the Slonczewski spin-polarization function in the switching process. This translates into a comprehensive modeling that was adopted to investigate the writing performance under voltage scaling of a $256\times256$ STT- magnetic random access memory array implemented at three different technology nodes. Obtained results show that scaling from 30- to 20-nm node allows a write energy saving of about 43%, while the supply voltage that assures the minimum-energy write operation increases. [ABSTRACT FROM PUBLISHER]

Spin-transfer torque magnetic tunnel junction (MTJ) is a promising candidate for nonvolatile memories thanks to its high speed, low power, infinite endurance, and easy integration with CMOS circuits. However, a relatively high current flowing through an MTJ is always required by most of the switching mechanisms, which results in a high electric field in the MTJ and a significant self-heating effect. This may lead to the dielectric breakdown of the ultrathin ( $\sim 1$ nm) oxide barrier in the MTJ and cause functional errors of hybrid CMOS/MTJ circuits. This paper analyzes the physical mechanisms of time-dependent dielectric breakdown (TDDB) in an oxide barrier and proposes an SPICE-compact model of the MTJ. The simulation results show great consistency with the experimental measurements. This model can be used to execute a more realistic design according to the constraints obtained from simulation. The users can estimate the lifetime, the operation voltage margin, and the failure probability caused by TDDB in the MTJ-based circuits. [ABSTRACT FROM AUTHOR]

The current-induced perpendicular magnetic anisotropy magnetic tunnel junctions (p-MTJs) offer a number of advantages, such as high density and high speed. As p-MTJs downscale to $\sim 40$ nm, further performance enhancements can be realized thanks to high spin-torque efficiency, i.e., lower critical current density and higher thermal stability. In this paper, we investigate the origin of high spin-torque efficiency and give a phenomenological theory to describe the critical current reduction due to the subvolume activation. Based on various physical theories and structural parameters, a compact model of nanoscale MTJ is developed and demonstrates a satisfactory agreement with experimental results. Dynamic, static, and stochastic switching behaviors have been addressed and validated. Then, we perform mixed simulations for hybrid MTJ/CMOS read/write circuits, magnetic random access memory, and magnetic flip-flop to evaluate their performance. Analyses of energy consumption are given to show the prospect of MTJ technology node miniaturization. [ABSTRACT FROM AUTHOR]

The rapid development of the magnetic tunnel junction (MTJ) spin torque oscillator (STO) technology demands an analytical model to enable building MTJ STO-based circuits and systems so as to evaluate and utilize MTJ STOs in various applications. In Part I of this paper, an analytical model based on the macrospin approximation has been introduced and verified by comparing it with the measurements of three different MTJ STOs. In Part II, the full Verilog-A implementation of the proposed model is presented. To achieve a reliable model, an approach to reproducing the phase noise generated by the MTJ STO has been proposed and successfully employed. The implemented model yields a time domain signal, which retains the characteristics of operating frequency, linewidth, oscillation amplitude, and DC operating point, with respect to the magnetic field and applied DC current. The Verilog-A implementation is verified against the analytical model, providing equivalent device characteristics for the full range of biasing conditions. Furthermore, a system that includes an MTJ STO and CMOS RF circuits is simulated to validate the proposed model for system- and circuit-level designs. The simulation results demonstrate that the proposed model opens the possibility to explore STO technology in a wide range of applications. [ABSTRACT FROM AUTHOR]

Magnetic tunnel junctions (MTJs) composed of ferromagnetic layers with perpendicular magnetic anisotropy (PMA) are of great interest for achieving high-density nonvolatile memory and logic chips owing to its scalability potential together with high thermal stability. Recent progress has demonstrated a capacity for high-speed performance and low power consumption through current-induced magnetization switching. In this paper, we present a compact model of the CoFeB/MgO PMA MTJ, a system exhibiting the best tunnel magnetoresistance ratio and switching performance. It integrates the physical models of static, dynamic, and stochastic behaviors; many experimental parameters are directly included to improve the agreement of simulation with experimental measurements. Mixed simulation based on the 65-nm technology node of a magnetic flip-flop validates its relevance and efficiency for MTJ/CMOS memory and logic chip design. [ABSTRACT FROM AUTHOR]