Nickvash Kani, Shaloo Rakheja, Azad Naeemi
In this paper we systematically evaluate the variation in the reversal delay of a nanomagnet driven by a longitudinal spin current while under the influence of thermal noise. We then use the results to evaluate the performance of an All-Spin-Logic (ASL) circuit. First, we review and expand on the physics of previously-published analytical models on stochastic nanomagnet switching. The limits of previously established models are defined and it is shown that these models are valid for nanomagnet reversal times < 200 ps. Second, the insight obtained from previous models allows us to represent the probability density function (PDF) of the nanomagnet switching delay using the double exponential function of the Frechet distribution. The PDF of a single nanomagnet is extended to more complex nanomagnet circuit configurations. It is shown that the delay-variation penalty incurred by nanomagnets arranged in parallel configuration is dwarfed by the average delay increase for nanomagnets arranged in a series configuration. Finally, we demonstrate the impact of device-level performance variation on the circuit behavior using ASL logic gates. While the analysis presented in this paper uses an ASL-AND gate as the prototype switching circuit in the spin domain, the physical concepts are generic and can be extended to any complex spin-based circuit.
Sou-Chi Chang, Azad Naeemi, Dmitri E. Nikonov, Alexei Gruverman
In this paper, a theoretical approach, comprising the non-equilibrium Green's function method for electronic transport and Landau-Khalatnikov equation for electric polarization dynamics, is presented to describe polarization-dependent tunneling electroresistance (TER) in ferroelectric tunnel junctions. Using appropriate contact, interface, and ferroelectric parameters, measured current-voltage characteristic curves in both inorganic (Co/BaTiO$_{3}$/La$_{0.67}$Sr$_{0.33}$MnO$_{3}$) and organic (Au/PVDF/W) ferroelectric tunnel junctions can be well described by the proposed approach. Furthermore, under this theoretical framework, the controversy of opposite TER signs observed experimentally by different groups in Co/BaTiO$_{3}$/La$_{0.67}$Sr$_{0.33}$MnO$_{3}$ systems is addressed by considering the interface termination effects using the effective contact ratio, defined through the effective screening length and dielectric response at the metal/ferroelectric interfaces. Finally, our approach is extended to investigate the role of a CoO$_{x}$ buffer layer at the Co/BaTiO$_{3}$ interface in a ferroelectric tunnel memristor. It is shown that, to have a significant memristor behavior, not only the interface oxygen vacancies but also the CoO$_{x}$ layer thickness may vary with the applied bias.
Hai Li, Dmitri E. Nikonov, Chia-Ching Lin, Kerem Camsari, Yu-Ching Liao, Chia-Sheng Hsu, Azad Naeemi, Ian A. Young
Spintronic devices are a promising beyond-CMOS device option thanks to their energy efficiency and compatibility with CMOS. To accurately capture their multi-physics dynamics, a rigorous treatment of both spin and charge and their inter-conversion is required. Here we present physics-based device models based on 4x4 matrices for the spin-orbit coupling part of the magneto-electric spin-orbit (MESO) device. Also, a more rigorous physics model of ferroelectric and magnetoelectric switching of ferromagnets, based on Landau-Lifshitz-Gilbert (LLG) and Landau-Khalatnikov (LK) equations, is presented. With the combined model implemented in a SPICE circuit simulator environment, simulation results were obtained which show feasibility of MESO implementation and functional operation of buffers, oscillators, and majority gates.
Chia-Sheng Hsu, Sou-Chi Chang, Dmitri E. Nikonov, Ian A. Young, Azad Naeemi
The negative capacitance (NC) stabilization of a ferroelectric (FE) material can potentially provide an alternative way to further reduce the power consumption in ultra-scaled devices and thus has been of great interest in technology and science in the past decade. In this article, we present a physical picture for a better understanding of the hysteresis-free charge boost effect observed experimentally in metal-ferroelectric-insulator-metal (MFIM) capacitors. By introducing the dielectric (DE) leakage and interfacial trapped charges, our simulations of the hysteresis loops are in a strong agreement with the experimental measurements, suggesting the existence of an interfacial oxide layer at the FE-metal interface in metal-ferroelectric-metal (MFM) capacitors. Based on the pulse switching measurements, we find that the charge enhancement and hysteresis are dominated by the FE domain viscosity and DE leakage, respectively. Our simulation results show that the underlying mechanisms for the observed hysteresis-free charge enhancement in MFIM may be physically different from the alleged NC stabilization and capacitance matching. Moreover, the link between Merz's law and the phenomenological kinetic coefficient is discussed, and the possible cause of the residual charges observed after pulse switching is explained by the trapped charge dynamics at the FE-DE interface. The physical interpretation presented in this work can provide important insights into the NC effect in MFIM capacitors and future studies of low-power logic devices.
Rouhollah Mousavi Iraei, Nickvash Kani, Sourav Dutta, Dmitri E. Nikonov, Sasikanth Manipatruni, Ian A. Young, John T. Heron, Azad Naeemi
We propose a heterostructure device comprised of magnets and piezoelectrics that significantly improves the delay and the energy dissipation of an all-spin logic (ASL) device. This paper studies and models the physics of the device, illustrates its operation, and benchmarks its performance using SPICE simulations. We show that the proposed device maintains low voltage operation, non-reciprocity, non-volatility, cascadability, and thermal reliability of the original ASL device. Moreover, by utilizing the deterministic switching of a magnet from the saddle point of the energy profile, the device is more efficient in terms of energy and delay and is robust to thermal fluctuations. The results of simulations show that compared to ASL devices, the proposed device achieves 21x shorter delay and 27x lower energy dissipation per bit for a 32-bit arithmetic-logic unit (ALU).
Siri Narla, Piyush Kumar, Azad Naeemi
In this work, we present a novel non-volatile spin transfer torque (STT) assisted spin-orbit torque (SOT) based ternary content addressable memory (TCAM) with 5 transistors and 2 magnetic tunnel junctions (MTJs). We perform a comprehensive study of the proposed design from the device-level to application-level. At the device-level, various write characteristics such as write error rate, time, and current have been obtained using micromagnetic simulations. The array-level search and write performance have been evaluated based on SPICE circuit simulations with layout extracted parasitics for bitcells while also accounting for the impact of interconnect parasitics at the 7nm technology node. A search error rate of 3.9x10^-11 is projected for exact search while accounting for various sources of variation in the design. In addition, the resolution of the search operation is quantified under various scenarios to understand the achievable quality of the approximate search operations. Application-level performance and accuracy of the proposed design have been evaluated and benchmarked against other state-of-the-art CAM designs in the context of a CAM-based recommendation system.
Sourav Dutta, Dmitri E. Nikonov, Sasikanth Manipatruni, Ian A. Young, Azad Naeemi
Spin waves are propagating disturbances in magnetically ordered materials, analogous to lattice waves in solid systems and are often described from a quasiparticle point of view as magnons. The attractive advantages of Joule-heat-free transmission of information, utilization of the phase of the wave as an additional degree of freedom and lower footprint area compared to conventional charge-based devices have made spin waves or magnon spintronics a promising candidate for beyond-CMOS wave-based computation. However, any practical realization of an all-magnon based computing system must undergo the essential steps of a careful selection of materials and demonstrate robustness with respect to thermal noise or variability. Here, we aim at identifying suitable materials and theoretically demonstrate the possibility of achieving error-free clocked non-volatile spin wave logic device, even in the presence of thermal noise and clock jitter or clock skew.
Chenyun Pan, Azad Naeemi
Due to the massive parallel computing capability and outstanding image and signal processing performance, cellular neural network (CNN) is one promising type of non-Boolean computing system that can outperform the traditional digital logic computation and mitigate the physical scaling limit of the conventional CMOS technology. The CNN was originally implemented by VLSI analog technologies with operational amplifiers and operational transconductance amplifiers as neurons and synapses, respectively, which are power and area consuming. In this paper, we propose a hybrid structure to implement the CNN with magnetic components and CMOS peripherals with a complete driving and sensing circuitry. In addition, we propose a digitally programmable magnetic synapse that can achieve both positive and negative values of the templates. After rigorous performance analyses and comparisons, optimal energy is achieved based on various design parameters, including the driving voltage and the CMOS driving size. At a comparable footprint area and operation speed, a spintronic CNN is projected to achieve more than one order of magnitude energy reduction per operation compared to its CMOS counterpart.
Chia-Sheng Hsu, Sou-Chi Chang, Dmitri E. Nikonov, Ian A. Young, Azad Naeemi
In this paper, the multi-domain nature of ferroelectric (FE) polarization switching dynamics in a metal-ferroelectric-metal (MFM) capacitor is explored through a physics-based phase field approach, where the three-dimensional time-dependent Ginzburg-Landau (TDGL) equation and Poisson's equation are self-consistently solved with the SPICE simulator. Systematically calibrated based on the experimental measurements, the model well captures transient negative capacitance in pulse switching dynamics, with domain interaction and viscosity being the key parameters. It is found that the influence of pulse amplitudes on voltage transient behaviors can be attributed to the fact that the FE free energy profile strongly depends on how the domains are interacted. This finding has an important implication on the charge-boost induced by stabilization of negative capacitance in an FE + dielectric (DE) stack since the so-called capacitance matching needs to be designed at a specific operation voltage or frequency. In addition, we extract the domain viscosity dynamics during polarization switching according to the experimental measurements. For the first time, a physics-based circuit-compatible SPICE model for multi-domain phase field simulations is established to reveal the effect of domain interaction on the FE energy profile and microscopic domain evolution.
Zeki C. Seskir, Piotr Migdał, Carrie Weidner, Aditya Anupam, Nicky Case, Noah Davis, Chiara Decaroli, İlke Ercan, Caterina Foti, Paweł Gora, Klementyna Jankiewicz, Brian R. La Cour, Jorge Yago Malo, Sabrina Maniscalco, Azad Naeemi, Laurentiu Nita, Nassim Parvin, Fabio Scafirimuto, Jacob F. Sherson, Elif Surer, James Wootton, Lia Yeh, Olga Zabello, Marilù Chiofalo
In this article, we provide an extensive overview of a wide range of quantum games and interactive tools that have been employed by the community in recent years. The paper presents selected tools, as described by their developers. The list includes Hello Quantum, Hello Qiskit, Particle in a Box, Psi and Delta, QPlayLearn, Virtual Lab by Quantum Flytrap, Quantum Odyssey, ScienceAtHome, and The Virtual Quantum Optics Laboratory. Additionally, we present events for quantum game development: hackathons, game jams, and semester projects. Furthermore, we discuss the Quantum Technologies Education for Everyone (QUTE4E) pilot project, which illustrates an effective integration of these interactive tools with quantum outreach and education activities. Finally, we aim at providing guidelines for incorporating quantum games and interactive tools in pedagogic materials to make quantum technologies more accessible for a wider population.
Odysseas Zografos, Sourav Dutta, Mauricio Manfrini, Adrien Vaysset, Bart Sorée, Azad Naeemi, Praveen Raghavan, Rudy Lauwereins, Iuliana P. Radu
A spin wave majority fork-like structure with feature size of 40\,nm, is presented and investigated, through micromagnetic simulations. The structure consists of three merging out-of-plane magnetization spin wave buses and four magneto-electric cells serving as three inputs and an output. The information of the logic signals is encoded in the phase of the transmitted spin waves and subsequently stored as direction of magnetization of the magneto-electric cells upon detection. The minimum dimensions of the structure that produce an operational majority gate are identified. For all input combinations, the detection scheme employed manages to capture the majority phase result of the spin wave interference and ignore all reflection effects induced by the geometry of the structure.
Sourav Dutta, Dmitri E. Nikonov, George Bourianoff, Sasikanth Manipatruni, Ian A. Young, Azad Naeemi
Magnetic skyrmions have been the focus of intense research with promising applications in memory, logic and interconnect technology. Several schemes have been recently proposed and demonstrated to nucleate skyrmions. However, they either result in an uncontrolled skyrmion bubble production or are mostly targeted towards integration with racetrack memory device. In this work, we propose a novel scheme for a controlled single skyrmion nucleation in a confined nanowire geometry with sub-100 nm width using a generalized approach of "localized spin current injection" technique in material systems exhibiting low Dzyaloshinskii-Moriya interaction (DMI). Our proposed nucleation mechanism follows a pathway involving the creation of a reversed magnetic domain containing one or more pairs of vertical Bloch lines (VBLs) that form an edge-to-edge domain wall as the VBLs get annihilated at the edge of the nanowire. However, pinning of the edge domain walls within a narrow gap using notches or anti-notches results in the creation of a magnetic bubble with defect-free domain wall that eventually relaxes into a circular skyrmion structure. Our simulations predict that the proposed mechanism allows skyrmion nucleation on sub-nanosecond timescale, shows robustness to variations like local pinning sites and is applicable for any skyrmion-based logic, memory and interconnect application.
Yu-Ching Liao, Dmitri E. Nikonov, Sourav Dutta, Sou-Chi Chang, Chia-Sheng Hsu, Ian A. Young, Azad Naeemi
The switching dynamics of a single-domain BiFeO3/CoFe heterojunction is modeled and key parameters such as interface exchange coupling coefficient are extracted from experimental results. The lower limit of the magnetic order response time of CoFe in the BiFeO3/CoFe heterojunction is theoretically quantified to be on to the order of 100 ps. Our results indicate that the switching behavior of CoFe in the BiFeO3/CoFe heterojunction is dominated by the rotation of the Neel vector in BiFeO3 rather than the unidirectional exchange bias at the interface. We also quantify the magnitude of the interface exchange coupling coefficient J_int to be 0.32 pJ/m by comparing our simulation results with the giant magnetoresistance (GMR) curves and the magnetic hysteresis loop in the experiments. To the best of our knowledge, this is the first time that J_int is extracted quantitatively from experiments. Furthermore, we demonstrate that the switching success rate and the thermal stability of the BiFeO3/CoFe heterojunction can be improved by reducing the thickness of CoFe and increasing the length to width aspect ratio of the BiFeO3/CoFe heterojunction. Our theoretical model provides a comprehensive framework to study the magnetoelectric properties and the manipulation of the magnetic order of CoFe in the BiFeO3/CoFe heterojunction.
Xiang Li, Shy-Jay Lin, Mahendra DC, Yu-Ching Liao, Chengyang Yao, Azad Naeemi, Wilman Tsai, Shan X. Wang
As spin-orbit-torque magnetic random-access memory (SOT-MRAM) is gathering great interest as the next-generation low-power and high-speed on-chip cache memory applications, it is critical to analyze the magnetic tunnel junction (MTJ) properties needed to achieve sub-ns, and ~fJ write operation when integrated with CMOS access transistors. In this paper, a 2T-1MTJ cell-level modeling framework for in-plane type Y SOT-MRAM suggests that high spin Hall conductivity and moderate SOT material sheet resistance are preferred. We benchmark write energy and speed performances of type Y SOT cells based on various SOT materials experimentally reported in the literature, including heavy metals, topological insulators and semimetals. We then carry out detailed benchmarking of SOT material Pt, beta-W, and BixSe(1-x) with different thickness and resistivity. We further discuss how our 2T-1MTJ model can be expanded to analyze other variations of SOT-MRAM, including perpendicular (type Z) and type X SOT-MRAM, two-terminal SOT-MRAM, as well as spin-transfer-torque (STT) and voltage-controlled magnetic anisotropy (VCMA)-assisted SOT-MRAM. This work will provide essential guidelines for SOT-MRAM materials, devices, and circuits research in the future.
Sou-Chi Chang, Sasikanth Manipatruni, Dmitri E. Nikonov, Ian A. Young, Azad Naeemi
A novel scheme for non-volatile digital computation is proposed using spin-transfer torque (STT) and automotion of magnetic domain walls (DWs). The basic computing element is composed of a lateral spin valve (SV) with two ferromagnetic (FM) wires served as interconnects, where DW automotion is used to propagate the information from one device to another. The non-reciprocity of both device and interconnect is realized by sizing different contact areas at the input and the output as well as enhancing the local damping mechanism. The proposed logic is suitable for scaling due to a high energy barrier provided by a long FM wire. Compared to the scheme based on non-local spin valves (NLSVs) in the previous proposal, the devices can be operated at lower current density due to utilizing all injected spins for local magnetization reversals, and thus improve both energy efficiency and resistance to electromigration. This device concept is justified by simulating a buffer, an inverter, and a 3-input majority gate with comprehensive numerical simulations, including spin transport through the FM/non-magnetic (NM) interfaces as well as the NM channel and stochastic magnetization dynamics inside FM wires. In addition to digital computing, the proposed framework can also be used as a transducer between DWs and spin currents for higher wiring flexibility in the interconnect network.
Delin Zhang, Mukund Bapna, Wei Jiang, Duarte Pereira de Sousa, Yu-Ching Liao, Zhengyang Zhao, Yang Lv, Protyush Sahu, Deyuan Lyu, Azad Naeemi, Tony Low, Sara A Majetich, Jian-Ping Wang
Perpendicular magnetic tunnel junctions (p-MTJs) switched utilizing bipolar electric fields have extensive applications in energy-efficient memory and logic devices. Voltage-controlled magnetic anisotropy linearly lowers the energy barrier of ferromagnetic layer via electric field effect and efficiently switches p-MTJs only with a unipolar behavior. Here we demonstrate a bipolar electric field effect switching of 100-nm p-MTJs with a synthetic antiferromagnetic free layer through voltage-controlled exchange coupling (VCEC). The switching current density, ~1.1x10^5 A/cm^2, is one order of magnitude lower than that of the best-reported spin-transfer torque devices. Theoretical results suggest that electric field induces a ferromagnetic-antiferromagnetic exchange coupling transition of the synthetic antiferromagnetic free layer and generates a field-like interlayer exchange coupling torque, which cause the bidirectional magnetization switching of p-MTJs. A preliminary benchmarking simulation estimates that VCEC dissipates an order of magnitude lower writing energy compared to spin-transfer torque at the 15-nm technology node. These results could eliminate the major obstacle in the development of spin memory devices beyond their embedded applications.
Siri Narla, Piyush Kumar, Mohammad Adnaan, Azad Naeemi
In this paper we present a comprehensive design and benchmarking study of Content Addressable Memory (CAM) at the 7nm technology node in the context of similarity search applications. We design CAM cells based on SRAM, spin-orbit torque, and ferroelectric field effect transistor devices and from their layouts extract cell parasitics using state of the art EDA tools. These parasitics are used to develop SPICE netlists to model search operations. We use a CAM-based dataset search and a sequential recommendation system to highlight the application-level performance degradation due to interconnect parasitics. We propose and evaluate two solutions to mitigate interconnect effects.
Md Nahid Haque Shazon, Piyush Kumar, Luqiao Liu, Daniel C. Ralph, Azad Naeemi
This paper presents physical modeling and benchmarking for two-terminal spin-orbit torque magnetic random-access memory (2T-SOT-MRAM). The results indicate that the common SOT materials that provide only in-plane torque can provide little to no improvement over spin-transfer-torque (STT) MRAM in terms of write energy. However, emerging SOT materials that provide out-of-plane torques with efficiencies as small as 0.1 can result in significant improvements in the write energy for such 2-terminal devices, especially when the magnet lateral dimensions are scaled down to 30 or 20 nm. Additionally, a novel 2T-SOT MRAM device is proposed that can increase the path electrons pass through the SOT layer; hence, increasing the generated spin current and the energy efficiency of the device. Our benchmarking results indicate that an out-of-plane SOT efficiency of 0.051 for 20nm wide devices can result in write energies approaching SRAM at the 7nm technology node.
Qiuwen Lou, Chenyun Pan, John McGuiness, Andras Horvath, Azad Naeemi, Michael Niemier, X. Sharon Hu
Deep neural network (DNN) accelerators with improved energy and delay are desirable for meeting the requirements of hardware targeted for IoT and edge computing systems. Convolutional neural networks (CoNNs) belong to one of the most popular types of DNN architectures. This paper presents the design and evaluation of an accelerator for CoNNs. The system-level architecture is based on mixed-signal, cellular neural networks (CeNNs). Specifically, we present (i) the implementation of different layers, including convolution, ReLU, and pooling, in a CoNN using CeNN, (ii) modified CoNN structures with CeNN-friendly layers to reduce computational overheads typically associated with a CoNN, (iii) a mixed-signal CeNN architecture that performs CoNN computations in the analog and mixed signal domain, and (iv) design space exploration that identifies what CeNN-based algorithm and architectural features fare best compared to existing algorithms and architectures when evaluated over common datasets -- MNIST and CIFAR-10. Notably, the proposed approach can lead to 8.7$\times$ improvements in energy-delay product (EDP) per digit classification for the MNIST dataset at iso-accuracy when compared with the state-of-the-art DNN engine, while our approach could offer 4.3$\times$ improvements in EDP when compared to other network implementations for the CIFAR-10 dataset.
Yu-Ching Liao, Dmitri E. Nikonov, Sourav Dutta, Sou-Chi Chang, Sasikanth Manipatruni, Ian A. Young, Azad Naeemi
The switching dynamics of a single-domain BiFeO$_3$ thin films is investigated through combining the dynamics of polarization and Neel vector. The evolution of the ferroelectric polarization is described by the Landau-Khalatnikov (LK) equation, and the Landau-Lifshitz-Gilbert (LLG) equations for spins in two sublattices to model the time evolution of the antiferromagnetic order (Neel vector) in a G-type antiferromagnet. This work theoretically demonstrates that due to the rotation of the magnetic hard axis following the polarization reversal, the Neel vector can be switched by 180 degrees, while the weak magnetization can remain unchanged. The simulation results are consistent with the ab initio calculation, where the Neel vector rotates during polarization rotation, and also match our calculation of the dynamics of order parameter using Landau-Ginzburg theory. We also find that the switching time of the Neel vector is determined by the speed polarization switching and is predicted to be as short as 30 ps.