Local bifurcation with spin-transfer torque in superparamagnetic tunnel junctions

Magnetic tunnel junctions offer significant and near-term improvements to new computer chips, most immediately from non-volatile memory applications [1]. These devices consist of two magnetic layers whose relative alignment – parallel or antiparallel – determine the device's two-terminal resistance. When the energy barrier between these two states is sufficiently small, thermal fluctuations can cause the device to exhibit random telegraph noise in its resistive state. In this case, the device is called a superparamagnetic tunnel junction [2].Computing with random telegraph noise can offer favorable properties such as noise-tolerance, massive parallelism, and – for certain operations – low power and area footprints. The field of stochastic computing addresses questions of engineering such systems but has mostly been restricted to the use of low-quality pseudorandom number generators. The low periodicity and high cross-correlations between these devices have restricted traditional stochastic computing by forcing frequent regeneration of stochastic bitstreams. Crossing in and out of the stochastic domain can incur significant energy penalties [3].In our work [4], we introduce a low-energy circuit for extracting programmable randomness from superparamagnetic tunnel junctions. The required probability is determined via a digital input signal, rather than an analog current, so ohmic losses are minimized (Figure 1). Using detailed analog circuit simulation, we find that our device requires only half the energy of the traditional all-CMOS solution, while also offering infinite-period truly random bitstreams.To demonstrate the value of truly random bitstreams, we designed a deep neural network modeled after LeNet5 [5], a famous convolutional neural network used for handwriting recognition. Traditional neural networks multiply neuron outputs by a synaptic weight, add these products together at the input of another neuron, and then apply a nonlinear operation to that input sum. In our implementation, the values passed between neurons are encoded in the expected value of the voltage on any given wire. To multiply two signals together, we need only use a Boolean AND gate to construct the joint distribution of the wires. Feeding many wires into a Boolean OR gate generates a polynomial function which looks like linear addition near the origin, but acquires high-order nonlinear corrections when the inputs are strong. However, the OR gate only functions in this way because the inputs can be regarded as statistically independent, which would be impossible with pseudorandom number generators absent an unacceptable increase in energy consumption.We implement LeNet5 using superparamagnetic tunnel junctions together with these simple logic gates and train a simulation of this deep neural network. We are able to achieve 97 % accuracy on handwritten digit recognition using only 150 nJ per inference. This energy efficiency represents a factor of 1.4 to 7.7 improvement over comparable proposals that do not use tunnel junctions. However, after systematic optimization, the best CMOS-only solution is able to achieve 99.1 % accuracy [6]. Questions about the best way to train OR-gate neurons for optimal performance is a question for future research. Nevertheless, our demonstration shows that taking a digital approach to utilizing SMTJ fluctuations can unlock extremely energy-efficient circuit designs with the potential for offering stochastic neural networks computing in near-term application specific integrated circuits. **

Low-barrier nanomagnets have attracted a great deal of research interest for their use as sources of high-quality true random number generation. More recently, low-barrier nanomagnets with tunable output have been shown to be a natural hardware platform for unconventional computing paradigms such as probabilistic spin logic. Efficient generation and tunability of high-quality random bits is critical for these novel applications. However, current spintronic random number generators are based on superparamagnetic tunnel junctions with tunability obtained through spin transfer torque, which unavoidably leads to challenges in designing concatenated networks using these two terminal devices. The more recent development of utilizing spin orbit torque (SOT) allows for a three-terminal device design, but can only tune in-plane magnetization freely, which is not very energy efficient due to the needs of overcoming a large demagnetization field. In this work, we experimentally demonstrate a stochastic device with perpendicular magnetic anisotropy that is completely tunable by SOT without the aid of any external magnetic field. Our measurements lead us to hypothesize that a tilted anisotropy might be responsible for the observed tunability. We carry out stochastic Landau-Lifshitz-Gilbert simulations to confirm our experimental observation. Finally, we build an electrically coupled network of two such stochastic nanomagnet-based devices and demonstrate that finite correlation or anticorrelation can be established between their output fluctuations by a weak interconnection, despite having a large difference in their natural fluctuation timescale. Simulations based on a dynamical model for autonomous circuits composed of low-barrier nanomagnets show close agreement with the experimental results.

Using the linearized Landau–Lifshitz-Gilbert (LLG) equation in the rotation coordinate, we calculate the critical switching current density of a perpendicular magnetic tunnel junction (MTJ), where magnetization switching is achieved by the interplay of spin-transfer and spin-orbit torques. In terms of the critical current density, we find that as the current density inducing the spin-orbit torque (jSOT) increases, the current density inducing the spin-transfer torque (jSTT) decreases nonlinearly. In the presence of the spin-orbit field-like torque (β), the critical switching current density by the spin-transfer torque is proportional to the damping constant (α) as the conventional spin-transfer torque switching, while the critical switching current density by the spin-orbit torque increases with α when Heff≫HSOT . We also investigated the β dependence of the critical switching current density. For a given jSOT , the critical switching current density for the spin-transfer torque, jSTT,c decreases linearly with increasing β and nonlinearly decreases with increasing jSOT for a given β. Further, we discuss the β dependence of the critical switching current density on energy.

Superparamagnetic tunnel junctions (SMTJs) are promising components for neuromorphic computing due to their ultra-low-power operation enabled by low energy barriers. As a specific application, SMTJs have been employed to implement Boolean logic operations, which can serve as the foundation for brain-morphic computing. However, previous studies have not thoroughly investigated the noise-influenced behavior of SMTJ-based logic operations. To address this gap, we numerically explore the logical stochastic resonance (LSR) behavior in an SMTJ under the influence of colored noise. Our results demonstrate that high-frequency-dominant noises (white, blue, and violet) significantly enhance the robustness of logic operations under subthreshold driving conditions, inducing both noise-induced and noise-free LSR modes. In contrast, low-frequency-dominant noises (red and pink) suppress junction frequencies, inducing only noise-free LSR with reduced noise tolerance. This work also highlights the distinct advantages of the two LSR modes: noise-free LSR ensures stability across varying noise intensities, while noise-induced LSR enables low-power operation in controlled noise environments. By disregarding the transitional process of logic state switching, both the best noise robustness in noise-free LSR and the minimum power consumption under noise-induced LSR can be improved. Compared to SMTJ-based logic computing devices without noise-driven operation, SMTJ-based LSR systems can achieve over 60% energy savings.

In addition to the conventional PVT (Process, Voltage and Temperature) variation, time-dependent current fluctuation such as random telegraph noise (RTN) poses a new challenge on VLSI reliability. In this paper, we show that compared with the static random variation, RTN amplitude of a particular device is not constant across supply voltages and temperatures. A device may show large RTN amplitude at one operating condition and small amplitude at another operating condition. As a result, RTN amplitude distribution becomes uncorrelated across a wide range of voltage and temperature. The emergence of uncorrelated distribution causes significant degradation of worst-case values. Analysis results based on variability models from a 65 nm silicon-on-insulator process show that uncorrelated RTN degrades the worst-case threshold voltage value significantly compared with that where RTN is not considered. Delay variation analysis shows that consideration of RTN in the statistical analysis have little impact at high supply voltage. However, at low voltage operation, RTN can degrade the worst-case value by more than 5 %.

In this paper, the random telegraph noise (RTN) statistics in silicon nanowire transistors (SNWTs) are comprehensively studied. The capture/emission time constants and probabilities are found to be strongly impacted by the quantum confinement in SNWTs, which cannot be fully explained by classical RTN theory. A full quantum RTN model for SNWTs is proposed for fundamental understanding of the experiments. The characteristics of non-stationary RTN in SNWTs under high-field biases are studied for the first time, based on the developed statistical trap-response (STR) characterization method. The trap capture probability is found to be much different from that of the quasi-stationary RTN, leading to large errors in circuit aging prediction if using traditional RTN distributions. These new understandings are critical for robust SNWT circuit design against RTN.

Low frequency random telegraph noise (RTN) of electrical origin is reported in magnetic tunnel junction heads with ultrathin tunnel barriers (<1 nm). The RTN is characterized by abrupt and randomly stepped voltage spikes which modulates 1/f noise property in frequency domain. The appearance of electrical RTN is restricted to limited ranges of bias voltage and temperature. Dependence of RTN statistics on temperature suggests that the dynamic resistance fluctuations could be generally described by a thermal activation model. The extracted activation energy, EA, is found to be 0.3×10−19 J, which is much smaller than reported activation energies for magnetic RTN in early giant magnetoresistive heads.

As devices scale closer to the atomic size, a complete understanding of the physical mechanisms involving defects in high-κ dielectrics is essential to improve the performance of electron devices and to mitigate key reliability phenomena, such as Random Telegraph Noise (RTN). In fact, crucial aspects of defects in HfO2 are still under investigation (e.g., the presence of metastable states and their properties), but it is well known that oxygen vacancies (V+s) and oxygen ions (O0s) are the most abundant defects in HfO2. In this work, we use simulations to gain insights into the RTN that emerges when a constant voltage is applied across a TiN/(4 nm)HfO2/TiN stack. Signals exhibit different RTN properties over bias and, thus, appear to originate from different traps. Yet, we demonstrate that they can be instead promoted by the same O0s which change their capture (τc) and emission (τe) time constants with the applied bias, which, in turn, changes the extent of their electrostatic interactions with the traps that assist charge transport (V+s). For a certain bias, RTN is given by the modulation of the trap-assisted current at V+s induced by trapping/detrapping events at O0s, which are, in turn, influenced by the bias itself and by trapped charge at nearby O0s. In this work, we demonstrate that accounting for the effect of trapped charge is essential to provide accurate estimation of the RTN parameters, which allow us to retrieve information about traps and to explain key mechanisms behind complex RTN signals.

Random telegraph noise (RTN) having two discrete current levels was characterised in reverse current of GaN based light-emitting diodes. Through compared magnitude of the hysteresis with RTN amplitude in reverse current, it is confirmed that RTN causes the current-voltage (I-V) hysteresis. The mechanism of RTN was analysed by using a tunnelling equation. In addition, activation energy of the trap leading to RTN was characterised by analysis of the time constants with voltage and temperature.

It is demonstrated from a statistical perspective that the generation of random telegraph noise (RTN) changes before and after the application of negative-bias temperature instability (NBTI) stress. The NBTI stress generates a large number of permanent interface traps and, at the same time, a large number of RTN traps causing temporary RTN and one-time RTN. The interface trap and the RTN trap show different features in the recovery process. That is, a re-passivation of interface states is the minor cause of the recovery after the NBTI stress, and in contrast, rapid disappearance of the temporary RTN and the one-time RTN is the main cause of the recovery. The RTN traps are less likely to become permanent. This two-type trap, namely, the interface trap and RTN trap, model simply explains NBTI degradation and recovery in scaled p-channel metal–oxide–semiconductor field-effect transistors.

With continued scaling of CMOS technology, numerous concerns have been raised about random telegraph noise (RTN) possibly matching or exceeding the random process variation in threshold voltage (V th )[1], [2]. These studies are usually limited by the small sample size of the measurements, relying on modeling for projecting to high sigma. In this work, we use a modified ring oscillator (RO) circuit to measure the RTN in individual transistors (7500 NMOS and 7500 PMOS), for Intel's current 14nm technology. We analyze this data, carefully characterizing the noise signatures and accounting for the devices not showing RTN. We show that magnitude of V th fluctuation due to RTN (ΔV th RTN) at the ∼3.7 sigma level is th RTN is uncorrelated to V th random variation. From these observations, we conclude that RTN is not a significant limitation for circuit design at Intel's 14nm node.

We review a unified approach for computing: (i) spin-transfer torque in magnetic trilayers like spin-valves and magnetic tunnel junction, where injected charge current flows perpendicularly to interfaces; and (ii) spin-orbit torque in magnetic bilayers of the type ferromagnet/spin-orbit-coupled-material, where injected charge current flows parallel to the interface. Our approach requires to construct the torque operator for a given Hamiltonian of the device and the steady-state nonequilibrium density matrix, where the latter is expressed in terms of the nonequilibrium Green's functions and split into three contributions. Tracing these contributions with the torque operator automatically yields field-like and damping-like components of spin-transfer torque or spin-orbit torque vector, which is particularly advantageous for spin-orbit torque where the direction of these components depends on the unknown-in-advance orientation of the current-driven nonequilibrium spin density in the presence of spin-orbit coupling. We provide illustrative examples by computing spin-transfer torque in a one-dimensional toy model of a magnetic tunnel junction and realistic Co/Cu/Co spin-valve, both of which are described by first-principles Hamiltonians obtained from noncollinear density functional theory calculations; as well as spin-orbit torque in a ferromagnetic layer described by a tight-binding Hamiltonian which includes spin-orbit proximity effect within ferromagnetic monolayers assumed to be generated by the adjacent monolayer transition metal dichalcogenide.

Random Telegraph Noise is a relevant source of variability in integrated circuits and a growing issue due to device scaling. Jitter is one of its consequences; therefore, it is an important parameter of performance measurements for electronic components and systems. In this paper, the relationship between Random Telegraph Noise and different concepts of jitter is studied. Firstly, a gate delay variability study of a CMOS inverter is discussed. Then, an absolute, a periodic, and a cycle-to-cycle jitter are evaluated in a five-stage ring oscillator. All the data were generated with a spice simulator modified to properly account for Random Telegraph Noise, using the Monte Carlo technique.

In this paper, we investigate the random telegraph noise (RTN) in hafnium-oxide resistive random access memories in high resistive state (HRS). The current fluctuations are analyzed by decomposing the multilevel RTN signal into two-level RTN traces using a factorial hidden Markov model approach, which allows extracting the properties of the traps originating the RTN. The current fluctuations, statistically analyzed on devices with a different stack reset at different voltages, are attributed to the activation and deactivation of defects in the oxidized tip of the conductive filament, assisting the trap-assisted tunneling transport in HRS. The physical mechanisms responsible for the defect activation are discussed. We find that RTN current fluctuations can be due to either the coulomb interaction between oxygen vacancies (normally assisting the charge transport) and the electron charge trapped at interstitial oxygen defects, or the metastable defect configuration of oxygen vacancies assisting the electron transport in HRS. A consistent microscopic description of the phenomenon is proposed, linking the material properties to the device performance.

An observation on random telegraph noise (RTN) signal in the read current of a FinFET Dielectric RRAM (FIND RRAM) device is presented in this work. The RTN signal of a FIND RRAM cell is found to change with stress and ambient temperature. Cells with more cycling stress show a stronger tendency to exhibit RTN signals. RTN signals in FIND cells can be generally alleviated by high temperature anneal, and an on chip annealing scheme is proposed and demonstrated.