A True Random Number Generator for Probabilistic Computing using Stochastic Magnetic Actuated Random Transducer Devices

Magnetic tunnel junctions (MTJs), which are the fundamental building blocks of spintronic devices, have been used to build true random number generators (TRNGs) with different trade-offs between throughput, power, and area requirements. MTJs with high-barrier magnets (HBMs) have been used to generate random bitstreams with $\lesssim$ 200~Mb/s throughput and pJ/bit energy consumption. A high temperature sensitivity, however, adversely affects their performance as a TRNG. Superparamagnetic MTJs employing low-barrier magnets (LBMs) have also been used for TRNG operation. Although LBM-based MTJs can operate at low energy, they suffer from slow dynamics, sensitivity to process variations, and low fabrication yield. In this paper, we model a TRNG based on medium-barrier magnets (MBMs) with perpendicular magnetic anisotropy. The proposed MBM-based TRNG is driven with short voltage pulses to induce ballistic, yet stochastic, magnetization switching. We show that the proposed TRNG can operate at frequencies of about 500~MHz while consuming less than 100~fJ/bit of energy. In the short-pulse ballistic limit, the switching probability of our device shows robustness to variations in temperature and material parameters relative to LBMs and HBMs. Our results suggest that MBM-based MTJs are suitable candidates for building fast and energy-efficient TRNG hardware units for probabilistic computing.Comment: 10 pages, 10 figures, Accepted at ISQED 2023 for poster presentatio

Magnetic Tunnel Junction Random Number Generators Applied to Dynamically Tuned Probability Trees Driven by Spin Orbit Torque

Perpendicular magnetic tunnel junction (pMTJ)-based true-random number generators (RNG) can consume orders of magnitude less energy per bit than CMOS pseudo-RNG. Here, we numerically investigate with a macrospin Landau-Lifshitz-Gilbert equation solver the use of pMTJs driven by spin-orbit torque to directly sample numbers from arbitrary probability distributions with the help of a tunable probability tree. The tree operates by dynamically biasing sequences of pMTJ relaxation events, called 'coinflips', via an additional applied spin-transfer-torque current. Specifically, using a single, ideal pMTJ device we successfully draw integer samples on the interval 0,255 from an exponential distribution based on p-value distribution analysis. In order to investigate device-to-device variations, the thermal stability of the pMTJs are varied based on manufactured device data. It is found that while repeatedly using a varied device inhibits ability to recover the probability distribution, the device variations average out when considering the entire set of devices as a 'bucket' to agnostically draw random numbers from. Further, it is noted that the device variations most significantly impact the highest level of the probability tree, iwth diminishing errors at lower levels. The devices are then used to draw both uniformly and exponentially distributed numbers for the Monte Carlo computation of a problem from particle transport, showing excellent data fit with the analytical solution. Finally, the devices are benchmarked against CMOS and memristor RNG, showing faster bit generation and significantly lower energy use.Comment: 10 pages, 8 figures, 2 table

A Study on Performance and Power Efficiency of Dense Non-Volatile Caches in Multi-Core Systems

In this paper, we present a novel cache design based on Multi-Level Cell Spin-Transfer Torque RAM (MLC STTRAM) that can dynamically adapt the set capacity and associativity to use efficiently the full potential of MLC STTRAM. We exploit the asymmetric nature of the MLC storage scheme to build cache lines featuring heterogeneous performances, that is, half of the cache lines are read-friendly, while the other is write-friendly. Furthermore, we propose to opportunistically deactivate ways in underutilized sets to convert MLC to Single-Level Cell (SLC) mode, which features overall better performance and lifetime. Our ultimate goal is to build a cache architecture that combines the capacity advantages of MLC and performance/energy advantages of SLC. Our experiments show an improvement of 43% in total numbers of conflict misses, 27% in memory access latency, 12% in system performance, and 26% in LLC access energy, with a slight degradation in cache lifetime (about 7%) compared to an SLC cache

Probabilistic computing with voltage-controlled dynamics in magnetic tunnel junctions

Probabilistic (p-) computing is a physics-based approach to addressing computational problems which are difficult to solve by conventional von Neumann computers. A key requirement for p-computing is the realization of fast, compact, and energy-efficient probabilistic bits. Stochastic magnetic tunnel junctions (MTJs) with low energy barriers, where the relative dwell time in each state is controlled by current, have been proposed as a candidate to implement p-bits. This approach presents challenges due to the need for precise control of a small energy barrier across large numbers of MTJs, and due to the need for an analog control signal. Here we demonstrate an alternative p-bit design based on perpendicular MTJs that uses the voltage-controlled magnetic anisotropy (VCMA) effect to create the random state of a p-bit on demand. The MTJs are stable (i.e. have large energy barriers) in the absence of voltage, and VCMA-induced dynamics are used to generate random numbers in less than 10 ns/bit. We then show a compact method of implementing p-bits by using VC-MTJs without a bias current. As a demonstration of the feasibility of the proposed p-bits and high quality of the generated random numbers, we solve up to 40 bit integer factorization problems using experimental bit-streams generated by VCMTJs. Our proposal can impact the development of p-computers, both by supporting a fully spintronic implementation of a p-bit, and alternatively, by enabling true random number generation at low cost for ultralow-power and compact p-computers implemented in complementary metal-oxide semiconductor chips

High Frequency Dynamics of Magnetic Tunnel Junctions

Magnetism has been utilized since ancient civilizations to build tools for day to day life for example, magnetic compass. Understanding of nature behind magnets has ever since evolved passing significant milestones such as, discovery of interplay between magnetism and electricity leading to invention of electric motor and dynamo and, microscopic insight developed following discovery of quantum mechanics. About twenty years ago we passed arguably the most recent milestone with the prediction of the ability to manipulate a nano sized magnet with the aid of the spin of an electronic current. With the advent of magnetic tunnel junctions (MTJ), one of the main applications of this has been spin transfer torque nano oscillators (STNO) that have attracted great attention. Recently, a new emerging field regarding magnetic skyrmions in MTJs has shown even more promising aspects such as higher energy efficiency for real world applications. In the first half of this thesis, we present a tri- layer MTJ based STNO offering 6 GHz microwave emission for both current polarities at zero external magnetic field which is the highest frequency achieved in absence of any bias field to-date, to the best of our knowledge. We have investigated into spin dynamics of this STNO discussing about out of plane (OOP) precessions along with micromagnetic simulations. In the second half of this thesis, we present observation of skyrmionic signature in an MTJ at cryogenic temperature producing random telegraph signal (RTS). We have studied the dependencies of this RTS upon various physical parameters. RTS seen in MTJs involving ferromagnetic states has attracted attention in the research community as it is an ideal candidate to realize neuromorphic computers which are inspired on human brain offering tremendous improved performance in specific tasks over conventional boolean computing. We believe this investigation into RTS involving skyrmionic states in an MTJ will further electrify this on going expedition

Electrical coupling of superparamagnetic tunnel junctions mediated by spin-transfer-torques

In this work, the effect of electrical coupling on stochastic switching of two in-plane superparamagnetic tunnel junctions (SMTJs) is studied, using experimental measurements as well as simulations. The coupling mechanism relies on the spin-transfer-torque (STT) effect, which enables the manipulation of the state probability of an SMTJ. Through the investigation of time-lagged cross-correlation, the strength and direction of the coupling are determined. In particular, the characteristic state probability transfer curve of each SMTJ leads to the emergence of a similarity or dissimilarity effect. The cross-correlation as a function of applied source voltage reveals that the strongest coupling occurs for high positive voltages for our SMTJs. In addition, we show state tuneability as well as coupling control by the applied voltage. The experimental findings of the cross-correlation are in agreement with our simulation results