arXiv subjects

Supriyo Datta

Publications and source records attributed to Supriyo Datta.

At least 55 records · Page 3Linked to original sources

arXiv2017

Stochastic p-bits for Invertible Logic

Conventional logic and memory devices are built out of deterministic units such as transistors, or magnets with energy barriers in excess of 40-60 kT. We show that stochastic units, p-bits, can be interconnected to create robust correlations that implement Boolean functions with impressive accuracy, comparable to standard circuits. Also they are invertible, a unique property that is absent in digital circuits. When operated in the direct mode, the input is clamped, and the network provides the correct output. In the inverted mode, the output is clamped, and the network fluctuates among possible inputs consistent with that output. We present an implementation of an invertible gate to bring out the key role of a three-terminal building block to enable the construction of correlated p-bit networks. The results for this implementation agree well with those from a universal model, showing that p-bits need not be magnet-based: any three-terminal tunable random bit generator should be suitable. We present an algorithm for designing a Boltzmann machine (BM) with symmetric connections that implements a given truth table. We then show how BM Full Adders can be interconnected in a partially directed manner to implement large operations such as 32-bit addition. Hundreds of p-bits get precisely correlated such that the correct answer out of 2^33 possibilities can be extracted by looking at the mode of a number of time samples. With perfect directivity a small number of samples is enough, while for less directed connections more samples are needed, but even in the former case invertibility is largely preserved. This combination of accuracy and invertibility is enabled by the hybrid design that uses bidirectional units to construct circuits with partially directed connections. We establish this result with examples including a 4-bit multiplier which in inverted mode functions as a factorizer.

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arXiv2017

Low Barrier Nanomagnets as p-bits for Spin Logic

It has recently been shown that a suitably interconnected network of tunable telegraphic noise generators or "p-bits" can be used to perform even precise arithmetic functions like a 32-bit adder. In this paper we use simulations based on the stochastic Landau-Lifshitz-Gilbert (sLLG) equation to demonstrate that similar impressive functions can be performed using unstable nanomagnets with energy barriers as low as a fraction of a kT. This is surprising since the magnetization of low barrier nanomagnets is not telegraphic with discrete values of +1 and -1. Rather it fluctuates randomly among all values between -1 and +1, and the output magnets are read with a thresholding device that translates all positive values to 1 and all negative values to zero. We present sLLG-based simulations demonstrating the operation of a 32-bit adder with a network of several hundred nanomagnets, exhibiting a remarkably precise correlation: The input magnets {A} and {B} as well as the output magnets {S} all fluctuate randomly and yet the quantity A+B-S is sharply peaked around zero! If we fix {A} and {B}, the sum magnets {S} rapidly converge to a unique state with S=A+B so that the system acts as an adder. But unlike standard adders, the operation is invertible. If we fix {S} and {B}, the remaining magnets {A} converge to the difference A=S-B. These examples suggest a new direction for the field of nanomagnetics away from stable high barrier magnets towards stochastic low barrier magnets which not only operate with lower currents, but are also more promising for continued downscaling.

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arXiv2017

Intrinsic optimization using stochastic nanomagnets

This paper draws attention to a hardware system which can be engineered so that its intrinsic physics is described by the generalized Ising model and can encode the solution to many important NP-hard problems as its ground state. The basic constituents are stochastic nanomagnets which switch randomly between the $\pm 1$ Ising states and can be monitored continuously with standard electronics. Their mutual interactions can be short or long range, and their strengths can be reconfigured as needed to solve specific problems and to anneal the system at room temperature. The natural laws of statistical mechanics guide the network of stochastic nanomagnets at GHz speeds through the collective states with an emphasis on the low energy states that represent optimal solutions. As proof-of-concept, we present simulation results for standard NP-complete examples including a 16-city traveling salesman problem using experimentally benchmarked models for spin-transfer torque driven stochastic nanomagnets.

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arXiv2017

Evaluating Spintronic Devices Using The Modular Approach

Over the past decade a large family of spintronic devices have been proposed as candidates for replacing CMOS for future digital logic circuits. Using the recently developed Modular Approach framework, we investigate and identify the physical bottlenecks and engineering challenges facing current spintronic devices. We then evaluate how systematic advancements in material properties and device design innovations impact the performance of spintronic devices, as a possible continuation of Moore's Law, even though some of these projections are speculative and may require technological breakthroughs. Lastly, we illustrate the use of the Modular Approach as an exploratory tool for probabilistic networks, using superparamagnetic magnets as building blocks for such networks. These building blocks leverage the inherent physics of stochastic spin-torque switching and could provide ultra-compact and efficient hardware for beyond-Boolean computational paradigms.

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arXiv2016

Spin switches for compact implementation of neuron and synapse

Nanomagnets driven by spin currents provide a natural implementation for a neuron and a synapse: currents allow convenient summation of multiple inputs, while the magnet provides the threshold function. The objective of this paper is to explore the possibility of a hardware neural network (HNN) implementation using a spin switch (SS) as its basic building block. SS is a recently proposed device based on established technology with a transistor-like gain and input-output isolation. This allows neural networks to be constructed with purely passive interconnections without intervening clocks or amplifiers. The weights for the neural network are conveniently adjusted through analog voltages that can be stored in a non-volatile manner in an underlying CMOS layer using a floating gate low dropout voltage regulator. The operation of a multi-layer SS neural network designed for character recognition is demonstrated using a standard simulation model based on coupled Landau-Lifshitz-Gilbert (LLG) equations, one for each magnet in the network.

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arXiv2016

Ultrafast Spin-Transfer-Torque Switching of Synthetic Ferrimagnets

The switching speed and the write current required for spin-transfer-torque reversal of spintronic devices such as magnetic tunnel junctions (MTJ) currently hinder their wide implementation into memory and logic devices. This problem is further exacerbated as the dimensions of MTJ nanostructures are scaled down to tens of nanometers in diameter, as higher magnetic anisotropy materials are required to meet thermal stability requirements that demand higher switching current densities. Here, we propose a simple solution to these issues based on synthetic ferrimagnet (SFM) structures. It is commonly assumed that to achieve a given switching delay, the current has to exceed the critical current by a certain factor and so a higher critical current implies a higher switching current. We show that this is not the case for SFM structures which can provide significantly reduced switching delay for a given current density, even though the critical current is increased. This non-intuitive result can be understood from the requirements of angular momentum conservation. We conclude that a 20 nm diameter MTJ incorporating the proposed SFM free layer structure can be switched in tens of picosecond time scales. This remarkable switching speed can be attained by employing current perpendicular magnetic anisotropy materials with experimentally demonstrated exchange coupling strengths.

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arXiv2016

A building block for hardware belief networks

Belief networks represent a powerful approach to problems involving probabilistic inference, but much of the work in this area is software based utilizing standard deterministic hardware based on the transistor which provides the gain and directionality needed to interconnect billions of them into useful networks. This paper proposes a transistor like device that could provide an analogous building block for probabilistic networks. We present two proof-of-concept examples of belief networks, one reciprocal and one non-reciprocal, implemented using the proposed device which is simulated using experimentally benchmarked models.

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arXiv2014

Modeling Multi-Magnet Networks Interacting Via Spin Currents

The significant experimental advances of the last few decades in dealing with the interaction of spin currents and nanomagnets, at the device level, has allowed envisioning a broad class of devices that propose to implement information processing using spin currents and nanomagnets. To analyze such spin-magnet logic circuits, in general, we have developed a coupled spin-transport/ magnetization-dynamics simulation framework that could be broadly applicable to various classes of spin-valve/ spin-torque devices. Indeed, the primary purpose of this chapter is to describe in detail, the overall approach we have developed to include a description of spin transport coupled with magnetization dynamics and to show how it was benchmarked against available data on experiments. We address non-collinear spin-transport in Section-2 using a lumped "4-component spin-circuit formalism" that describes the interaction of non-collinear magnets (required for modeling spin torque), by computing 4-component currents and voltages at every node of a "circuit". For modeling the magnetization dynamics, we use the standard Landau-Lifshitz-Gilbert (LLG) equation with the Slonczewski and the field-like terms included for spin torque. Section-3 describes how this LLG model is coupled with the spin transport model to analyze spin-torque experiments and spin-magnet circuits in general. We include MATLAB codes in the Appendix to facilitate a "hands-on" understanding of our model and hope it will enable interested readers to conveniently analyze their own experiments, develop a deeper insight into spin-magnet circuits or come up with their own creative designs.

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arXiv2014

What constitutes a nanoswitch? A Perspective

Progress in the last two decades has effectively integrated spintronics and nanomagnetics into a single field, creating a new class of spin-based devices that are now being used both to Read (R) information from magnets and to Write (W) information onto magnets. Many other new phenomena are being investigated for nano-electronic memory as described in Part II of this book. It seems natural to ask whether these advances in memory devices could also translate into a new class of logic devices. What makes logic devices different from memory is the need for one device to drive another and this calls for gain, directionality and input-output isolation as exemplified by the transistor. With this in mind we will try to present our perspective on how W and R devices in general, spintronic or otherwise, could be integrated into transistor-like switches that can be interconnected to build complex circuits without external amplifiers or clocks. We will argue that the most common switch used to implement digital logic based on complementary metal oxide semiconductor (CMOS) transistors can be viewed as an integrated W-R unit having an input-output asymmetry that give it gain and directionality. Such a viewpoint is not intended to provide any insight into the operation of CMOS switches, but rather as an aid to understanding how W and R units based on spins and magnets can be combined to build transistor-like switches. Next we will discuss the standard W and R units used for magnetic memory devices and present one way to integrate them into a single unit with the input electrically isolated from the output. But we argue that this integrated W-R unit would not provide the key property of gain. We will then show that the recently discovered giant spin Hall effect could be used to construct a W-R unit with gain and suggest other possibilities for spin switches with gain.

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arXiv2013

Charge-Resistance Approach to Benchmarking Performance of Beyond-CMOS Information Processing Devices

Multiple beyond-CMOS information processing devices are presently under active research and require methods of benchmarking them. A new approach for calculating the performance metric, energy-delay product, of such devices is proposed. The approach involves estimating the device properties of resistance and switching charge, rather than dynamic evolution characteristics, such as switching energy and time. Application of this approach to a wide class of charge-based and non-charge based devices is discussed. The approach suggests pathways for improving the performance of beyond-CMOS devices and a new realistic limit for energy-delay product in terms of the Planks constant.

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arXiv2013

Non-volatile Spin Switch for Boolean and Non-Boolean Logic

We show that the established physics of spin valves together with the recently discovered giant spin-Hall effect could be used to construct Read and Write units that can be integrated into a single spin switch with input-output isolation, gain and fan-out similar to CMOS inverters, but with the information stored in nanomagnets making it non-volatile. Such spin switches could be interconnected, with no external amplification, just with passive circuit elements, to perform logic operations. Moreover, since the digitization and storage occurs naturally in the magnets, the voltages can be used to implement analog weighting for non-Boolean logic.

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arXiv2011

All Spin Logic device with inbuilt Non-Reciprocity

The need for low power alternatives to digital electronic circuits has led to increasing interest in logic devices where information is stored in nanomagnets. This includes both nanomagnetic logic (NML) where information is communicated through magnetic fields of nanomagnets and all-spin logic (ASL) where information is communicated through spin currents. A key feature needed for logic implementation is non-reciprocity, whereby the output is switched according to the input but not the other way around, thus providing directed information transfer. The objective of this paper is to draw attention to possible ASL-based schemes that utilize the physics of spin-torque to build in non-reciprocity similar to transistors that could allow logic implementation without the need for special clocking schemes. We use an experimentally benchmarked coupled spin-transport/ magnetization-dynamics model to show that a suitably engineered single ASL unit indeed switches in a non-reciprocal manner. We then present heuristic arguments explaining the origin of this directed information transfer. Finally we present simulations showing that individual ASL devices with inbuilt directionality can be cascaded to construct circuits.

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arXiv2010

Switching energy-delay of all-spin logic devices

The need to find low power alternatives to digital electronic circuits has led to increasing interest in alternative switching schemes like the magnetic quantum cellular automata(MQCA) that store information in nanomagnets which communicate through their magnetic fields. A recent proposal called all spin logic (ASL) proposes to communicate between nanomagnets using spin currents which are spatially localized and can be conveniently routed. The objective of this paper is to present a model for ASL devices that is based on established physics and is benchmarked against available experimental data and to use it to investigate switching energy-delay of ASL devices.

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arXiv2010

Landauer vs. Boltzmann and Full Dispersion vs. Debye Model Evaluation of Lattice Thermal Conductivity

Using a full dispersion description of phonons, the thermal conductivities of bulk Si and Bi2Te3 are evaluated using a Landauer approach and related to the conventional approach based on the Boltzmann transport equation. A procedure to extract a well-defined average phonon mean-free-path from the measured thermal conductivity and given phonon-dispersion is presented. The extracted mean-free-path has strong physical significance and differs greatly from simple estimates. The use of simplified dispersion models for phonons is discussed, and it is shown that two different Debye temperatures must be used to treat the specific heat and thermal conductivity (analogous to the two different effective masses needed to describe the electron density and conductivity). A simple technique to extract these two Debye temperatures is presented and the limitations of the method are discussed.

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arXiv2009

Voltage Asymmetry of Spin-Transfer Torques

We present a Non-Equilibrium Green's Function based model for spin torque transfer (STT) devices which provides quantitative agreement with experimentally measured (1) differential resistances, (2) Magnetoresistance (MR), (3) In-plane torque and (4) out-of-plane torque over a range of bias voltages, using a single set of three adjustable parameters. We believe this is the first theoretical model that is able to cover this diverse range of experiments and a key aspect of our model is the inclusion of multiple transverse modes. We also provide a simple explanation for the asymmetric bias dependence of the in-plane torque, based on the polarization of the two contacts in energy range of transport.

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arXiv2009

On Landauer vs. Boltzmann and Full Band vs. Effective Mass Evaluation of Thermoelectric Transport Coefficients

The Landauer approach to diffusive transport is mathematically related to the solution of the Boltzmann transport equation, and expressions for the thermoelectric parameters in both formalisms are presented. Quantum mechanical and semiclassical techniques to obtain from a full description of the bandstructure, E(k), the number of conducting channels in the Landauer approach or the transport distribution in the Boltzmann solution are developed and compared. Thermoelectric transport coefficients are evaluated from an atomistic level, full band description of a crystal. Several example calculations for representative bulk materials are presented, and the full band results are related to the more common effective mass formalism. Finally, given a full E(k) for a crystal, a procedure to extract an accurate, effective mass level description is presented.

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arXiv2009

Switching Energy of Ferromagnetic Logic Bits

Power dissipation in switching devices is believed to be the single most important roadblock to the continued down scaling of electronic circuits. There is a lot of experimental effort at this time to implement switching circuits based on magnets and it is important to establish power requirements for such circuits and their dependence on various parameters. This paper analyzes switching energy which is dissipated in the switching process of single domain Ferromagnets used as cascadable logic bits. We obtain generic results that can be used for comparison with alternative technologies or guide the design of magnet based switching circuits. Two central results are established. One is that the switching energy drops significantly if the ramp time of an external pulse exceeds a critical time. This drop occurs more rapidly than what is normally expected of adiabatic switching for a capacitor. The other result is that under the switching scheme that allows for logic operations, the switching energy can be described by a single equation in both fast and slow limits. Furthermore, these generic results are used to quantitatively examine the possible operation frequencies and integration densities of these logic bits which show that nanomagnets can have scaling laws similar to CMOS technology.

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arXiv2009

Conductance asymmetry of graphene pn junction

We use the non-equilibrium Green function (NEGF) method in the ballistic limit to provide a quantitative description of the conductance of graphene pn junctions - an important building block for graphene electronics devices. In this paper, recent experiments on graphene junctions are explained by a ballistic transport model, but only if the finite junction transition width, Dw, is accounted for. In particular, the experimentally observed anamolous increase in the resistance asymmetry between nn and np junctions under low source/drain charge density conditions is also quantitatively captured by our model. In light of the requirement for sharp junctions in applications such as electron focusing, we also examine the pn junction conductance in the regime where Dw is small and find that wavefunction mismatch (so-called pseudo-spin) plays a major role in sharp pn junctions.

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