Fundamental Thermal Limits on Data Retention in Low-Voltage CMOS Latches and SRAM

Rezaei, Elahe; Donato, Marco; Patterson, William R.; Zaslavsky, Alexander; Bahar, R. Iris

doi:10.1109/tdmr.2020.2996627

Cited by 17 publications

(11 citation statements)

References 24 publications

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“…After finishing this work we became aware of a recent article [76], in which a similar stochastic description is employed to numerically compute the error rate of a SRAM memory cell. It should be noted that the transition rates employed in that article are actually not thermodynamically consistent, i.e., they do not respect the local detailed balance conditions (which is however not a serious problem in the regime of operation they consider).…”

Section: Discussionmentioning

confidence: 99%

Stochastic Thermodynamics of Non-Linear Electronic Circuits: A Realistic Framework for Computing around kT

Freitas,

Delvenne,

Esposito

2020

Preprint

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We present a general formalism for the construction of thermodynamically consistent stochastic models of non-linear electronic circuits. The devices constituting the circuit can have arbitrary I-V curves and may include tunnel junctions, diodes, and MOS transistors in subthreshold operation, among others. We provide a full analysis of the stochastic non-equilibrium thermodynamics of these models, identifying the relevant thermodynamic potentials, characterizing the different contributions to the irreversible entropy production, and obtaining different fluctuation theorems. Our work provides a realistic framework to study thermodynamics of computing with electronic circuits. We demonstrate this point by constructing a stochastic model of a CMOS inverter. We find that a deterministic analysis is only compatible with the assumption of equilibrium fluctuations, and analyze how the non-equilibrium fluctuations induce deviations from its deterministic transfer function. Finally, building on the CMOS inverter, we propose a full-CMOS design for a probabilistic bit (or binary stochastic neuron) exploiting intrinsic noise.

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Section: Discussionmentioning

confidence: 99%

Stochastic Thermodynamics of Non-Linear Electronic Circuits: A Realistic Framework for Computing around kT

Freitas,

Delvenne,

Esposito

2020

Preprint

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“…Physically, it models the voltage differences due to a single charge transfer (called charging effect), which can become relevant for small devices or at low temperatures [40]. The usual modelling using just the I-V characteristics fails to incorporate it [21,22].…”

Section: Model For the Cmos Invertermentioning

confidence: 99%

Large deviations theory for noisy non-linear electronics: CMOS inverter as a case study

Gopal,

Esposito,

Freitas

2022

Preprint

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The latest generation of transistors are nanoscale devices whose performance and reliability are limited by thermal noise in low-power applications. Therefore developing efficient methods to compute the voltage and current fluctuations in such non-linear electronic circuits is essential. Traditional approaches commonly rely on adding Gaussian white noise to the macroscopic dynamical circuit laws, but do not capture rare fluctuations and lead to thermodynamic inconsistencies. A correct and thermodynamically consistent approach can be achieved by describing single-electron transfers as Poisson jump processes accounting for charging effects. But such descriptions can be computationally demanding. To address this issue, we consider the macroscopic limit which corresponds to scaling up the physical dimensions of the transistor and resulting in an increase of the number of electrons on the conductors. In this limit, the thermal fluctuations satisfy a Large Deviations Principle which we show is also remarkably precise in settings involving only a few tens of electrons, by comparing our results with Gillespie simulations and spectral methods. Traditional approaches are recovered by resorting to an ad hoc diffusive approximation introducing inconsistencies. To illustrate these findings, we consider a low-power CMOS inverter, or NOT gate, which is a basic primitive in electronic design. Voltage (resp. current) fluctuations are obtained analytically (semi-analytically) and reveal interesting features.

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“…A common strategy to reduce the energy consumption of electronic computing devices is to reduce the voltage at which they are powered. However, this strategy is limited by the fact that as the operation voltage is reduced, different sources of electrical noise start to play an increasingly important role [1][2][3][4]. The most fundamental and unavoidable one is given by the thermal fluctuations intrinsic to any device.…”

Section: Introductionmentioning

confidence: 99%

“…It originates from the interaction with degrees of freedom that are not explicitly described, but that can be normally assumed to be at thermal equilibrium. A rigorous description of intrinsic thermal noise in complex and non-linear electronic circuits is thus a fundamental problem in modern engineering, of great importance for the search of new efficient computing schemes [3][4][5][6][7]. However, it is also a hard problem that is usually given approximate treatments involving different kinds of approximations that are difficult to control, and that in general compromise thermodynamic consistency [8,9].…”

Section: Introductionmentioning

confidence: 99%

“…Due to their speed and low-energy consumption, SRAM cells are employed as internal memory in virtually all modern processors. The occurrence of errors induced by thermal noise in low-power implementations has been mainly studied using numerical methods based on stochastic simulations [4,10]. The reason is that in low-power regimes, current fluctuations are Poissonian and cannot be faithfully described as Gaussian noise [11], which considerably complicates analytical treatments.…”

Section: Introductionmentioning

confidence: 99%

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Reliability and entropy production in nonequilibrium electronic memories

2022

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We find the relation between reliability and entropy production in a realistic model of electronic memory (lowpower metal-oxide-semiconductor-based SRAM) where logical values are encoded as metastable nonequilibrium states. We employ large deviation techniques to obtain an analytical expression for the bistable quasipotential describing the nonequilibrium steady state and use it to derive an explicit expression bounding the error rate of the memory. Our results go beyond the dominant contribution given by classical instanton theory and provide accurate estimates of the error rate as confirmed by comparison with stochastic simulations.

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Fundamental Thermal Limits on Data Retention in Low-Voltage CMOS Latches and SRAM

Cited by 17 publications

References 24 publications

Stochastic Thermodynamics of Non-Linear Electronic Circuits: A Realistic Framework for Computing around kT

Stochastic Thermodynamics of Non-Linear Electronic Circuits: A Realistic Framework for Computing around kT

Large deviations theory for noisy non-linear electronics: CMOS inverter as a case study

Reliability and entropy production in nonequilibrium electronic memories

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