A Probability-Density Function Approach to Capture the Stochastic Dynamics of the Nanomagnet and Impact on Circuit Performance

TL;DR

This paper models the stochastic switching delay of nanomagnets using a probability density function approach, evaluating its impact on the performance of spin-based logic circuits, especially under thermal noise influences.

Contribution

It introduces a novel PDF-based model for nanomagnet switching delays and extends it to complex circuits, providing insights into delay variation effects on circuit performance.

Findings

Delay variation is significant in series nanomagnet configurations.

The PDF model accurately captures nanomagnet switching delay distribution.

Device-level variations notably affect circuit behavior, especially in series arrangements.

Abstract

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.