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

In this paper, we systematically evaluate the variation in the reversal delay of a nanomagnet driven by a longitudinal spin current 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 Fréchet 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.