Energy-Efficient Computing With Probabilistic Magnetic Bits—Performance Modeling and Comparison Against Probabilistic CMOS Logic

This paper focuses on the design, performance modeling, and evaluation of probabilistic logic using superparamagnetic nanomagnets for which there exists a strong interplay between deterministic dynamics and intrinsic thermal noise. The switching element in the spin domain is chosen as the giant spin-Hall effect (GSHE) device that operates based on the dipolar coupling phenomenon in a two-magnet system to achieve low-energy ( $\approx ~1.3$ fJ/b) and low-power ( $\approx ~0.5~\mu $ W) switching characteristics. The use of spin currents on the order of a few tens of mA/ $\mu $ m2 in the subcritical regime to operate the GSHE device yields nondeterministic switching behavior with probability of correctness less than 100%. Therefore, the proposed technique allows us to trade off circuit accuracy for tremendous reduction in energy and power dissipation. In this paper, we identify the required dimensions and material parameters of the read–write units to ensure robust magnetic dipolar coupling for reliable operation of the GSHE switch. Then, through Monte Carlo simulations, we evaluate the probabilistic switching behavior of the GSHE switch as a function of the input spin current amplitude and pulsewidth for various orientations of the magnetization vectors. The delay of the GSHE switch is quantified using a probability distribution function owing to the randomness imparted to the dynamics by intrinsic thermal noise of the nanomagnets. The relationship between the probability of correctness and the energy dissipation of the GSHE switch is quantified. The results are extended to evaluate the performance and circuit error rate of complex logic gates, such as NAND and NOR, constructed using the GSHE switch. It is shown that unlike the probabilistic CMOS (PCMOS) logic, the circuit error rate in the GSHE logic becomes a function of the input vector combination and the prior state of the switch. These nuances are captured in the compact model of the circuit error rate of multiple-input GSHE logic developed in this paper. The performance of the probabilistic GSHE logic is compared with that of PCMOS logic at the 14 nm technology node. Since the noise generation process in PCMOS logic has a limited bandwidth of tens of megahertz and consumes tens of microwatt power, the peripheral circuitry becomes prohibitive. By utilizing the inherent thermal stochasticity, nanomagnets provide a clear advantage to implement probabilistic computing platform targeted toward error-tolerant applications such as those from the image processing and machine learning domains.