A Variation-Aware Timing Modeling Approach for Write Operation in Hybrid CMOS/STT-MTJ Circuits

In this paper, a variation-aware simulation framework for hybrid circuits comprising MOS transistors and magnetic tunnel junction (MTJ) devices is presented. The framework is based on one-time characterization via micromagnetic multi-domain simulations, overcoming the inaccuracies introduced by single-domain analysis, which most of the existing frameworks are based on. As further distinctive capability, non-Gaussian stochastic variations of the MTJ write switching time are explicitly modeled through a Skew Normal distribution, making the model suitable for low-power and low-voltage designs. The framework involves the use of a Verilog-A look-up table-based model, which assures easy integration with commercial design tools. Our strategy is evaluated on a spin-transfer torque-magnetoresistive random access memory (MRAM) working in RAM and true random number generator (TRNG) modes. In RAM mode, while the commonly-used approach based on Gaussian-distributed switching statistics tends to underestimate the pulse width required for a write error rate of 10⁻⁶ by about 20%, our Skew Normal-based strategy allows tracking reference micromagnetic results with an average error less than 4%. In TRNG mode, our approach also allows a better tracking of the reference 50%-switching probability contour with an error less than 1%. However, the incorporation of the Skew Normal distribution in our Verilog-A model results in an increase of the CPU time by 50% on average as compared with the use of the built-in statistical functions.