A Fokker-Planck Solver to Model MTJ Stochasticity

TL;DR

This paper develops and benchmarks Fokker-Planck equation solvers for modeling the stochastic switching behavior of Magnetic Tunnel Junctions in MRAM, including a calibration method for silicon data.

Contribution

It introduces a regression scheme to calibrate MTJ models with silicon data, enabling accurate circuit-level simulations.

Findings

Finite Volume Method and analytical solvers are benchmarked for FP equations.

A regression scheme effectively fits MTJ parameters to measured data.

Silicon-calibrated models improve MRAM macro transient simulations.

Abstract

Magnetic Tunnel Junctions (MTJs) constitute the novel memory element in STT-MRAM, which is ramping to production at major foundries as an eFlash replacement. MTJ switching exhibits a stochastic behavior due to thermal fluctuations, which is modeled by s-LLGS and Fokker-Planck (FP) equations. This work implements and benchmarks Finite Volume Method (FVM) and analytical solvers for the FP equation. To deploy an MTJ model for circuit design, it must be calibrated against silicon data. To address this challenge, this work presents a regression scheme to fit MTJ parameters to a given set of measured current, switching time and error rate data points, yielding a silicon-calibrated model suitable for MRAM macro transient simulation.