A Fokker-Planck Solver to Model MTJ Stochasticity

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 behaviour due to thermal fluctuations, which is modelled 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.