Write error rate of spin-transfer-torque random access memory including micromagnetic effects using rare event enhancement

摘要

Spin-transfer-torque random access memory (STT-RAM) is a promising candidatefor the next-generation of random-access-memory due to improved scalability,read-write speeds and endurance. However, the write pulse duration must be longenough to ensure a low write error rate (WER), the probability that a bit willremain unswitched after the write pulse is turned off, in the presence ofstochastic thermal effects. WERs on the scale of 10$^{-9}$ or lower aredesired. Within a macrospin approximation, WERs can be calculated analyticallyusing the Fokker-Planck method to this point and beyond. However, dynamicmicromagnetic effects within the bit can affect and lead to faster switching.Such micromagnetic effects can be addressed via numerical solution of thestochastic Landau-Lifshitz-Gilbert-Slonczewski (LLGS) equation. However,determining WERs approaching 10$^{-9}$ would require well over 10$^{9}$ suchindependent simulations, which is infeasible. In this work, we explorecalculation of WER using "rare event enhancement" (REE), an approach that hasbeen used for Monte Carlo simulation of other systems where rare eventsnevertheless remain important. Using a prototype REE approach tailored to theSTT-RAM switching physics, we demonstrate reliable calculation of a WER to10$^{-9}$ with sets of only approximately 10$^{3}$ ongoing stochastic LLGSsimulations, and the apparent ability to go further.