Electrical Modeling of Stochastic Spin Transfer Torque Writing in Magnetic Tunnel Junctions for Memory and Logic Applications

Magnetic tunnel junctions (MTJ) are considered as one of the most promising candidates for the next generation of nonvolatile memories and programmable logic chips. Spin transfer torque (STT) in CoFeB/MgO/CoFeB MTJs with perpendicular magnetic anisotropy (PMA) exhibits noticeable performance enhancements compared to that with In-plane magnetic anisotropy, particularly in terms of thermal stability, critical current for switching, access speed and power consumption. However, the STT switching of MTJ has been revealed stochastic, which results from unavoidable thermal fluctuations of magnetization. This leads to the occurrence of write errors which deeply affects the reliability of hybrid CMOS/MTJ circuits. In this paper, we present the first spice-compact model of CoFeB/MgO/CoFeB structure PMA-MTJ integrating STT stochastic behaviors. Depending on the relative magnitude between the switching current (I) and the critical current (Ico), the STT stochastic behaviors of this PMA-MTJ can be categorized into two regions: Sun model (I > Ico) and Neel-Brown model (I < 0.8Ico). The Monte-Carlo simulations for single cell and hybrid CMOS/MTJ circuits show the stochastic behaviors in both writing and sensing operations. This model can be very useful for investigating the reliability issues during the design and simulation before process fabrication.