Analytical Macrospin Modeling of the Stochastic Switching Time of Spin-Transfer Torque Devices

Owing to their nonvolatility, outstanding endurance, high write and read speeds, and CMOS process compatibility, spin-transfer torque magnetoresistive memories (MRAMs) are prime candidates for innovative memory applications. However, the switching delay of their core components-the magnetic tunnel junctions (MTJs)-is a stochastic quantity. To account for this in electronic design, only partial models (working in extreme regimes) are available. In this paper, we propose an analytical model for the stochastic switching delay of a current-driven MTJ, with in-plane magnetization, that agrees with physical simulations, from low- to high-current regimes through intermediate regime. We performed physical macrospin simulations of MTJs for a wide range of current. We developed an analytical model for the mean switching delay that fits those simulations results, and smoothly connects well-accepted models for the extreme low and extreme high currents limits. In addition, a probability distribution in agreement with our simulations results is proposed, leading to a full model of the stochastic switching delay. An example for the application of the model is proposed. Our analytical model can help to evaluate the error rate in MRAM designs, and allow designing innovative electronic circuits that exploit the intrinsic stochastic behavior of MTJs as a beneficial feature.