Analysis and Compact Modeling of Magnetic Tunnel Junctions Utilizing Voltage-Controlled Magnetic Anisotropy

A macrospin compact model of a perpendicularly magnetized voltage-controlled magnetic tunnel junction (MTJ) is introduced, for the evaluation of electronic and magnetic characteristics associated with its switching behavior. The voltage-driven precessional switching has been shown to outperform current-driven switching in terms of energy, speed, and bit density. However, to realize the device in embedded system memory applications, developing a compact model for simulating hybrid MTJ/CMOS circuits is necessary. This framework also needs to be compatible with conventional computer-aided circuit design tools and flows. In this paper, the voltage-controlled magnetic anisotropy effect is included as a component of the effective magnetic field in a Landau-Lifshitz-Gilbert (LLG) equation-based model. The compact model is described by Verilog-A, providing a numerical solution for a 3-D magnetization trajectory and the corresponding conductance change of the MTJ. We also include the thermal noise effect in the LLG equation to allow the evaluation of stochastic switching behavior under a wide variety of bias conditions, which can be quantified in terms of write error rate (WER). It is shown that the model allows for optimization of write pulse shape and design considerations to achieve the lowest WER for given MTJ parameters.