Influence of Size and Shape on the Performance of VCMA-Based MTJs

In this paper, we investigate the relationship between size, shape, and the performance of the voltage-controlled magnetic anisotropy (VCMA)-based magnetic tunnel junctions (MTJs) suitable for gigabit scale MRAMs with 10 years of retention time. A Fokker-Planck simulation framework is developed to model the magnetization dynamics in the presence of thermal noise. Here, we numerically show that the optimization of the MTJ geometry can significantly improve the performance of the VCMA-based MTJs. Using an elliptical MTJ with aspect ratio (AR) of 3 reduces the required supply voltage and energy consumption by 80.7% and 92%, respectively, compared to a circular MTJ when the minimum feature size is 50 nm. The design requirements on the VCMA coefficient, {\xi } , are also reduced by 67%. However, the influence of AR is observed to diminish with reduction in the minimum feature size of the MTJ. For instance, when the minimum feature size is 20 nm, the required supply voltage and energy consumption reduce only by 60.29% and 65.30%, respectively. We, then, perform a comprehensive scaling analysis on the VCMA-based MTJs by varying size, geometry, and {\xi } of the MTJs. The predicted scaling trends are then compared with those of the STT MTJs.