Electrical Modeling of Double-Barrier Magnetic Tunnel Junc-tion with Reliability Analyses

Abstract

With the shrinking of complementary metal oxide semiconductor (CMOS) technology size, the considerable power consumption on logic and memory circuit system has been becoming an unavoidable bottleneck [1]. Spin transfer torque magnetoresistive memories (STT-MRAMs) are prime candidates for non-volatile memory applications. As the basic storage unit of STT-MRAM, magnetic tunnel junction (MTJ) has been extensively studied [2]–[4]. For instance, double-barrier MTJ (DMTJ), taking advantages of the enhancement of STT effect, significantly reduces the critical switching current $(\mathrm {I}_{C0})$ and switching duration $(\tau)$ [5]. MTJ with two CoFeB free layers (FLs) coupled by Ta layer can effectively improves the thermal stability $\left({ \Delta\mathrm {E}}\right)$ [6]. In this paper, we proposed an electrical modeling of DMTJ with CoFeB/Ta/CoFeB FLs (see Fig. 1 (a)). Compared with conventional MTJ, the propose DMTJ has superiorities in $\mathrm {I}_{C0}$, $\tau $, and $ \Delta\mathrm {E}$. It can replace MTJ to reduce the device size, improve the reliability of memory and lower the writing energy consumption. Furthermore, this model integrates the stochastic STT switching behavior, the temperature influence and the variation of the layers' thicknesses, which can deeply affect the reliability of hybrid CMOS/MTJ circuits. Fig. 1 (b) shows the principle block diagram of the integrated physical models. In the following, we explain some key blocks modeled in the Verilog-A code. For DMTJ, STTs generated by both the transmitted and reflected spin polarized electrons add together. This enhancement strongly decreases the $\mathrm {I}_{C0}$ and $\tau $, which can be expressed as\begin{align*} \mathrm {I}_{C0}= 2 \alpha \gamma \mathrm {e}\times (\mathrm {K}_{EFF} \times Volume)/ \mu _{B} \mathrm {g}_{DMTJ}(1) (1) \tau =\left[{ \mathrm {C}+ In \left({ \pi ^{2} \Delta\mathrm {E}/ 4 }\right) }\right] \times (em/ 4 \mu _{B} \mathrm {g}_{DMT} \mathrm {J}) \times (\mathrm {I}_{write}- \mathrm {I}_{C0})^{-1}(2)\end{align*}