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.

I. Introduction

Spintronics is an emergent technology beyond CMOS which can help reducing the static and dynamic power consumption of CMOS circuits beyond the 90 nm technology node [1]. Magnetic tunnel junctions (MTJ) are key basic elements in spintronics. They essentially consist of three layers (a thin tunnel oxide layer sandwiched between two ferromagnetic (FM) layers) [2]. Due to the tunnel magnetoresistance (TMR) effect, the nanopillar resistance, or , depends on the relative orientation, Parallel (P) or Anti-Parallel (AP), of the magnetization of the two FM layers [3]. Remarkably, in MgO based MTJs, the can reach a quite high value (e.g., >600%) at room temperature, which allows the state of MTJs to be easily detected by CMOS sense amplifiers [4]. It is possible to switch from one configuration to the opposite by using the Spin-Transfer Torque phenomenon (STT) [Fig. 1(a)]. Nowadays, STT-RAM are regarded as one of the most promising candidates for next generation of nonvolatile memories and programmable logic chips thanks to their performances in terms of power consumption, miniaturization and integration with CMOS process [5], [6]. MTJ with perpendicular magnetic anisotropy (PMA) attract even more attention compared to their In-plane magnetized counterparts because of their improved performances in many aspects [7], [8]. STT PMA MTJ can combine good thermal stability, low critical current and high access speed. We presented recently a spice compact model for memory and logic simulation, which integrates the static and dynamic behaviors of STT PMA MTJ [9]. Fig. 1.

(a) Spin transfer torque switching mechanism: the MTJ state changes from parallel (P) to anti-parallel (AP) under positive electron flow direction . It changes from AP to P under negative electron flow direction . Note that the red arrows represent the electron flow and not the current (b) experimental measurement of STT stochastic switching behaviors, high writing current drives faster speed and higher switching probability.