A Compact MTJ Model Incorporating Temperature and Voltage Dependencies using Verilog-A

A compact model for MTJs incorporating temperature and voltage dependencies is presented. Written in Verilog-A, the model is intended to aid in the development of emerging spintronics circuits (i.e. STT-MRAM). Matching with detailed micromagnetic simulations and measurements from 65nm CoFeB/MgO/CoFeB MTJs is shown. Introduction Recent advances in MgO based magnetic tunnel junctions (MTJs) show strong potential in STT switched magnetic random access memory (STT-MRAM) [1]. STT-MRAM has the potential to rival the densities of DRAM, the speed of SRAM, and is non-volatile without degrading over time like flash [2]. The greatest hindrance in the design of STT-RAM, and other spintronics circuits, is the lack of a compact MTJ model capable of accurately modeling temperature and voltage dependencies. This work presents such a model implemented in Verilog-A. Also presented is a comparison of the model’s simulation results to a detailed micromagnetic simulator and actual device measurements from 90nm CoFeB/MgO/CoFeB MTJs. Compact Model A. Dynamic Equation The precessional motion of magentization ( ~ M ) of the free layer of a MTJ, in the presence of an external magnetic field ( ~ Heff ) and spin-torque-transfer (STT), can be accurately described by Slonczewski’s generalized Landau-Lifshitz-Gilbert equation (LLGE) [3]. The normalized LLGE with STT is given by: ∂ ~ m ∂t = −γMS ~ m× ( ~heff + Je Jp b (θ) (~ m× ~ p)− α ∂ ~ m ∂t ) , (1) where MS = | ~ M |, γ is the absolute value of the gyromagnetic ratio (γeμ0), ~ m is the unit vector in the direction of ~ M , ~ p is the unit vector in the direction of the magnetization of the fixed layer, ~heff = ~ Heff/Ms, Je is the current density (see Fig. 1), θ is the angle between ~ m and ~ p, and α > 0 is the material dependant Gilbert damping constant. The efficiency factor of spin-polarization (b (θ), see Fig. 2) and the characteristic current density (Jp) are further defined as: