Compact Modeling of MTJs for use in STT-MRAM Progress Update Compact Modeling of MTJs for use in STT-MRAM Richard Dorrance Advisor: Prof. Dejan Marković March 12, 2010

Motivation Magnetic Tunnel Junctions (MTJs) exhibit magnetic hysteresis Excellent potential as memory Integratable with CMOS Non-volatile Spin-Transfer-Torque (STT) is a recently discovered phenomena Predicted in 1996, observed in 2000 No good compact model currently exists Existing models oversimplify and ignore critical nonlinearities (temperature and voltage) Problem for simulating STT-MRAM

STT-MRAM

Basic MTJ Structure

Spintronic Operation Spin Injector/Polarizer Ferromagnetic layers tend to spin-polarize a current Spin Detector Ferromagnetic layers tend to scatter anti-parallel currents

Compact Model Landau–Lifshitz–Gilbert Equation Julliere’s Conductance Model Direction of Magnetization of the Free Layer % of Electrons Spin-Polarized in the p Direction Direction of Magnetization of the Fixed Layer Landé Factor of an Electron “Normalized” Effective Magnetic Field Current Density Magnetization Saturation Absolute Value of Electron Charge Gilbert Damping Constant Bhor Magneton Gyromagnetic Ratio Thickness of the Free Layer Conductance due to Elastic Tunneling Spin-independent Conductance

Temperature Nonlinearities Saturation Magnetization Weiss theory of ferromagnetism Spin-Polarization Affects resistance and STT Modeled by:

Voltage Nonlinearities TMR changes for an applied bias voltage Simple fitting function

Simulation Setup Compare transient behavior of MTJ model with a commercially available Micromagnetic Simulator: ±1 mA, 10 ns pulses (30 ns total) Total simulation time: Micromagnetic Simulator: 13.5 hours Verilog-A Model: 0.750 seconds

Simulation Results b(θ) not implemented

Future Work Validation/refinement of model to measured devices Explore the use of fitted function to replace b(θ) b(θ) currently model a simple 5-layer structure MTJ have 20+ layers with synthetic ferromagnets Model C-STT 3rd Magnetic Layer (Perpendicular) easier to switch switching has greater thermal independence

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