1. 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

2. 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

3. STT-MRAM

4. Basic MTJ Structure

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

6. 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

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

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

9. 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: seconds

10. Simulation Results
b(θ) not
implemented

11. 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

12. References
[1] J. C. Slonczewski, J. Magn. Magn. Mater., vol. 159, pp. L1 – L7, [2] A. Raghunathan, et al., Magnetics, IEEE Trans., vol. 45, pp. 3954–3957, Oct [3] C. H. Shang, et al., Phys. Rev. B, vol. 58, pp. R2917–R2920, Aug [4] Y. Lu, et al., J. Appl. Phys. vol. 83, no. 11. AIP, 1998, pp. 6515–6517. [5] X. Kou, et al., Applied Physics Letters, vol. 88, no. 21, p , [6] P. Wiśniowski, et al., Physica Status Solidi, vol. 201, pp. 1648–1652, [7] P. Padhan, et al., Applied Physics Letters, vol. 90, no. 14, p , 2007.