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MTJ Matlab Model

MTJ Matlab Model. A Physics Based Approach. The Landau–Lifshitz–Gilbert Equation. Describes the precessional motion of magnetization in a solid. (Magnetization is related to magnetic field by µ 0 ) The equation can be modified to include Spin Torque Transfer via Slonczewski's STT term:.

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MTJ Matlab Model

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  1. MTJ Matlab Model A Physics Based Approach

  2. The Landau–Lifshitz–Gilbert Equation • Describes the precessional motion of magnetization in a solid. (Magnetization is related to magnetic field by µ0) • The equation can be modified to include Spin Torque Transfer via Slonczewski's STT term:

  3. The Full LLG + STT Model

  4. Matlab Simulation Results • Implemented in 3 Matlab files: • instantiateMTJ.m: creates an MTJ object • MTJtransient.m: simulates a single time step given an input current to the MTJ • getMTJresistance.m: calculates the resistance across the MTJ. (Assumed to be linear between Rp and Rap) • Observed DC and AC response of the model appears to correlate very well to published MTJ behavior. • Simulation results use the following MTJ parameters (extracted from Ilya’s MTJ cell moding email):

  5. Simulated DC Response (1) Switching Current: ~432 μA

  6. Simulated DC Response (2) Switching Voltage: ~620 mV

  7. Simulated AC Response (1)

  8. Simulated AC Response (2)

  9. Simulated AC Response (3) High Frequency Resistance Oscillations

  10. Simulated AC Response (4) ~1.5 ns difference in switching times

  11. Summary of Results • DC Response • Behaves very similar to literature • Predicted switching threshold of 432 μA, very close to Ilya’s prediction. • AC Response • Switching is delayed, resistance change is rapid • Resistance displays damped oscillations during switching • Resistance oscillates when near switching current (does this actually happen?) resulting in a lower “DC” resistance • Small variations in the MTJ can have a large impact on switching delay

  12. Future Work • Current Matlab model does not take into account temperature dependences. • Model could be easily adapted to capture temperature effects • Develop model into VerilogA and SPICE • SPICE implementation potentially problematic • Fit model to experimental MTJ data from Ilya

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