1. A Review of MTJ Compact Models
Literature Review
A Review of MTJ Compact Models
Richard Dorrance Advisor: Prof. Dejan Marković
April 15, 2011

2. STT-MRAM and How it Works
STT = Spin-Torque-Transfer
Use current to flip free layer between two resistive states

3. Compact Model Requirments
Bias Voltage
Temperature
Probabilistic
Switching
Regions of
Operation

4. [1] J. D. Harms, et al. (U. Minnesota)
Switching time vs. current fitting.
User defined delay for switching.
SPICE.

5. [2] A. Nigam, et al. (UVA & Grandis)
Calculate the total transmission probability and density of available states (implemented in SPICE).
Accuracy: ±10% RP, RAP, TMR
Physics based… I think…
Measured Model

6. [3] L.-B. Faber, et al. (U. Paris XI)
Model switching probabilities across several parameters.
Switching based on user defined threshold and delay.
Inaccurate below 10ns pulse widths.
Switching Probabilities
Spectre Model

7. [4] A. Raychowdhury, (Intel)
Uses a linearized LLGE, modified/fitted for thermally activated switching. Crude bias voltage approximation.
Semi- physics, semi-empirical.

8. [5] D. Datta, et al. (Purdue & UCB)
Uses a Non-Equilibrium Green’s Function (NEGF) based quantum transport model. (Physics Based)
Voltage Bias
Out of Plain Fields

9. [6] M. Madec, et al. (ULP)
Traditional LLGE model for precessional switching.
Modified Jullière conductance model to include bias voltage dependencies.
Thermally activated switching not considered.
VHDL-AMS implementation.

10. Limitations of Current Models
Few model bias voltage dependencies.
No published model incorporates temperature effects.
Empirical models cannot predict behavior.
Most physics models are too cumbersome for compact modeling.
Most models are ill-suited for incorporating statistical variation.

11. References
J. D. Harms, et al., “SPICE Macromodel of Spin-Torque-Transfer-Operated Magnetic Tunnel Junctions,” IEEE Transactions on Electron Devices, vol. 57, no. 6, pp , June 2010.
A. Nigam, et al., “Self Consistent Parameterized Physical MTJ Compact Model for STT-RAM,” CAS 2010, vol. 2, pp , Oct
L.-B. Faber, et al., “Dynamic Compact Model of Spin-Transfer Torque Based Magnetic Tunnel Junction (MTJ),” DTIS '09, pp , April 2009.
A. Raychowdhury, “Model Study of 1T-1STT MTJ” MWSCAS 2010, pp. 5-8, Aug
D. Datta, et al., “Quantitative Model for TMR and Spin-Transfer Torque in MTJ Devices,” IEDM 2010, pp , Dec
M. Madec, et al., “Compact Modeling of Magnetic Tunnel Junction,” NEWCAS-TAISA 2008, pp , June 2008.