Post on 02-Feb-2016
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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 µ0)
The equation can be modified to include Spin Torque Transfer via Slonczewski's STT term:
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t
mmMhmM
t
mSeffS
pj mmmT xS
j tMe
JT
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The Full LLG + STT Model
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Transfer TorqueSpin
Effect Damping :Gilbert
Lifshitz–Landau
pjSeffS mmmTt
mmMhmM
t
m
xSj tMe
JT
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Material Magnetization Reduced Planck constant
Magnetization Saturation Torque Factor of Current
Effective Magnetic Field Current Density
Damping Constant Elementary Charge
Gyromagnetic Ratio Permeability of Free Space
Vector Direction of the Spin Torque Thickness of the Magnetic Layer
SM
effh
m
pm xt0eJ
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):
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RP 640Ω Length 140nm
RAP 1550Ω Width 90nm
α 0.01 Thickness 1nm
Simulated DC Response (1)
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-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 10
200
400
600
800
1000
1200
1400
1600
1800
2000
Applied Current (mA)
Mea
sure
d R
esis
tanc
e (
)MTJ Resistance vs. Current
Switching Current:~432 μA
Simulated DC Response (2)
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-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 10
200
400
600
800
1000
1200
1400
1600
1800
2000
Applied Voltage (V)
Mea
sure
d R
esis
tanc
e (
)MTJ Resistance vs. Voltage
Switching Voltage:~620 mV
Simulated AC Response (1)
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0 2 4 6 8 10 12 14 16 18 20500
600
700
800
900
1000
1100
1200
1300
1400
1500
1600
Time (ns)
Mea
sure
d R
esis
tanc
e (
)
Sample Transient Response of MTJ:Above Switching Threshold
Rp
RapMTJ Resistance
Simulated AC Response (2)
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0 2 4 6 8 10 12 14 16 18 20500
600
700
800
900
1000
1100
1200
1300
1400
1500
1600
Time (ns)
Mea
sure
d R
esis
tanc
e (
)
Sample Transient Response of MTJ:Well Below Switching Threshold
Rp
RapMTJ Resistance
Simulated AC Response (3)
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0 2 4 6 8 10 12 14 16 18 20500
600
700
800
900
1000
1100
1200
1300
1400
1500
1600
Time (ns)
Mea
sure
d R
esis
tanc
e (
)
Sample Transient Response of MTJ:Very Near, But Not Above Switching Threshold
Rp
RapMTJ Resistance
High Frequency Resistance Oscillations
Simulated AC Response (4)
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0 2 4 6 8 10 12 14 16 18 20500
600
700
800
900
1000
1100
1200
1300
1400
1500
1600
Time (ns)
Mea
sure
d R
esis
tanc
e (
)Varying the Layer Thickness by 5%
Nominal
-5%+5%
~1.5 ns difference in switching times
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
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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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