Compact Modeling of MTJs for use in STT-MRAM
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Compact Modeling of MTJs for use in STT-MRAM
Richard DorranceAdvisor: Prof. Dejan Marković
March 12, 2010
Progress Update
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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
2
-400 -200 0 200 4001.5
2
2.5
3
3.5
4
4.5
Res
ista
nce
[k
]
Current [A]
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STT-MRAM
3
STDArray
(1K)
LVTArray
(2K)
STDArray
(1K)
LVTArray
(2K)
RowDecoder
RowDecoder
COL MUX
COL MUX
Sense Amp& I/O Buffer
COL MUX
COL MUX
Sense Amp& I/O BufferR
ow
Pre
-De
cod
er
CO
LD
eco
de
r
BL_
L<
7>
BL_
L<
6>
BL_
L<
0>
BL_
R<
7>
BL_
R<
6>
BL_
R<
0>
BL_
M<
1>
BL_
M<
0>
BL_
L<
15
>
BL_
L<
14
>
BL_
L<
00
>
BL_
R<
15
>
BL_
R<
14
>
BL_
R<
00
>
BL_
M<
1>
BL_
M<
0>
BL
_L
<7
>
BL
_L
<6
>
BL
_L
<0
>
BL
_R
<7
>
BL
_R
<6
>
BL
_R
<0
>
BL
_M
<1
>
BL
_M
<0
>
BL
_L
<1
5>
BL
_L
<1
4>
BL
_L
<0
0>
BL
_R
<1
5>
BL
_R
<1
4>
BL
_R
<0
0>
BL
_M
<1
>
BL
_M
<0
>
CSEL_T<3:0>
CSEL_B<3:0>
EN_T_EV
EN_T_OD
EN_B_EV
EN_B_OD
MB
L_
L
MB
L_
R
RBL_L RBL_R
MB
L_
L
MB
L_
R
RBL_L RBL_R
MB
L_L
MB
L_R
RBL_L RBL_R MB
L_L
MB
L_R
RBL_L RBL_R
WL_T<63>
WL_T<62>
WL_T<61>
WL_T<02>
WL_T<01>
WL_T<00>
WL_B<63>
WL_B<62>
WL_B<61>
WL_B<02>
WL_B<01>
WL_B<00>
D<1:0>
Q<1:0>
D<3:2>
Q<3:2>
A<2:0>A<8:3> A<9>
COL RES
COLRES
PROGRES
COL RES
COLRES
PROGRES
R_
L<
7>
R_
L<
0>
R_
R<
7>
R_
R<
0>
R_
M
R_
L<
7>
R_
L<
0>
R_
R<
7>
R_
R<
0>
R_
M
COL RES
COLRES
PROGRES
COL RES
COLRES
PROGRES
R_
L<7
>
R_
L<0
>
R_
R<
7>
R_
R<
0>
R_
M
R_
L<7
>
R_
L<0
>
R_
R<
7>
R_
R<
0>
R_
MMUX (17-to-1) MUX (17-to-1)RSEL<16:0> RSEL<33:17>
PR
B1
PR
B0
RPROG<3:0>
Poly
n+ n+
M1
M2SL
WL M3
M4
MTJ
M5 BL
To Sense Amp
WL
BL
SL
fingersnm
m
L
W2
80
27.1
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Basic MTJ Structure
4
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Spintronic Operation
5
Spin Injector/Polarizer– Ferromagnetic layers tend to spin-polarize a current
Spin Detector– Ferromagnetic layers tend to scatter anti-parallel currents
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Compact Model
6
t
mpmb
J
JhmMγ
t
m
p
eeffS
1
2/33
4
cos314
PPb
Be
SSp g
deMMγJ
Landau–Lifshitz–Gilbert Equation
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
SM
effh
m
dBeeJegP
p
2( ) 1 cos( )T SIG G P G
TG SIG
Julliere’s Conductance Model
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Temperature Nonlinearities
7
Saturation Magnetization– Weiss theory of ferromagnetism
Spin-Polarization– Affects resistance and STT– Modeled by:
0( ) 1s s CM T M T T
3/20( ) 1 spP T P T
0 Tc/3 2Tc/3 Tc0
0.2
0.4
0.6
0.8
1
MS/M
S0
0 100 200 300 400100
200
300
400
500
TM
R [
%]
Temperature [K]
Mod[5][7]Exp
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Voltage Nonlinearities
TMR changes for an applied bias voltage– Simple fitting function
8
200
1,
VV
TTMRVTTMR
-400 -200 0 200 400
100
110
120
130
140
150
160
TM
R [
%]
VBIAS
[mV]
MeasuredModel
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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
9
ExperimentalMTJ data
W L Ms0 TC B GT
d tox P0 sp V0 GSI
Device parametersVerilog-A
magneticsimulator
V I T
TMR RP R(T) R’(T)
Simulation env.
Compact model
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Simulation Results
10
0 10 20 300.5
1.0
1.5
2.0
Res
ista
nce
[k
]
Time [ns]
TEMPERATURE: 380 K
MODEL -MAG SIM
0 10 20 300.5
1.0
1.5
2.0
Res
ista
nce
[k
]
Time [ns]
TEMPERATURE: 300 K
MODEL -MAG SIM
b(θ) notimplemented
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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
11
3rd Magnetic Layer
(Perpendicular)– easier to switch– switching has greater thermal independence
1
2/33
4
cos314
PPb
1cos BAPb
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References
[1] J. C. Slonczewski, J. Magn. Magn. Mater., vol. 159, pp. L1 – L7, 1996.
[2] A. Raghunathan, et al., Magnetics, IEEE Trans., vol. 45, pp. 3954–3957, Oct. 2009.
[3] C. H. Shang, et al., Phys. Rev. B, vol. 58, pp. R2917–R2920, Aug 1998.
[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. 212115, 2006.
[6] P. Wiśniowski, et al., Physica Status Solidi, vol. 201, pp. 1648–1652, 2004.
[7] P. Padhan, et al., Applied Physics Letters, vol. 90, no. 14, p. 142105, 2007.
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