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Compact Modeling of MTJs for use in STT-MRAM

Richard DorranceAdvisor: Prof. Dejan Marković

March 12, 2010

Progress Update

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]

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

Basic MTJ Structure

4

Spintronic Operation

5

Spin Injector/Polarizer– Ferromagnetic layers tend to spin-polarize a current

Spin Detector– Ferromagnetic layers tend to scatter anti-parallel currents

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

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

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

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

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

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

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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