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A Comprehensive Study on Interface Perpendicular MTJ Variability

Won Ho Choi, Jongyeon Kim, Ibrahim Ahmed, and Chris H. Kim

University of MinnesotaDept. of ECE

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Outline• Introduction• Interface Perpendicular MTJ (I-PMTJ)• Strategy for PMTJ Variability Analysis• Variation Factors and Material Parameters• Variability Analysis Results• Conclusion

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Interface Perpendicular Magnetic Tunnel Junction (I-PMTJ)

• Discovery of interface anisotropy in CoFeB [3] • Perpendicular anisotropy when tF < tc (critical thickness,

~1.5nm)• Maturity from CoFeB+MgO but limited thermal stability• Double MgO is used to increase thermal stability [4, 5]

Hk⊥

Hdz

Free layerTunnel barrier

Pinned layer

1.00.5My-

1.01.00.0-

0.5

-1.0 -

0.5 0.00.5

0.0

0.5

1.0

-0.5

-1.0

Mx

Mz

H. Sato, et al., Journal of Magnetics, 2014.

[3] S. Ikeda, et al., Nature Mater., 2011. [4] H. Sato, et al., APL, 2012. [5] K. Tsunoda, et al., IEDM, 2014.

J. Kim, et al., DRC, 2014.

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I-PMTJ Dimensional-Dependent Parameters

• Hk, ∆, and IC of interface perpendicular magnetic tunnel junction (I-PMTJ) depend on dimension parameters

: Parameters that depend on I-PMTJ dimensions

TkVMH

B

seffk

2⋅⋅

=∆ ⊥

sdzF

i

sef fk MN

tK

MH ⋅⋅−⋅=⊥ π4)()2(

ηα

⋅⋅⋅⋅

= ⊥

VHMeI effkS

C

)(2

ParameterThermal stabilityEffective perpendicular anisotropy field Critical switching current Volume of the magnet Thickness of the free layer Interface anisotropy energy density Magnetic damping factor Saturation magnetization Demagnetizing factor in z direction Boltzmann constant Absolute temperature Reduced Planck’s constantSpin transfer efficiency

Description Δ Hk eff ICVtF Ki α MsNdz kB T ћη

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Methodology for I-PMTJ Variability Analysis

Magnet dimensions to meet ∆

Ic (tsw=5ns)

Quadratic mean initial angle:

Macrospin simulationDimension dependent HKeff

Free layer magnetization:Fixed layer magnetization:

Spin torque amplitude:

LLG solving:

Δ

STT components (Precessional switching)

,)/(2 2

TkVMNtt

B

sdzFc −=∆

π

F

cs

ttMK

22π=⊥

sF

sst Met

JA2

=

)](),(),([4)]()/2(,0,0[)(

tMNtMNtMNMtMMKtH

zdzydyxdxs

zSeffK

⋅−= ⊥⊥

π

)()(1 2

is tK effK eff MMMAHMMHMd tMd

××⋅+××⋅−×−=⋅+ αγα

],,[ iziyixi MMMM =)](),(),([)( tMtMtMtM zyx=

)2/1(sin 1 ∆= −θ

W, L, tF → Ndx, Ndy, Ndz

W L tF

Monte Carlo simulation Random variables extraction with 3σ

Variability analysisEvaluation of IC, ∆, tretention variability

Magnet material specification

Ms, α, P, tc

System specificationFchip: Chip failure rate, m: Memory size, tretension: Retention time

∆−−−= )exp(exp10τ

retentionchip

tmF

W L tF 3σ 3σ 3σ

• Dedicated MTJ model for variability analysis by incorporating dimension-dependent HKeff into LLG equation

Variation Factors and Material Parameters

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64MB L3 cache memory, Δ = 70 for 10yrs retention

Sat. Magnetization, MS (103A/m)

Interface

1077

Polarization factor, P 0.6

Length, width of free layer, L, W (nm)

μ=22, μ=22(3σ/μ=12%***)

Gilbert Damping, α tF dependent**

Thickness of free layer, tF (nm) μ=2.78(3σ/μ=4***~9%)

Effective critical thickness, tC (nm) 3 (1.5 x 2, double MgO interface*)

Quantity PMTJ [3], [5], [6]

* To increase the Δ for 10yrs retention, double MgO interface is used [5]** tF dependent α is used [3], *** ITRS roadmap

Anisotropy source

[3] S. Ikeda, et al., Nature Mater., 2011. [5] K. Tsunoda, et al., IEDM, 2014. [6] J. Hayakawa, et al., Jpn. JAP, 2005.

Simulated IC and Its Variation

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I C (µ

A)

Occ

urre

nce

050

100150200250300350400450500

0 2 4 6 8 100

50100150200250300350400450500

20 40 60 80 100

358K, Δ = 70 for 10yrs retention358K, Δ = 70 for 10yrs retention

µ=61.22, σ/µ=5.6%@ tSW =5ns

tSW (ns) IC (µA)

3σ/μ of W, L = 12%, 3σ/μ of tF = 4%

tSW =5ns

• A constant switching time tsw of 5ns was chosen for all variability simulations

• IC roughly follows a Gaussian distribution

∆ (Thermal Stability Factor) and tretentionVariations

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• ∆ and log(tretention) roughly follow Gaussian distributions• Over 40% of the MTJs fail to meet the 10 year retention

time target

Occ

urre

nce

∆ (Thermal Stability Factor)

Occ

urre

nce

t retention (s)

10yrs

0

50

100

150

200

250

300

350

400

450500

50 60 70 80 90 100

µ = 70.17, σ/µ = 5.2%

0

50

100

150

200

250

300

101 105 109 1013 1017

358K, Δ = 70 for 10yrs retention

σ = 2.2e+12@ tSW =5ns @ tSW =5ns

3σ/μ of W, L = 12%, 3σ/μ of tF = 4%358K, Δ = 70 for 10yrs retention3σ/μ of W, L = 12%, 3σ/μ of tF = 4%

tF Variation versus ∆ Variation

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• ∆ variation depends strongly on tF variation• Retention time variation estimated from ∆ variation

4

5

6

7

8

9

3 4 5 6 7 8 9 103σ/μ of tF (%)

σ/μ

of Δ

(%)

358K, Δ = 70 for 10yrs retention, 3σ/μ of W, L = 12%

tretention versus IC Variation Plots

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• tretention variability has a stronger dependency on tFvariation compared to IC variability

3σ/μ of tF = 4%

40

60

80

100

10-3 105 1013 1021 1029

t retention (s)10-3 105 1013 1021 1029

t retention (s)

10yrs 10yrs

3σ/μ of tF = 9%358K, 3σ/μ of W, L = 12%

I C (µ

A)

σ tretention, 4%

Δ = 70

358K, 3σ/μ of W, L = 12%

Δ = 70

σ tretention, 9%

σ IC, 4% σ IC, 9%

Variability-Considered ∆ Overdesign [10]

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• ∆ will have to be overdesigned (Δ1 Δ2) to ensure that all MTJs meet the target retention time

0

250

500

40 60 80 100Δ (a.u.)

Typical Δ design:

When Δ is increased: All samples meet the spec.

Occ

urre

nce

(a.u

.)

System spec.

Out of spec.

Δ1 Δ2

[10] K. Hofmann, et al., VLSI Tech. Symp. 2014.

Re-plotted Correlation Maps after Increasing ∆

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• IC increases when overdesigning ∆• Tighter tF control (9%4%) results in lower ∆ (8782)

and IC (10.72µA6.89µA) for achieving a worst case retention time of 10 years

3σ/μ of tF = 4% 3σ/μ of tF = 9%358K, 3σ/μ of W, L = 12% 358K, 3σ/μ of W, L = 12%

10-3 105 1013 1021 1029

t retention (s)

I C (µ

A)

10yrs

10-3 105 1013 1021 1029

t retention (s)

10yrs

40

60

80

100

∆ = 82

∆ = 70

∆ = 87

∆ = 70

Conclusion

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• A comprehensive study on I-PMTJ variability was performed with realistic parameters using a physics-based model

• Variability of ∆ and tretention is more sensitive to tFvariation compared to IC variability Tighter tF control allows a smaller increase in ∆ and IC to ensure all MTJ’s meet a 10 year retention time

• This work was supported in part by C-SPIN, one of six centers of STARnet, a Semiconductor Research Corporation program, sponsored by MARCO and DARPA

Acknowledgement