200x [MIT Sildes] the Effects of Pre-Existing Voids on Electromigration Lifetime Scaling

7/31/2019 200x [MIT Sildes] the Effects of Pre-Existing Voids on Electromigration Lifetime Scaling

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Outline

Stress evolution and void formation

Movies

Void dynamics and current density

Pre-existing voids

Dealing with voids: atomic reservoirs


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Electromigration

e-

Cathode:TensileStress

Anode:Compressive

Stress

Cu

current-induced atomic diffusion

q*zjkT

DcJ aa

atomic flux:

caused by a momentum transferfrom electrons


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Electromigration and Back Stress

e-

Back-stress

CathodeTensile

Void

Top View

Anode

CompressiveExtrusion


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xkT

Dcq*zj

kT

DcJ aaa

atomic flux

diffusivityatomic

concentration

resistivitycurrent

density

fundamental

charge

atomic

volume

back

stress

electromigration flux

Total atomic flux:

Electromigration and Back Stress

cathode

anodeq*zj

kT

DcJ aa

xkT

DcJ aa

back stress flux

compressive tensile

anode cathode


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q*zjkT

DcJ aa


xkT

DcJ aa

back stress flux

jq*zxkT

DB

xt

stresseffective

moduluscurrent

density

B = effective modulusof surroundingmaterial that resists

force due toelectromigrationbuild-up

stress per electromigratedatom depends on B

The Effective Modulus

M.A. Korhonen and P. Borgesen, K.N. Tu, and C.-Y. Li, J. Appl. Phys. 73, 3790 (1993).


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nuc= stressrequired tonucleate a

voidtensile

compressive

0

e-, Cu


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voidtensile

compressive

0

e-, Cu


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voidtensile

compressive

0

e-, Cu


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voidtensile

compressive

0

e-, Cu


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voidtensile

compressive

0

e-, Cu


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In-Situ Scanning Electron Microscopy

M.A. Meyer, M. Herrmann, E. Langer, E. Zschech, Microelec. Eng., 64, p375 (2002)E. Zschech, M.A. Meyer, and E. Langer, MRS Symp. Proc. 812, F7.5.1 (2004)

side

view

topview

Z.-S. Choi, R. Mnig, and C.V. Thompson, J. Mater. Res. 23, 383 (2008).

cathode

cathode


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In-Situ Observations of Voiding

FIB

Thickness of thinned Si3N4 ~100nm Ga ion penetration depth in FIB < 40nm

- Pre-Thin Cap SiN using Focused Ion Beam (FIB)

- Electrical testing and observation in SEM

- After Testing, FIB remaining nitride and characterize

microstructure using Electron Backscattered Diffraction Analysis(EBSD)


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SEM





microstructure using Electron Backscattered Diffraction Analysis(EBSD)


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microstructure using Electron Backscattered DiffractionAnalysis (EBSD)

EBSD


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In-Situ SEM of EM in Si3N4-Capped Sample

Duration of test: 4.15hours1m

Temperature: 370oC

Current density: 3MA/cm2Width = 2.25m

e-, Cu


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1m Duration of test: 45.7hours

Void Motion and Grain Orientations

e-

Out-of-plane

grain orientation

Temperature: 370oCCurrent density: 3MA/cm2

Width: 1.0m


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Temperature: 370oCCurrent density: 3MA/cm2

Width: 0.3m

Duration of test: 14.8hours

e-

Void Motion and Grain Orientations

Out-of-plane

grain orientation


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Qualitative Summary of Observations

Some voids first appear at a significant distance from thecathode.

Voids tend to grow in place before drifting.

Drifting voids do not appear to grow while drifting.

Drifting voids change shape as they move from grain tograin.

Drifting voids can become pinned.

Pinned voids can shrink or grow.

Fatal voids at a distance from the cathode are morecommon in narrower lines.


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Qualitative Summary of Observations


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Voids Form at Grain Boundaries

Voids grow when surface diffusion to the grainboundary exceeds the diffusion away from the grainboundary;

If void Nucleates: time-to-nucleation j-2

If void Pre-exists: time to reach critical size j-1


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Voids De-Pins at a Critical Size

Once a void reaches a critical size, it will de-pin anddrift:

j-5/2

P. Brgesen, M.A. Korhonen, D.D. Brown, and C.Y. Li,AIP Conf. Proc. 263, 219 (1992).

2/1gb

j*qz4

3volumeDepinning

Time to depinning


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Surface Electromigration and Void Motion

e-

Void in a single grain.

Void drift rate (Ds Dint(SiN))

Generally, Ds >> D int(SiN)

Ds

Dint(SiN)Dint(SiN)

Direction of the void drift

Void drift rate DS

Time to reach a critical size j-1


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Void nucleates and grows if: Dint(SiN)_a > Dint(SiN)_b

Void de-pins if: r > [(3gb)/(4qz*j )]1/2

Void drifts: drift rate Ds

Summary of Effects of Grain Structure on Void Dynamics

t j-1 or j-2

t j-5/2

t j-1


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0

20

40

60

80

100

2.25 m0.3 m 1.0 m

DriftVelocity(n

m/min)

Drift Velocity vs. Line Width

Wider lines have lower lifetime and larger lifetime variation


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C.W. Chang et al, Effects of Micro-Voids on the Line-Width Dependence of Electromigration Failure of

Dual- Damascene Copper Interconnects, Appl. Phys. Letts. 90, 193505 (2007)

Narrow lines: high t50 and high

t50

(hrs)


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Voids can form atcathode

Voids can form awayfrom cathode and

grow

Voids can form awayfrom cathodes and

drift to cathode

Scenarios


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compressive tensile

anode cathode

-

Cu

+ tensile

- compressive

nuc= critical stress

for void nucleation


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-

Cu

+ tensile

- compressive

compressive tensile

anode cathode

q*zj

kT

DcJ aa



for void nucleation


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compressive tensile

anode cathode


for void nucleation

once the stress at the anode reaches the critical stress for void nucleation,

a void will form

q*zj

kT

DcJ aa



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compressive tensile

anode cathode

xkT

DcJ aa

back stress flux

q*zj

kT

DcJ aa



for void nucleation


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-

Cu

+ tensile

- compressive

compressive tensile

anode cathode

x

kT

Dcq*zj

kT

Dc aa

Flux Balance:

electromigration fluxand

back stress fluxbalance


for void nucleation


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-

Cu

+ tensile

- compressive

nuc

extru

L

xq*zj

*zq

jL

j*qz


for void nucleation

extru = critical stressfor extrusion


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-

Cu

+ tensile

- compressive

nuc

extru

L

'immortal'

*zq

jL cr

j*qz

cr

cr

the critical

stress

differencerequired to

cause a

tensile or

compressive

failure

nuc

Blech Effect:

extru


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Flux Divergences at Grain Boundaries


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Flux Divergences at Grain Boundaries

For reasonable values of diffusivity difference and length of high-diffusivity region. A force balance in the high-diffusivity region will

prevent stress from exceeding that at the cathode.

If there is a void at a grain boundary away from the cathode, thevoid must have pre-existed.

(Z.-S. Choi, PhD thesis, to be published)


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S.P. Hau-Riege, J. Appl. Phys. 91, 2014 (2002)b

Y. Kakuhara et al, J. J. Appl. Phys. 48, 096504 (2009)

The Case for Pre-Existing Voids

Observations of voids away from cathodes is common:

Observation of voids inunstressed de-processedlines and in TEM arecommon:

C.W. Chang et al, Appl.Phys. Letts. 90, 193505

(2007)


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The Case for Pre-Existing Voids

Stresses required to nucleate a void >1GPa.R.J. Gleixner et al, J. Mater. Res. 12, 2081 (1997).

Critical stress for void formation implied from critical lengthexperiments ~40MPa.

S.P. Hau-Riege, Appl. Phys. 91, 2014 (2002).

The critical void size ~1nm


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Current Density Scaling

Voids that move have more complex scaling: n = -1 to -2.5

and, varies with j


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Dealing with Voids: Atomic Reservoirs

No reservoir

Extension reservoir

Multi-level reservoir


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Atomic Reservoirs: Multi-segment lines

(i) no reservoir t50 = 35.3 hrs.(ii) inactive reservoir t50 = 110.2 hrs.(iii) active reservoir t50 = 242.1 hrs.

(T. Chookajorn and C.V. Thompson, unpublished work)


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Summary:

Consequences of Void Formation Away from the Cathode

Rate of failure depends on de-pinning, and drift. Currentdensity scaling becomes complex.

Rate of failure depends strongly on the grain structure.

Voids at cathodes and voids away from cathodes create

mixed populations of lifetime scaling, and multimodal failurestatistics.

Different populations have different critical lengths.

Pre-existing voids need only grow and drift.

Reservoirs can be used to collect void volume.

200x [MIT Sildes] the Effects of Pre-Existing Voids on Electromigration Lifetime Scaling

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