ECTC2005ECTC2005Tin Whisker FormationTin Whisker Formation
A Stress AnalysisA Stress Analysis
Chen Xu – Cookson ElectronicsG. T. Galyon – IBM (presenting)
S. Lal – FCIB. Notohardjono – IBM
1
Mr. WhiskerMr. Whisker
Courtesy of Peter Bush/SUNY-Buffalo
2
AgendaAgenda• Integrated Theory for Whisker Formation & Stress• Kirkendahl Effect and Stress• Intermetallic Formation and Stress• Finite Element Stress for Tin Film• Film Stress Measurements – XRD• Film Stress Measurements- Flexure Beam
– Flexure Beam Observations– Flexure Beam Limitations
• Wrap Up
3
Integrated Theory: Elements Of Integrated Theory: Elements Of
• Compressive stress- A necessary factor– Compressive stress sources
• Must be high impedance or sustaining sources, e.g.– Intermetallic formation– High humidity (oxide reactions at film surface)– Temperature cycling (differential thermal expansion)– Built in film stresses (additives/gaseous entrapment)
• Arguments to the contrary are potentially flawed– e.g., non sustaining stresses– e.g. Flexure beam observations– e.g. Bent lead-frame experiments
• Recrystallization – A necessary factor (?)– Not covered in this presentation
• Tin Self-Diffusion – A necessary factor– Not covered in this presentation
4
Stress States in FilmsStress States in Films
• Stress States in Film Structures• Kirkendahl Effect and Intermetallic Formation
• Finite Element Analysis (FEA) of zonal film structure
• Theory (FEA) reconciliation with measurement
• XRD and Flexure Beam Data must be reconciled
• Stress State and Film Microstructure• Zonal Structures
• E.g. the extent of IMC at the time of stress
measurement
5
Compressive Stress ScorecardCompressive Stress Scorecard
ProS. Madra
grain-boundary/grain growth modelConK. Tsuji
ProR. Schetty
ProHutchinson, et al.
Tin-indium samplesProM. Barsoum, et al.
grain-boundary/grain growth modelConP. Bush
ProBoettinger, et al.
ProOsenbach, et al.
Tin-manganese samplesConK. Chen, et al.
ProK.N. Tu, et al.
ProW. Choi, et al.
ProP. Oberndorff, et al.
ProC. Xu
ProS. Lal
ProGalyon/Palmer
CommentConProAuthor/s
6
Compressive Stress Scorecard (contCompressive Stress Scorecard (cont’’d)d)
1987 (internal stresses/not mechanical)ProB.D. Dunn
1998ProLee & Lee
1984ProEndicott & Kisner
1983ProKawanaka, et al.
1974, Zinc whiskersProU. Lindborg
1969ProFuruta & Hamamura
1963ProPitt & Henning
1961ProV.K. Glazunova, N.T.Kuryavtsev
1961ProV.K. Glazunova
1958ProW.C. Ellis, D. Gibbons,R.g. Treuting
1955ProR.R. Hasiguti
1954, Tin on steelProFisher,Darken,Carroll
CommentConProAuthor/s
7
copper tin
copper tin
Kirkendahl vacancies-actionzone
Shrinkage actionTensile Stress
Copper diffusion – action zoneInterstitial Cu + Cu6Sn5 +Sn
Compressive Stress
Kirkendahl Effect for Tin/Copper Couple
Reactionzone
Reactionzone
8
nickel tin
nickel tin
Tin diffusion –action zoneSn + Ni3Sn4 IMC
Compressive stress
Kirkendahl vacancies-action zoneShrinkage action
Tensile stress
Kirkendall Effect for Tin/Nickel/Copper
Reactionzone Reaction zone
9
FIB Cross Section of Sn/Cu with Kirkendahl VoidingFIB Cross Section of Sn/Cu with Kirkendahl Voiding
Put one or two FIB x-sections here
KirkendahlVoids
10
FIB Cross Section of Sn/Cu with Kirkendahl VoidingFIB Cross Section of Sn/Cu with Kirkendahl Voiding
Kirkendahl Voids
11
FIB X-sections - 0.5u immersion Sn/Cu /1 yr. oldFIB X-sections - 0.5u immersion Sn/Cu /1 yr. old
Full IMC penetration0.75 u tin film
Kirkendahl voiding underIMC
12
Sample Molar Volume CalculationsSample Molar Volume CalculationsFor Zone-2 of a Sn/Cu coupleFor Zone-2 of a Sn/Cu couple
Y ≡ gm-moles of tin per unit volume (V) in zone-2 before interdiffusionX ≡ gm-moles of copper diffusing into volume (V) & reacting to form IMC
Y (Sn) -> (X/6) (Cu6Sn5) + (Y-(5X/6)) Sn (eq. 1) Y gm-moles of tin -> X/6 gm-moles of IMC + (Y-(5X/6)) gm-moles of tin
Y (16cc/gm-mole) -> (X/6) (118 cc/gm-mole) + (Y-(5X/6)) (16cc/gm-mole)16Y ccs -> 16Y ccs + 6.6X ccs (eq. 2)
right side of equation 2 is always >> than the left hand sideTherefore; zone-2 is “expansionary” due to IMC formation (Always)
13
Molar Volume Calculations (contMolar Volume Calculations (cont’’d)d)
For example:
11Sn -> 1 Cu6Sn5 + 6Sn in molar volumes is:
176 ccs-> 118 ccs + 96 ccs 176ccs < 214 ccs (a 22% volume increase in zone-2)
For example:
12Sn-> 2 Cu6Sn5 + 2Sn
192ccs-> 236 ccs + 32 ccs 192ccs < 268 ccs (a 39% volume increase in zone-2)
14
Kirkendall zone – vacancy rich copper
Copper substrate
Cu6Sn5+Sn
Sn
SnZone 1
Zone 2
(compression)
Zone 3
(tension)
Zone 4
The 4-zone structure for a tin/copper couple after intermetallic forma tion
L L
Kirkendall zone – vacancy rich copper
Copper substrate
Cu6Sn5+Sn
Sn
SnZone 1
Zone 2
(compression)
Zone 3
(tension)
Zone 4
The 4-zone structure for a tin/copper couple after intermetallic forma tion
L L
Oxide layer
4-Zone Structure for Sn/Cu4-Zone Structure for Sn/Cu
15
4-zone Sn/Cu Structure - Stress Distribution in zone-24-zone Sn/Cu Structure - Stress Distribution in zone-2
Vacancy rich copper (Kirkendall Zone) -tension
copper substrate
Cu6Sn5
(compression)
Sn (compression)
Sn
Vacancy rich copper (Kirkendall Zone) -tension
copper substrate
Cu6Sn5
(compression)
Sn (compression)
Sn
Stress-tension at time zero -compressive over time
Stress is the same fortin and IMC in zone-2
It cannot be that tinand IMC are at
different stress levelsat or
near equilibrium
Oxide layer
16
Sample Molar Volume CalculationsSample Molar Volume CalculationsFor Zone-3 of a 4-layer Sn/Ni/Cu coupleFor Zone-3 of a 4-layer Sn/Ni/Cu couple
• 3Ni -> Ni3Sn4– Molar Volume of Ni = 6.6 cc/gm-mole– Molar Volume of Ni3Sn4 = 75.25 cc/gm-mole– The molar volume for 3Ni < molar volume for Ni3Sn4– 19.8ccs < 34ccs (an expansionary action)
• For Sn/Ni/Cu– The vacancy rich region is in the tin (tension)– The expansion action is in the nickel (compression)
There is no known visual confirmation of Kirkendahlvacancies for Sn/Ni/Cu structures at this time (5/05)
17
Zone-1
(compression)
Zone-2
(tension)
Zone-3
(compression)
Zone-4
(tension)
Ni3Sn4+ Ni
Ni
Ni
Copper substrate
Tin film
Tin film
Zone-1
(compression)
Zone-2
(tension)
Zone-3
(compression)
Zone-4
(tension)
Ni3Sn4+ Ni
Ni
Ni
Copper substrate
Tin film
Tin film
The 4-zone structure for Sn/Ni/Cu after intermetallic formation
Zonal Structure for Tin with Nickel Underlay
Oxide layer
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Kirkendahl Effect: CuKirkendahl Effect: Cu33Sn Intermetallic FormationSn Intermetallic Formation
• Cu3Sn forms from Cu6Sn5 for T > 60 oC
• At temperatures > 60 degs. C– If Cu6Sn5 -> 2Cu3Sn + 3Sn– 118 ccs/gm-mole -> 70ccs/gm-mole +48ccs/gm-mole– 118ccs->118ccs (no expansion or contraction)
• The Above Reaction provides excess tin (Sn) atoms• Excess Sn atoms permit continued outdiffusion/relaxation
• Excess tin atoms outdiffuse towards surface
• Outdiffusion reduces stress in Cu3Sn zone• Converts compressive stress to less compressive• Can convert stresses to tensile stress• Can show evidence of Kirkendall voids in Cu3Sn
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CuCu33Sn Intermetallic Formation ?Sn Intermetallic Formation ?
Kirkendall zone – vacancy rich copper
Copper substrate
Cu6Sn5+Sn
Sn
Sn
The 4-zone structure for a tin/copper couple after annealing
Cu3Sn
Zone -1
Zone-2
Zone-3
Zone-4
Kirkendall zone – vacancy rich copper
Copper substrate
Cu6Sn5+Sn
Sn
Sn
The 4-zone structure for a tin/copper couple after annealing
Cu3Sn
Zone -1
Zone-2
Zone-3
Zone-4
Sn Sn
Oxide layer
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X-section of CuX-section of Cu33Sn w Kirkendall VoidsSn w Kirkendall Voids
Picture from RPI research to be inserted.
Reference: M. Glicksman / A. Lupulescu, RPI, 2002
porosity in Cu3Snrequires outdiffusion
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X-section of CuX-section of Cu33Sn w Kirkendall VoidsSn w Kirkendall Voids
TinFilm
Cu6Sn5
Cu3Sn
Cu Substrate
Kirkendahlvoiding in Cu3SnKirkendahl voiding in Cu
Finite ElementFinite ElementAnalysisAnalysisTin FilmsTin Films
B. NotohardjonoG. Galyon (presenting)
C.XuS. Lal
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Finite Element AnalysisFinite Element AnalysisZonal Structures For Sn/CuZonal Structures For Sn/Cu
• Objective: Correlate Theory to Measurement
• Finite Element Analysis Strategy
– Break up substrate/film into zones
– Assume expansions/contractions for each zone– Calculate stress states– Compare to experimental data
24
Kirkendall zone – vacancy rich copper
Copper substrate
Cu6Sn5+Sn
Sn
SnZone 1
Zone 2
(compression)
Zone 3
(tension)
Zone 4
The 4-zone structure for a tin/copper couple after intermetallic forma tion
L L
Kirkendall zone – vacancy rich copper
Copper substrate
Cu6Sn5+Sn
Sn
SnZone 1
Zone 2
(compression)
Zone 3
(tension)
Zone 4
The 4-zone structure for a tin/copper couple after intermetallic forma tion
L L
Oxide layer
Four Zone Structure for Sn/Cu
25
Finite Element Stress AnalysisFinite Element Stress AnalysisModel Parameters for Sn/CuModel Parameters for Sn/Cu
• Set zonal thickness and properties– E.g., Zone-1 at 5 microns: 100% tin– E.g., Zone-2 at 2 microns: mixture of tin and IMC– E. g.,Zone-3 at 2 microns: vacancy rich copper– E.g., Zone-4 at 10 microns: copper substrate
• Let active zones expand/contract– Zone-2 will expand: inter-diffusion/IMC formation– Zone-3 will shrink: Kirkendall vacancy formation– Zones1/4 will react:
• Calculate stresses in reactive zones
• Compare FEA scenario to experimental results
26
0 .9 1.8
2.8
3.8
4.8
5.8
7 8 9
10
Legend: zone-2 expansion
Distance from Surface-microns
-10
-8
-6
-4
-2
0
2
4
6
8
Stre
ss-ksi
zone-2=0
zone-2=.0001
zone-2=.001
zone 2=.00125
zone 2=.002
4-Zone Structure Stress States zone-3 shrinkage = .001
zone 1 zone 2 zone 3
The flexure beamIs concave downfor all 5 scenarios
Finite Element AnalysisFinite Element Analysis
Zone 1 Tin Stressis increasingly
tensile withincreasing IMC
Formation
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0 .9 1.8 2.8 3.8 4.8
Legend: zone-2 expansion
Distance from Film Surface (microns)
-1
0
1
2
3
4
5
6
Stre
ss
-kp
si
zone-2=0
zone-2=.0001
zone-2=.001
zone-2=.00125
zone-2=.002
zone-2=.005
zone-2=.01
zone-2=.02
Zone-1 Stresses zone-3 shrinkage=.001An expanded presentation
for zone-1 showing how the Zone-1 stress becomes increasingly tensile with increasing zone-2 expansion
Finite Element AnalysisFinite Element Analysis
28
Out-Diffusion of Tin: Zone-2 to Zone-1Out-Diffusion of Tin: Zone-2 to Zone-1
• Tin will out-diffuse from Zone-2 to Zone-1– Diffusion driven by stress gradient / not concentration grad.– Diffusion will primarily be through grain bdries.– Bulk tin self-diffusion
• Increasingly important with increasing temperature• Very anisotropic: <001> >>> <100> or <010>• Accounts for Pedestal Structures from annealing (see Wed.
pm)
– Out-diffusion-> balances Zone-1/2 stress• Zone-2 stress decreases/Zone-1 stress decreases• Diffusion stops -> total strain energy is minimized.
29
Starting point tin in tension
Equilibrium point tin incompression
Past equilibrium-tin in highcompression
e.g. –out diffusion factor 1.2means that the 2% expansionhas been reduced 1.2% by outdiffusion from zone-2 to zone-1
Finite Element Analysis Finite Element Analysis ––outdiffusionoutdiffusion
30
0 .6 1.2 1.8 2.4 3.0
Zone-2 to Zone-1
Out-Diffusion Factor
0
2
4
En
erg
y pe
r cc (lb-in
x 10
+6
)
out-diffusion #0
2% expansion:zone-2
out-diffusion factor #3
2% expansion zone-2
out-diffusion factor #1.8
2% expansion zone-2
Note: Strain energy term is total strain energy for zones 1,2,3,4 in 4-zone model
Flexure isConcave Down with R decreasingWith increasingOut-diffusion
Strain Energy Strain Energy –– Outdiffusion Outdiffusion
31
Zone-1
(compression)
Zone-2
(tension)
Zone-3
(compression)
Zone-4
(tension)
Ni3Sn4+ Ni
Ni
Ni
Copper substrate
Tin film
Tin film
Zone-1
(compression)
Zone-2
(tension)
Zone-3
(compression)
Zone-4
(tension)
Ni3Sn4+ Ni
Ni
Ni
Copper substrate
Tin film
Tin film
The 4-zone structure for Sn/Ni/Cu after intermetallic formation
Oxide layer
Sn/Ni/Cu Zonal Structure
32
Finite Element Stress AnalysisFinite Element Stress AnalysisModel Parameters for Sn/Ni/CuModel Parameters for Sn/Ni/Cu
• Set zonal thickness and properties– zone-1 at 3 microns: 100% tin– Zone-2 at 2 microns: vacancy rich tin– Zone-3 at 2 microns: nickel plus Ni3Sn4 intermetallic– Zone-4 at 10 microns: copper substrate
• Let active zones expand/contract– Zone-2 will shrink: Kirkendall vacancy formation– Zone-3 will expand: intermetallic formation– Zones1/4 will react:
• Calculate stresses in reactive zones
33
0 1.8 3.8 5.8 8 10
distance from film surface (microns)
-200
-100
0
100
200
300
Stre
ss (psi)
zone-3= +1.0% zone-2=-0.1%
Z1 z2 z3 z4
FEA predicts that tin stress willbe tensile at the Sn/Ni interface andcompressive at the surface for a filmthickness >2-3 us.
These calculations assume that there isno built-in stress intrinsic to the tin itself. An intrinsic tin film stress would be additive.
compressive
tensile
compressive
Finite Element Analysis-Sn/Ni/CuFinite Element Analysis-Sn/Ni/Cu
34
FEA SummaryFEA Summary
• FEA of Zonal Structures– Predicts Flexure Beam and XRD σ measurement in
opposition to each other
– Predicts that XRD at time zero may be tensile andover time goes compressive
35
What Does Stress Data Say?What Does Stress Data Say?
• XRD Data– C. Xu, Y. Zhang, et al: Cookson/Enthone Y2000+
• Flexure Beam Data– Lee and Lee: Seoul National University Y1998– S. Lal: FCI Corporation – Private Communication
36
XRD XRD for for Sn/Ni/Cu Sn/Ni/Cu aged 40 days at ambientaged 40 days at ambient
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
8,0
8.5
9.0
9.5
10
-10
-5
0
5
10
15
20
Stre
ss-M
Pa
Thickness of Tin Film for Sn/Ni/Cu Structure
For tin films <2.0 microns allXRD stress values are tensile
For tin films >2.0 microns allXRD stress values are compressive
These values are consistentwith FEA analysis of a zonalSn/Ni/Cu structure
Transition from tensile tocompressive
Reference: Cookson Electronics, C. Xu, et al.
37
Lee and LeeLee and Lee’’s (1998) Flexure Beam Stress Datas (1998) Flexure Beam Stress Data
0 5
10
15
20
25
30
35
40
45
50
55
60
Aging Time (Days)
-10
-5
0
5
10
15
Stre
ss M
Pa
Complex Stoney’s Equationσ= ET2 (1/R – 1/Ro) 6 6(1-γ)t)
The stress at time zero istensile and within 2 daysis compressive.
We do not know what the radiiof curvatures were…we canassume that the beam wentfrom concave up to concavedown as the stress went fromtensile to compressive. But it’spossible the radius wasconcavedown thruout the test cycle.
tensile
compressive
Tin on Phos-Bronze Substrate
38
Com
pres
sive
Tens
ile
Aging Time
XRD Stress Data Over Time-SchematicXRD Stress Data Over Time-Schematic
Sn/Ni/Cu XRD Data Ref. C. Xu
Sn/Cu XRD DataRef. C. Xu
ThisRegion
Expectedbut
MinimalData to
Date
39
Flexure Beam Data (Schematic Format)Flexure Beam Data (Schematic Format)
Concave Up “Tensile”
Time
Concave Down“Compressive”
Tin Etched Off at Time Zero
Tin Etched off at Time t
Ref. S. Lal – FCI Corporation
Tin etched off at Time t
40
Theory and Experimental DataTheory and Experimental Data
• XRD Data–zonal theory easily explains–Kirkendall Effect Sn/Ni/Cu
• Explains tensile stress in Sn• Explains tensile to comp.
transition with increasingthickness
–Kirkendall Effect Sn/Cu• Explains -σ increase with time• Consistent with IMC expansion
• Flexure Beam Data–zonal theory easily explains–Time zero flexure
• Due to built-in stresses• No Kirkendall effect yet
– Zero residual flexure
–Stress relaxation over time• Represents all zones together• Not just the tin film• Kirkendall effect not dominant• Kirkendall effects slow relax.
Wrap UpWrap UpConclusionsConclusionsChallengeChallenge
G. Galyon-IBM (presenting)Chen Xu-Cookson
S. Lal-FCIB. Notohardjono-IBM
42
Wrap Up-ConclusionWrap Up-Conclusion
• Zonal Structure Analyses-Appropriate model
• Kirkendahl Effect- Primary Stress Source
• IMC Formation & Expansion- Primary Stress Source
• Stress Measurement in Tin Films
– Requires combination of XRD/Flexure/Microstructure
– Requires a corresponding FEA zonal structure scenario
• Recrystallization- To be addressed / future work
• Oxide Reactions-To be addressed / future work
• Thermal Cycling-To be addressed / future work
43
The ChallengeThe Challenge
• Go and do Likewise:– Check out the Integrated Theory Hypotheses– Check out the reported data
• E.g. Sn/Ni/Cu Stress States• Tin Films with concave up flexure beams / i.e. “tensile”
– Synchronize Flexure Beam / XRD / Microstructure• Check intermetallic formation as a function of “stress”
• Let’s share your inputs on a real time basis– Open invitation from the iNEMI modeling group– Chairman: G. T. Galyon ([email protected])
Back Up Material Back Up Material ––ECTC 2005ECTC 2005
XRD Stress Measurement TechniqueXRD Stress Analysis
Flexure Beam Analysis Technique
XRD StressXRD StressMeasurementMeasurement
Chen Xu-CooksonG. T. Galyon-IBM (presenting)
S. Lal-FCIB. Notohardjono-IBM
46
Why using XRD for the residual stress measurement?
DetectorX-ray
Non-destructive and spatial resolvedMonitoring the stress evolutionStress measurement on real partMeasuring the stress of individual layer
47
XRD Spectra Shifts & Stress TypeXRD Spectra Shifts & Stress Type
71 72 73 74
0
100
200
300
400
500
stress-free
tensile stress
compressive stress
Diffr
actio
n I
nte
nsity
2!
70 71 72 73 74 75
0
100
200
300
400
500
low microstress
high microstress
Diffr
actio
n I
nte
nsity
2!
Macro Stress Microstress
48
Stress Measurement using XRDStress Measurement using XRD
ex(y)=
u+1E
sx sin2y - uE
(sx + sy)St
rain
sin2y
Tensile Stress
Compressive Stress
49
Shear Stress Determination with SinShear Stress Determination with Sin22ΨΨ
0.0 0.1 0.2 0.3 0.4 0.5 0.6
-0.0016
-0.0014
-0.0012
-0.0010
-0.0008
-0.0006
-0.0004
-0.0002
0.0000
0.0002
sin2!
Str
ain
+!
-!
z
xyy
NoShearStress
ShearStress
50
Biaxial Stress State sinBiaxial Stress State sin22ΨΨ Data Data
0.0 0.1 0.2 0.3 0.4 0.5-0.0020
-0.0018
-0.0016
-0.0014
-0.0012
-0.0010
-0.0008
-0.0006
-0.0004
-0.0002
0.0000
0.0002
sin2!
"x= 851 MPa
"y= 842 MPa
Str
ain
x
y
Stress MeasurementsStress MeasurementsSn/Ni/Cu Sn/Ni/Cu & & Sn/CuSn/Cu
Chen Xu-CooksonG. T. Galyon-IBM (presenting)
52
Experimental SetupExperimental Setup
• D8 Discover withGADDS by Bruker.
• Cr-radiation and 0.5mmbeam.
• Diffraction peak (312) at2q=143.8o.
• The strains were measuredat 19 different y anglesfrom –45o to 45o.
53
Stress MeasurementStress Measurement
-0.0008
-0.0007
-0.0006
0.5µ Sn/Ni/Cu
Str
ain
2µ Sn/Ni/Cu1µ Sn/Ni/Cu
0.0 0.1 0.2 0.3 0.4 0.5
-0.0008
-0.0007
-0.0006
3µ Sn/Ni/Cu
Str
ain
sin2(!)
0.0 0.1 0.2 0.3 0.4 0.5
-0.0008
-0.0007
-0.0006
10µ Sn/Ni/Cu
sin2(!)
54
Stress MeasurementStress Measurement
0 2 4 6 8 10
-5
0
5
10
15bright Sn/Ni/Cu alloy, aged at RT for 40 days
Compressive Stress
Tensile Stress
Str
ess in
Sn
Film
(M
Pa
)
Sn Film Thickness (microns)
Reference Cookson Electronics: C. Xu, et al.
55
Com
pres
sive
Tens
ile
Aging Time
XRD Stress Data Over Time-SchematicXRD Stress Data Over Time-Schematic
Sn/Ni/Cu XRD Data Ref. C. Xu
Sn/Cu XRD DataRef. C. Xu
ThisRegion
Expectedbut
MinimalData to
Date
56
Flexure Beam Data (Schematic Format)Flexure Beam Data (Schematic Format)
Concave Up “Tensile”
Time
Concave Down“Compressive”
Tin Etched Off at Time Zero
Tin Etched off at Time t
Ref. S. Lal – FCI Corporation
Tin etched off at Time t
57
XRD Stress Analysis SummaryXRD Stress Analysis Summary
• XRD on Sn/Ni/Cu– Well behaved data set
• Stresses are biaxial– Results are in synch with Zonal Structure Theory
• Show predicted tensile/compression transition– Stress over Time analysis
• Tensile Stresses Increase with time to about 15 MPa
• XRD on Sn/Cu– Historical Data Set
• Stresses are biaxial• Compressive Stresses increase with time to 15-20 MPas
– Current data set very preliminary – Work in Progress• Latest Results will be discussed in Conference• Preliminary indications of tensile to compressive transition
Flexure BeamFlexure Beam
S. Lal-FCI (Presenting)G. Galyon-IBM
C. Xu-CooksonB. Notohardjono-IBM
59
Flexure Beam ApparatusFlexure Beam Apparatus
R = L2/2δ
Schematic ref. Lee and Lee, 1998.
60
Flexure Beam Stress AnalysisFlexure Beam Stress Analysis
• Stoney’s eq. σ= ET2/6(1-γ)tR– σ is film stress– E is Young’s modulus for substrate material– γ is Poisson’s ratio for substrate material– t = film thickness– T= substrate thickness– R = curvature radius of flexure beam
• Stoney’s eq. only valid for t/T ratios ≤ 0.01(1%)
• Std. Flexure Beam thicknesses 50-200 microns– An 0.5u film has t/T = 0.01 (1%) for a 50u beam– A 2.0u film has t/T= 0.01 (1%) for a 200u beam
61
Complex StoneyComplex Stoney’’s equations equation
• Etching off the tin…based on change in radius• σ= ET2/6(1-γ)t(1/R – 1/Ro)
– R is the radius after etching off tin– Ro is the radius before etching off tin
• Etchant Removes tin with varying stress levels– Leaves any intermetallic intact
• Result is an averaging of stresses thruout tin
• Etching of the intermetallic– Also removes copper layer– Need etchant that removes only intermetallic
• No known suitable etchant for Sn/Cu systems
62
Lee and LeeLee and Lee’’s (1998) Flexure Beam Stress Datas (1998) Flexure Beam Stress Data
0 5
10
15
20
25
30
35
40
45
50
55
60
Aging Time (Days)
-10
-5
0
5
10
15
Stre
ss M
Pa
Complex Stoney’s Equationσ= ET2 (1/R – 1/Ro) 6 6(1-γ)t)
The stress at time zero istensile and within 2 daysis compressive.
We do not know what the radiiof curvatures were…we canassume that the beam wentfrom concave up to concavedown as the stress went fromtensile to compressive. But it’spossible the radius wasconcavedown thruout the test cycle.
tensile
compressive
Tin on phos-bronze substrate
63
Flexure beam with Concave Up curvature (i.e. “smiley faced)Simple Stoney’s analysis shows tensile stress in tin film
Zone-1 tin
Zone-2 imc
Zone-3Kirkendall vacs.
Zone-4Cu substrate
Note: Zone-1 (tin) may be compressive if the curvature is due to shrinkage in either zones 2/3.
Neutral axis
4-zone structure: Flexure Beam Analysis4-zone structure: Flexure Beam Analysis
64
Zone 1-tin film
Zone 2-IMC+Sn
Zone 3-Cu K.Z
Zone 4-Cu
Neutral Axis
Flexure Beam with Concave Down Curvature (i.e. “Grumpy Faced” )Simple Stoney’s analysis shows compressive stress in tin film
Note: Zone-1 may be tensile even though Stoney’s eq. says it is in compression. i.e., If Zone-1 only “reacts” to the expansionary action of underlying zones it will be in tension even though the curvature is concave down
4-Zone Structure: Flexure Beam Analysis4-Zone Structure: Flexure Beam Analysis
65
Compressive StressCompressive StressDriving Force for Whisker FormationDriving Force for Whisker Formation
• Internal compressive stress– Agreed to by great majority of published authors– These authors agree
• Applied (external) mechanical stress– Not frequently addressed by published authors– Established by Fisher, Pitt, Glazunova– Some negative results (Dunn, private communications)– These authors agree: mech. Stress can induce whiskers
• Role of intermetallic at substrate interface– Majority believe IMC compresses film– These authors agree
