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Optimization of Visco-Elastic Material Models of Mold Compounds Used in Electronic Packages Based On Evolutionary AlgorithmsWeimarer Optimierungs- und Stochastiktage 4.029.-30. November 2007
Axel Mueller1, Sven Rzepka1, Johannes Will21Qimonda Dresden GmbH & Co. OHG, 2Dynardo GmbH
Mueller, Rzepka, Will · WOST 29.-30. November 2007 · Page 2 Copyright © Qimonda AG 2007 · All rights reserved.
Pilot Project w/ Dynardo
Simulation Task
Parameter Identification
Conclusions
Mueller, Rzepka, Will · WOST 29.-30. November 2007 · Page 3 Copyright © Qimonda AG 2007 · All rights reserved.
Pilot Project w/ Dynardo
Simulation Task
Parameter Identification
Conclusions
Mueller, Rzepka, Will · WOST 29.-30. November 2007 · Page 4 Copyright © Qimonda AG 2007 · All rights reserved.
Pilot Project w/ Dynardo
Application Of optiSLang To Material Modeling Tasks
Task I: ANSYSidentification of visco-elastic material data
• calibration of quasi-static data
• many parameters (> 20)
• simulation time ~10 min / leg
• optiSLang ⇔ ANSYS
• calibration of noisy data
• few parameters only (< 10)
• simulation time ~1 h / leg
• optiSLang ⇔ LS-DYNA
Topic Of This PresentationTopic Of This Presentation
Task II: LS-DYNAidentification of rate-
dependent solder data
Mueller, Rzepka, Will · WOST 29.-30. November 2007 · Page 5 Copyright © Qimonda AG 2007 · All rights reserved.
Pilot Project w/ Dynardo
Simulation Task
Parameter Identification
Conclusions
Mueller, Rzepka, Will · WOST 29.-30. November 2007 · Page 6 Copyright © Qimonda AG 2007 · All rights reserved.
Simulation Task
Microelectronic Packages Exposed To Temperature Loads
Manufacturing Operating Condition
E.Q. Component WarpageDuring Solder Reflow?
Thermal Cycle Test (JEDEC Standard)Solder Joint Reliability?
Printed Circuit Board
Electronic Component
Solder Joints
Mueller, Rzepka, Will · WOST 29.-30. November 2007 · Page 7 Copyright © Qimonda AG 2007 · All rights reserved.
Challenge
Multi-Layer Structures Composed of Complex Materials
Si-chipepoxy glue
adhesive
mold compound
Si-chip
organicsubstrate
Temperature-and Time
Dependent
Mueller, Rzepka, Will · WOST 29.-30. November 2007 · Page 8 Copyright © Qimonda AG 2007 · All rights reserved.
Material Characterization
Dynamic Mechanical Analysis (DMA)
Parameter:temperature T,frequency f
Frequency Data:storage modulus E‘(T),loss modulus E‘‘(T)
glas
s tr
ansi
tion
L 0
u(Ω), F(Ω)
tens
ile s
peci
men
Fig. 1: Tensile Specimen w/ Sine Load Fig. 2: Frequency Dependent E-T-Profiles
Mueller, Rzepka, Will · WOST 29.-30. November 2007 · Page 9 Copyright © Qimonda AG 2007 · All rights reserved.
Material Modeling
Parameterized Finite Element Model of the Test
1 vector for each frequency
0.1 Hz 1.0 Hz 10 Hz~10 min
Fig. 3: Finite Element Model Fig. 4: Output Parameter
Mueller, Rzepka, Will · WOST 29.-30. November 2007 · Page 10 Copyright © Qimonda AG 2007 · All rights reserved.
Pilot Project w/ Dynardo
Simulation Task
Parameter Identification
Conclusions
Mueller, Rzepka, Will · WOST 29.-30. November 2007 · Page 11 Copyright © Qimonda AG 2007 · All rights reserved.
Material Parameters For Calibration
41 input parameters in total: E0, E1, ν, C1, C2 and α i (2x18)
mlinear terermconstant t
)(
1
0
10
K
K
EE
TEETE ⋅+=
Elastic Modulus
Poisson Ratio
constT =)(ν
Relaxation Data (Master Curve @ T0)
Time-Temperature Shift Function
( ) ( )20201)ln( TTCTTCaT −⋅+−⋅=
( )Teff att exp⋅∆=∆ effective time step
( )
−⋅+⋅=
−⋅+⋅=
∑
∑
=∞
=∞
18
1
18
1
exp
exp
i i
Ki
K
i i
Gi
G
τtααK(T)K(t,T)
τtααG(T)t,TG
Mueller, Rzepka, Will · WOST 29.-30. November 2007 · Page 12 Copyright © Qimonda AG 2007 · All rights reserved.
Sensitivity Analysis (1)
Correlation and Coefficient of Determination
optiSLang creates 100 Latin Hypercube samplings. 0.1 :Constraint18
1i<∑
=iα
Study sensitivity of input parameters on output vector elements.
Sensitivities:
Definition design space Trial and Error, Experience
noneα ν,smallα ,ChighC ,E ,E
Ki
Gi2
110
→→→
Mueller, Rzepka, Will · WOST 29.-30. November 2007 · Page 13 Copyright © Qimonda AG 2007 · All rights reserved.
Sensitivity Analysis (2)
Variation Space
Few reference values are outside the variation space of the sensitivity study.
Variables that have significant effect on particular vector element
Reference Variation Space
Mueller, Rzepka, Will · WOST 29.-30. November 2007 · Page 14 Copyright © Qimonda AG 2007 · All rights reserved.
Identification (1)
Gi2110 α ,C ,C ,E ,E K
iα ν,
Initialization of Identification Task
Design space for identification has been reduced to 22 variables:
In addition, lower and upper bounds of some variables are adjusted.
10 best designs out of LH sampling are used to initialize identification.
Mueller, Rzepka, Will · WOST 29.-30. November 2007 · Page 15 Copyright © Qimonda AG 2007 · All rights reserved.
Identification (2)
0.1 :Constraint18
1i<∑
=iα
Objective Function and Constraints
Minimize root mean square error of experimental and simulated data.
Never analyze non-physical design option of optiSLang
Start w/ global search strategy using optiSLang default settings.
!
( ) ( )( )min
1loglog 2'
,', →
−−
= ∑i
EEF ExpiSimi (implemented as user vector routine)
Mueller, Rzepka, Will · WOST 29.-30. November 2007 · Page 16 Copyright © Qimonda AG 2007 · All rights reserved.
Evolution of Identification
Genetic Algorithm Evolutionary Run 1 Evolutionary Run 6
Final settings:mutation rate = 0.5standard deviation < 0.05
By design improvement strategy the quality of the global solution could be improved significantly.
After the global optimization run the solution could be improved about 50 %!
Mueller, Rzepka, Will · WOST 29.-30. November 2007 · Page 17 Copyright © Qimonda AG 2007 · All rights reserved.
Result Parameter Identification
Total Costs of Identification approx. 1000 Solver Calls.
Best design based on synchronous identificationof glass constants, master curve and time-temp.shift function.
Initial design using conventional approach(trial and error combined w/ experience).
Mueller, Rzepka, Will · WOST 29.-30. November 2007 · Page 18 Copyright © Qimonda AG 2007 · All rights reserved.
Identification Flow For Visco-Elastic Materials
Sensitivity AnalysisLatin Hypercube Sampling w/ 100 samples
remove parameter from the design space that don’t show sensitivityon the objective function
only for new material test
Global OptimizationGenetic Algorithm w/ population size 10 over 20 generations
search for “global optimum” in design space
only for new material, e.g. adhesive
Design ImprovementEvolutionary Search w/ 1 parent and 5 newborns over 20 generations
further improvement of the best design from “global optimization”
Best method to adjust already available data,e.g. for new filler size
Local OptimizationGradient based (NLPQL) method
fine tuning of the improved material parameters
not necessarily needed
Mueller, Rzepka, Will · WOST 29.-30. November 2007 · Page 19 Copyright © Qimonda AG 2007 · All rights reserved.
Pilot Project w/ Dynardo
Simulation Task
Parameter Identification
Conclusions
Mueller, Rzepka, Will · WOST 29.-30. November 2007 · Page 20 Copyright © Qimonda AG 2007 · All rights reserved.
Conclusions
optiSlang has been applied for identification of mold compound constitutivelaw by calibrating simulation to measurement (Dynamic Mechanical Analysis)
Sensitivity analysis should be applied first to reduce the dimension of thedesign space for efficient optimization.
Genetic Algorithms are efficient to identify parameter sets (master curve dataand time-temp. shift function constants) which already characterize the visco-elastic response of the material in first assumption.
Evolutionary search strategies can be applied very effectively to improve thematerial data further or to adjust already available data of a similar material, e.g. mold compound w/ different filler content or size.
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