2008 international ansys conference - the ansys experts€¦ · (coming from a doe, an optimization...

© 2008 ANSYS, Inc. All rights reserved. 1 ANSYS, Inc. Proprietary

2008 International 2008 International ANSYS ConferenceANSYS Conference

Multi-Objective Optimization of BGA Packages

Marco Spagnolo1,2

Alberto Bassanese1

Can Ozcan1

1: Ozen Engineering 2: EnginSoft


SummaryIn this presentation we will describe an optimisation procedure that can be conveniently and efficiently employed for determining :

- the design parameters that are critical for BGA packages;- their relative importance;- the actual BGA optimal design;

Both geometric parameters and material properties will be considered.2D and 3D approaches will be compared.Contents - The Software - FE models - Boundary Conditions - Loads - Workflow Set-up and Post-processing - Results - Conclusions


Finite Element Models

The subsequent approach was followed for:

- 2D model (APDL parametric model) without Underfill - 2D model (Workbench parametric model) without Underfill - 3D model* (APDL parametric model) without Underfill - 3D model* (APDL parametric model) with Underfill

Input VariablesGeometric ParametersMaterial properties

* only 3D model results are presented in this presentation.


Optimization Workflow Setupinput variables

input file

DOE

scheduler

external script nodes

output variables

objectives/constraints


Finite Element Model - Parameters


Finite Element Model - Parameters

t_mold

t_sm

ballh

…


Finite Element Model – Element Types

Element type choice

All entities but solder ball: SOLID 185

SOLID185 is used for 3-D modeling of solid structures.It is defined by eight nodes having three degrees of freedom at each node: translations in the nodal x, y, and z directions.The element has plasticity, hyperelasticity, stress stiffening, creep, large deflection, and large strain capabilities.


Finite Element Model – Element Types

Element type choice

Solder ball: VISCO 107

VISCO107 is used for 3-D modeling of solid structures.It is defined by eight nodes having three degrees of freedom at each node: translations in the nodal x, y and z directions.The element is designed to solve both isochoric (volume preserving) rate-independent and rate-dependent large strain plasticity problems. Iterative solution procedures must be used with VISCO107 since it is used to represent highly nonlinear behavior. Large deflections must be active in order to update the geometry in each substep


Finite Element Model – w/o. Underfill

VFBGA Design

http://www.asetwn.com.tw/content/2-4-1.html

http://www.asetwn.com.tw/content/2-4-1.html


Finite Element Model – Unit Cells


Finite Element Model – w. Underfill

Underfill Radius


Finite Element Model – Unit Cells


Boundary Conditions

Uz=0

Ux=0

Uy=0


Temperature Cycle Loading

• -40C to 125C uniform temperature loading


Geometric Input Parameters

t_sm => solder mask thickness

t_bcul => board copper layer thickness

t_brd => board thickness

t_cup => copper pad thickness

t_pcul => package copper layer thickness

t_core => substrate core layer thickness

t_da => die attach thickness

t_die => die thickness

t_mold => mold compound thickness

ballp => solder ball pitch

ballr => solder ball radius

w_mold => free side mold compound extension

w_brd => free side board extension

ndr_radius => underfill radius on the external side

ballh => solder ball height

w_cup => half width of copper pad

sm_open => solder mask opening

w_ndr => underfill extension

ballh_to_balld => ballh = 0.6-0.8 balld

w_cup_to_balld => w_cup = 0.2-0.6 balld

sm_open_to_w_cup => sm_open = 0.1-0.5 w_cup

w_ndr_to_balld => w-ndr = 0.8-1.2 balld

black: independent input variable

green: dependent input variable

red: internal constraint

SUMMARYInput Variables: 17


Material Input Variables

SUMMARY – 3D MODELS

With UF Whithout UF

Number of Considered Geometric Parameters: 17 16

Number of Considered Material Properties: 20 18

Total: 37 34

Material Prop. ID Factorsbrd_E Materials_Properties[0]brd_sm_CTE Materials_Properties[1]pkg_sm_E Materials_Properties[2]pkg_sm_CTE Materials_Properties[3]die_E Materials_Properties[4]die_CTE Materials_Properties[5]ball_E Materials_Properties[6]ball_CTE Materials_Properties[7]pkg_core_E Materials_Properties[8]pkg_core_CTE Materials_Properties[9]

Material Prop. ID Factorsbrd_core_E Materials_Properties[10]brd_core_CTE Materials_Properties[11]dieat_E Materials_Properties[12]dieat_CTE Materials_Properties[13]pkg_cu_E Materials_Properties[14]pkg_cu_CTE Materials_Properties[15]mold_E Materials_Properties[16]mold_CTE Materials_Properties[17]ndr_fill_E Materials_Properties[18]ndr_fill_CTE Materials_Properties[19]

CTE = Coefficient Of thermal Expansion E = Young’s Modulus


Input Parameters – Range Setup


Input Parameters – Range Setup

• Range for geometric parameters :

Range for material properties: standard configuration ± 25% (3 levels)

0.02 ≤ t_sm ≤ 0.05 t_bcul =0.03 mmt_brd =1.2 mm0.015 mm ≤ t_cup ≤ 0.045 mm0.015 mm ≤ t_pcul ≤ 0.040 mm0.1 mm ≤ t_core ≤ 0.3 mm 0.0125 mm ≤ t_da ≤ 0.5 mm

0.15 mm ≤ t_die ≤ 0.6 mm0.20 mm ≤ t_mold ≤ 0.8 mm0.40 mm ≤ ballp ≤ 1.20 mm0.10 mm ≤ ballr ≤ 0.4 mm1.0 mm ≤ w_mold ≤ 4.0 mm

0.6 ≤ ballh_to_balld ≤ 0.8 0.2 ≤ w_cup_to_balld ≤ 0.6 0.1 ≤ sm_open_to_w_cup ≤ 0.5 0.8 ≤ w_ndr_to_balld ≤ 1.2


Output Variables & Objectives

Output variable n.1: plastic_work

The plastic work is computed on the critical ball and is evaluated for the volume corresponding to 20% of ball height starting from top and bottom

Output variable n.2: delta_max

Delta_max is the relative displacement between the points A and B, respectively on the bottom and on the top of the critical solder ball

B

A20% ball height


Work flow for Optimization Setup

• First level text – Arial 28 pt.– Second level text – Arial 28 pt.

• Third level text – Arial 24 pt.– Fourth level text – Arial 22 pt.

• Fifth level text – Arial 20 pt.


Post-Processing - modeFrontier

Max Value of the

correlation

Index = 0.4

No linear correlation

between Input and

Output Variables RankingThe correlation index

Input and Output Variables• 125 Random Designs– DOE Main Effects – Correlation Matrix



• 125 Random Designs– DOE Student Chart – Plastic Work

sm_open_to_w_cup

t_core

brd_core_E pkg_core_CTE

ball_Edie_CTE

t_mold ballp mold_CTEpkg_sm_CTE

ball_CTEmold_E

w_cup_to_balld

pkg_sm_E

t_die

die_E

Input Variables

Effect Size



• 125 Random Designs– DOE Student Chart – Both Outputs

t_mold (1, -0.9)

ballp (0.7, 0.4)

mold_CTE (0.58, -1.0)

sm_open_to_w_cup

(-0.65, -0.07)

t_core

(-0.63, 0.4)

Input Variables

Plastic WorkRel. Displacement



• 125 Random Designs– DOE Student Chart – Overall

Full Name Factor Plastic Workbrd_sm_CTE Materials_Properties[1] -0.015 [0.476]

pkg_cu_CTE Materials_Properties[15] 0.021 [0.466]

dieat_CTE Materials_Properties[13] 0.044 [0.437]

w_mold 0.048 [0.427]

dieat_E Materials_Properties[12] 0.092 [0.365]

Full Name Factor Rel. Displ. t_da 0.028 [0.441]

t_sm -0.053 [0.399]

brd_core_E Materials_Properties[10] 0.067 [0.379]

sm_open_to_w_cup -0.068 [0.394]

ball_CTE Materials_Properties[7] -0.069 [0.359]

Full Name Factor Rel. Displ. Plastic Workdieat_CTE Materials_Properties[13] -0.146 [0.246] 0.044 [0.437]

w_mold -0.107 [0.298] 0.048 [0.427]

t_da 0.028 [0.441] 0.117 [0.320]

brd_E Materials_Properties[0] -0.127 [0.275] -0.132 [0.316]

t_pcul 0.151 [0.217] -0.184 [0.231]

Displacement Plastic Work



• 125 Random Designs– Initial DOE Population

Scatter Chart : The Design Space

plastic work

rela

tive

disp

lace

men

t



• Virtual Optimization with 3000 virtual designs

After running MOGAII within modeFROINTER

rela

tive

disp

lace

men

t

plastic work

Scatter Chart : The Design Space



• Response Surface (RS) Modeling – RSs are a collection of mathematical and statistical techniques

useful for the modeling of problems – RSM can be trained from an available database of designs

(coming from a DOE, an optimization or from experimental data)– Once trained, they can be used to extrapolate the outputs of the

system: a virtual optimization can be run, in which all (or a part) of the design are extrapolated from RSM, saving a lot of CPU time

– Predictions made within the observed space of variable values are called interpolations.

– Predictions outside the observed space are called extrapolations and require caution



• Response Surface (RS) Modeling – Kriging RSM– Kriging is a statistical method for RSM– Its aim is to minimize the standard deviations between the real

design values and the extrapolated values.– It is known to be an accurate method;– It has the ability to interpolate a given field with a limited number of

observations



• Kriging RSM 3D ExplorationLateral view

Top View

3D View

Lateral View

t_mold vs Plastic_work vs ballp

ballp

t_mold

t_mold

ballp

plas

tic_w

ork

plas

tic_w

ork



• Kriging RSM 3D Exploration

30

t_mold vs plastic_work vs ballp

3D View

t_mold

Plastic _work

ballp



• Virtual Optimization– Scatter Chart : The Design Space

After running MOGAII within modeFROINTER

plastic work

rela

tive

disp

lace

men

t

PARETO FRONTIEROPTIMUM DESIGN


Validation of Virtual Optimization

• Geometric configuration for the real optimal design


Validation of Virtual Optimization

• Confirmed plastic work and displacement results from real FEA solution


w. Underfill – Post Processing

• 3D model with underfill


w. Underfill – Post Processing

•

Rel. Displacement Minimization

sm_open_to_w_cup

T_mold

Mold CTE

W_cup_to_balld

Ball pitch

Ball radius

Underfill CTE

Plastic Work Minimization


Validation of Optimization

• Confirmation of results with a real FEA run


Conclusions

• 2D APDL model – Benefits:

• very fast simulations• critical input variables validated by 3D model

– Drawbacks:• wrong correlation between objectives

• 3D APDL model– Benefits:

• more reliable• conflict evidences between the objectives of the optimisation• material properties vs geometric parameters• presence of underfill is critical

– Drawbacks:• slower simulations• meshing difficulties


Conclusions

• Where do we use modeFrontier in our day-to-day simulation practice?– Matching Experimental Data by varying of material and geometric input data within

tolerance values:• Thermo-couple readings• Displacements of Moire Measurements• ...

– Performing DOE studies to understand main effects of critical parameters• Finding the best underfill material for reliability• ...

– Getting the best solution for reliability using multi objective optimization• Optimization for minimum plastic work• Optimization for minimum shear strains/stresses

– Six-Sigma Studies for variations in materials• Effect of glass transition temperature variation of underfills• Effect of modulus variation of underfills• ...

2008 international ansys conference - the ansys experts€¦ · (coming from a doe, an optimization...

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