Independent Study

Independent Study
Independent Study



      Bond Parameters Optimization in Thermosonic Copper Wire
               Bonding Process in Semiconductor Industry




                        Khrongkhet Khuantham




An Independent Study submitted in Partial Fulfillment of the requirements
   for the Degree of Master of Engineering (Engineering Management)
         International Graduate Program, Kasetsart University

                               2009
Independent Study
Khrongkhet Khuantham 2009 : Bond Parameters Optimization in Thermosonic
Copper Wire bonding Process in Semiconductor Industry. Master of Engineering
(Engineering Management), Department of Industrial Engineering.
Independent Study Advisor : Associated Professor Prapaisri Sudasna-na Ayudthya, Ph.D. 54
pages.


       This independent study relates to the thermosonic copper wire bonding process used
for providing electrical connection between the silicon chip and the external leads of the
semiconductor device using copper bonding wires on package type Heat Sink Thin Shrink
Small Outline 32 (HTSSOP32) that has total 32 leads fingers. The objective of the study was
to identify the significant factors affecting low average stitch pull test and determine the
optimum bond parameters necessary to maximize the stitch pull test level.


        The statistical design of experiment was applied to first indentify the significant
factors. The critical process parameters likely to create the low average stitch pull test level
were defined by the process engineer. The factors chosen for study were contact time, contact
power, contact force, base time, base power and base force parameter. A 26-1 Factorial design
was used to evaluate these. The result indicated the significant factors to be contact force,
base power and base force.


        The optimum levels of the three significant factors were determined by using a
Central Composite Design and Canonical Analysis. The result showed the stationary points
for the average stitch pull test surface. The optimum level of the factors are contact force of
218 grams-force ; base power of 86 DAC ; base force of 268 grams force. The resulting
average stitch pull test was 28.0764 grams force.




________________               _________________________                  ___ /___ /___

Student’ s Signature                 Advisor’ s Signature                 DD MM YY
Independent Study
i



                     TABLE OF CONTENTS



                                         Page

TABLE OF CONTENTS                         (i)

LIST OF TABLES                            (ii)

LIST OF FIGURES                           (iii)

INTRODUCTION                               1

     OBJECTIVES                            5

LITERATURE REVIEWS                         7

     FACTORS SCREENING EXPERIMENT         12

     RESPONSE SURFACE METHOD              14

     RESPONSE SURFACE ANALYSIS            18

MATERIALS AND METHODS                     22

RESULTS AND DISCUSSION                    24

     FRACTIONAL FACTORIAL RESULTS         25

     CENTRAL COMPOSITE RESULTS            30

CONCLUSION                                38

RECOMMENDATIONS                           39

REFERENCES                                40

APPENDICES

     APPENDIX A                           43

     APPENDIX B                           45

     APPENDIX C                           50
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ii



                                LIST OF TABLES


                                                                        Page

Table 1 : Physical properties comparing between Cu Al and Au wire        8

Table 2 : Advantages of copper wires over gold wires                     9
          and challenges of wire bonding using copper wires

Table 3 : Matrixes of 2k Central Composite design                        15

Table 4 : α and n 0 for experiment that have various factors             16

Table 5 : Process parameters with different operating levels             22

Table 6 : 26-1 Factorial Design of Experiment                            24

Table 7 : Result of response from 26-1 Factorial Experiment              25

Table 8 : Level of factors for 23 Central Composite Design experiment    30

Table 9 : Result of response from 23 Central Composite design            30
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                                LIST OF FIGURES

                                                                     Page

Figure 1 : Wire bonding characteristics                               1

Figure 2 : Stitch bond timing diagram                                 3

Figure 3 : Process Capability of Stitch pull test                     4

Figure 4 : Wire bonding diagram of HTSSOP32 Package                   6

Figure 5 : HTSSOP32 sample bonded device                              6

Figure 6 : Wire bond machine ASM Eagle60AP                            6

Figure 7 : MKE copper wire size 38 um                                 6

Figure 8 : PECO capillary for copper wire size 38 um                  6

Figure 9 : Wire bonding mechanism                                     7

Figure 10 : Copper wire bonding                                       8

Figure 11 : EFO assembly for gold and copper wire                     9

Figure 12 : Crack Stitch neck and wire pull test schematic            10

Figure 13 : Wire pull tester                                          11

Figure 14 : Pull hook                                                 11

Figure 15 : Total points in 23 Central Composite design               15

Figure 16 : Contour plot analysis                                     18

Figure 17 : Response surface of second-degree polynomial              20
            of 2 and 3 factors that optimum point is maximum point

Figure 18 : Response surface of second-degree polynomial              20
            of 2 and 3 factors that optimum point is minimum point

Figure 19 : Response surface of second-degree polynomial              21
            of 2 and 3 factors that optimum point is saddle point

Figure 20 : Pareto effect plot on factors that influence              26
            the average stitch pull test
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                       LIST OF FIGURES (Continued)

                                                                             Page

Figure 21 : Normality Probability Plot of average stitch pull test            26
           (Screening experiment)

Figure 22 : Residual Plot of average stitch pull test                         27
            (Screening experiment)

Figure 23 : Main Effects Plot for average stitch pull test, contact force     28

Figure 24 : Main Effects Plot for average stitch pull test, base power        28

Figure 25 : Main Effects Plot for average stitch pull test, base force        29

Figure 26 : Normality Probability Plot of average stitch pull test            31
            (Central composite experiment)

Figure 27 : Residual Plot of average stitch pull test                         32
            (Central composite experiment)

Figure 28 : Contour plot of response surface equation of the average          33
            stitch pull test that consists of base power and contact force

Figure 29 : Surface plot of response surface equation of the average          34
            stitch pull test that consists of base power and contact force

Figure 30 : Contour plot of response surface equation of the average          34
            stitch pull test that consists of base force and contact force

Figure 31 : Surface plot of response surface equation of the average          35
            stitch pull test that consists of base force and contact force

Figure 32 : Contour plot of response surface equation of the average          35
            stitch pull test that consists of base force and base power

Figure 33 : Contour plot of response surface equation of the average          36
            stitch pull test that consists of base force and base power

Figure 34 : Process Capability from the optimized bond parameters level       37
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                      LIST OF FIGURES (Continued)

                                                                          Page

Appendices

Appendix B-1 Create Factorial Design                                       45

Appendix B-2 Select design level and number of factor                      45

Appendix B-3 Select ½ fractional and number of replication                 46

Appendix B-4 Input factor name and level                                   46

Appendix B-5 Input response, average stitch pull test                      47

Appendix B-6 Analyze the data                                              47

Appendix B-7 Select the response and order of term in model                48

Appendix B-8 Select Normality plot and residual plot                       48

Appendix B-9 Pareto Chart of effect plot                                   49

Appendix C-1 Create Response Surface Design                                50

Appendix C-2 Select design type and number of factor                       50

Appendix C-3 Select number of center point, replication and alpha level    51

Appendix C-4 Input factor name and level                                   51

Appendix C-5 Input the response, average stitch pull test                  52

Appendix C-6 Analyze the data                                              52

Appendix C-7 Select the response and model term                            53

Appendix C-8 Minitab output                                                53

Appendix C-9 Create the surface and contour plot                           54
Independent Study
Bond Parameters Optimization in Thermosonic Copper Wire
            bonding Process in Semiconductor Industry


                                 Introduction

        Semiconductor industry is a highly competitive business with ever shorter
product life cycles. Therefore, one of challenges in this industry is quality
improvement with no additional investment. Highly competitive market has made
semiconductor manufacturers focus on their quality improvement activities in order to
get the highest rate of yield on expensive spending.

        In the past, the way to obtain the high quality integrated circuit (IC) was
product inspection after completion of a production process. This method tends to
solve problems after they had already occurred. It could not really solve the root cause
of the problem and ensure the quality level of products so Statistical Process Control
(SPC) is a concept about prevention and problem solving, which concentrates in
process control and improvement at the production process directly.

        SPC is applied through answering a series of questions, such as “How to
collect the data?”, “How to analyze the data and interpret the output result in order to
indicate the product quality level. It can help to collect the data from the controlled
process and analyze them in order to find out the process capability. While a process
engineer is trying to improve the process capability, one of the statistical method that
is applied is experimental design. Next step of research and analyze the data to find
out the factor effect and constraints in the process as using the advance statistical
method is called Response Surface Methodology, RSM.

         Manufacturing processes of IC chip- package consist of a taping, lapping, de-
taping, wafer mounting, wafer sawing, die attaching, epoxy curing, wire bonding,
molding, marking, trimming, solder plating, forming, testing and packing. The
purpose of wire bonding is to use gold wires to provide electrical connection between
the silicon chip and the external leads of the semiconductor device see Figure 1.




                      Figure 1 Wire bonding characteristics
Independent Study
2


       In recent years, Copper is rapidly gaining a foothold as an interconnection
material in semiconductor packaging because of its obvious advantages over
gold. These advantages include: 1) cost reduction of up to 90%; 2) superior electrical
and thermal conductivity; 3) less inter-metallic growths; 4) greater reliability of the
bond at elevated temperatures; and 5) higher mechanical stability.

        Although Cu wire has many advantages over Au wire, it has not been widely
used like Au wire, because it also brings many new challenges and quality problems
to wire bonding.


       Problem Statement

        This research study in Thermosonic copper wire bonding process because of
the material cost saving activity, copper were substituted for gold, which is the
predominant material used for plastic semiconductor package interconnections. The
development of a copper wire bonding process represents a significant step towards
the goal. However, semiconductor manufacturers still face problems on the low yield
rate of copper wire bond products concerning to poor bond ability of stitch bond (one
of copper wires bonding challenges) because they had just been finished the
qualification, testing and small scale pilot production.

        The problem of Cu wire bonding process that would be studied is low stitch
pull test (SPT) value of copper wire bonding, which is frequently found from copper
wire bonding process as there are six factors to be studied and analyzed, which are

       1. Contact time, which is time that occurred after capillary impact to lead
          surface. This period contact power and force are applied. If contact time is
          set to be zero, contact parameter will be ignored.

       2. Contact power, which is ultrasonic energy that is applied during contact
          time in order to prepare stitch shape to be proper before Base parameter
          would be applied.

       3. Contact force, which is force that is applied during contact time in order to
          prepare stitch shape to be proper before Base parameter would be applied.

       4. Base time, which is main time that used after contact time is completed for
          applying base power and force.

       5. Base power, which is main ultrasonic energy that is applied during base
          time. It is the main factor for stitch bond quality.

       6. Base force, which is main force that is applied during base time after
          contact period. It is also the main factor for stitch bond quality.

          These interest factors are illustrated in stitch bond timing diagram in
       Figure 2.
Independent Study
3




                     Figure 2 Stitch bond timing diagram


       Currently these six factors that might influence to the low stitch pull test
problem are set as the following level,


       1. Contact Time is set at 5 ms

       2. Contact Power is set at 35 DAC

       3. Contact Force is set at 240 gf

       4. Base Time is set at 30 gf

       5. Base Power is set at 100 DAC

       6. Base Force is set at 290 gf
4


        These bond parameters give poor process capabilities, both low mean of stitch
pull test and low Cpk, 0.69 bring about to high reject quantity of stitch pull test lower
than specification (15 gf) were observed as shown in process capability Figure 3
below,




               Figure 3 Process Capability of Stitch pull test
5


       Objectives

        1. To study in thermosonic copper wire bonding process to select the
significant factors that influence to the low Stitch pull test level that directly effect to
the low Cpk of stitch pull test as using 2k Fractional Factorial Design of experiment.

        2. To optimize response, which is average stitch pull test, from the significant
factors that have the effects in thermosonic copper wire bonding process from
Response surface method.

      3. To find the average stitch pull test equation from Response Surface
Methodology as follow to 2k Central Composite.

       4. To improve average stitch pull test level and Cpk in thermosonic copper
wire bonding process.


       Independent Study Scope

        This research would study in integrated circuit (IC) package type Heat Sink
Thin Shrink Small Outline (HTSSOP32) that has total 32 leads fingers as all devices
are prepared from only one Die bond machine type ASM AD830. During thermosonic
copper wire bonding process, this research would consider only average stitch pull
test value from total wires, 3 units x 35 wires/unit (wire bonding diagram and sample
bonded device of HTSSOP32 is illustrated in Figure 4 and Figure 5), which is 105
wires per run as there are research scope as the following,

       1. Wire bonding machine type ASM Eagle60AP , shown in Figure 6.

       2. Lead frame type is stamped CuNiPd(Au) 32 leads.

       3. Epoxy type using at Die bond is QMI-519.


       4. Die is ICN8 wafer fabrication.

       5. Copper wire type is MKE Cu wire size 38 um, shown in Figure 7.


       6. Capillary type is PECO copper wire capillary for 38 um wire size. See
          Figure 8.

       7. Wire bonding temperature is 230 C


       8. Wire Pull Test machine type is BT4000.
6




Figure 4 Wire bonding diagram                Figure 5 HTSSOP32
of HTSSOP32 Package                           sample bonded device




                    Figure 6 Wire bond machine ASM Eagle60AP




Figure 7 MKE copper wire              Figure 8 PECO capillary
size 38 um                            for copper wire size 38 um
7


                               Literature review


         Manufacturing processes of IC chip- package consist of a taping, lapping, de-
taping, wafer mounting, wafer sawing, die attaching, epoxy curing, wire bonding,
molding, marking, trimming, solder plating, forming, testing and packing. The
purpose of wire bonding is to use gold wires to provide electrical connection between
the silicon chip and the external leads of the semiconductor device.

        Tung-Hsu Hou et al., (2005) explained in an integrated system for setting the
optimal parameters in IC chip-package wire bonding processes that the wire bonding
process starts from positioning the capillary above a bond pad of the die with a gold
ball formed at the end of the gold wire. The capillary then descends and presses the
gold ball on the bond pad to form the first bond that is also called the ball bond. In a
thermo-sonic wire bonding system, ultrasonic power and vibration force are applied,
and heat is also applied to the pad to facilitate the bonding efficiency. After the ball is
bonded to the die, the capillary arises to the loop height position. The gold wire is
then led by the capillary to the inner lead of the substrate. The capillary deforms the
wire against the lead, producing a wedge-shaped bond that is called the stitch bond or
the second bond. The capillary then arises to the preset height and a new wire ball is
formed on the tail of the gold wire. A hydrogen flame or an electric frame may be
used to form the ball. The wire bonding mechanism is illustrated in Figure 9.




                               Figure 9 Wire bonding mechanism


       In recent years, Copper is rapidly gaining a foothold as an interconnection
material in semiconductor packaging because of its obvious advantages over
gold. These advantages include: 1) cost reduction of up to 90%; 2) superior electrical
and thermal conductivity; 3) less inter-metallic growths; 4) greater reliability of the
bond at elevated temperatures; and 5) higher mechanical stability.
8


      Copper is inherently 3 to 10 times cheaper than gold, so substituting gold
wires with copper wires can realize tremendous annual cost savings for a
semiconductor packaging company. See Figure 10, Copper wire bonding.




                             Figure 10 Copper wire bonding

        Copper wire, with an electrical resistivity of 0.017 micro ohm-m at room
temperature, is more electrically conductive by about 25%-30% than gold, which has
a resistivity of 0.022 micro-ohm-m at room temperature. This low electrical
resistivity of copper results in better electrical performance. In particular, copper
wire is a preferred bonding wire material for high-current or high-power applications,
since it can carry more current for a given wire diameter.

         Copper also has about 25% higher thermal conductivity than gold (385-401 W
 m-1 K-1 for Cu and 314-318 W m-1 K-1 for Au). Thus, copper wires dissipate heat
 within the package faster and more efficiently than gold wire, minimizing the thermal
 stress to which they are exposed. Excessive heat on the wires can promote grain
 growth, which lowers the strength of the wires. The heat-affected zone (HAZ) formed
 on the wire during free air ball formation also tends to be shorter in copper wires
 because of their better thermal conductivity. The shorter HAZ in copper wires give
 them better wire looping capability than gold, an important aspect of die stacking.
 See physical properties comparing with Au wire in table 1.
(http://www.siliconfareast.com/wirebond-copper.htm)


Table 1 Physical properties comparing between Cu Al and Au wire




        Although Cu wire has many advantages over Au wire, it has not been widely
used like Au wire, because it also brings many new challenges and quality problems
to wire bonding. See advantages and challenges of copper wire bonding in table 2,
9


Table 2 Advantages of copper wires over gold wires and challenges of wire bonding
using copper wires

-------------------------------------------------------------------------------------------------------
Advantages                                   Challenges
-------------------------------------------------------------------------------------------------------
Lower cost                                   Easy to be oxidized in air
Better thermal properties                    Additional bonding parameters for using
Better electrical properties                 forming inert gas
Excellent ball neck strength                 Need more ultrasonic energy and higher bonding
Higher Stiffness                             force, which can damage Si substrate
High loop stability                          Poor bond ability for stitch/wedge bonds
-------------------------------------------------------------------------------------------------------

        Copper is easy to be oxidized in air, and therefore copper wire bonders must
have additional tools to prevent copper oxidation (Hong et al., 2005). Additional
bonding parameters for using forming inert gas need to be optimized (Chen et al.,
2006), and additional cost of forming gas must be considered (Goh and Zhong, 2007).
Although N2 gas can be a suitable option, a forming gas mixture of 95 per cent N2/ 5
per cent H2 has been shown to be the best choice (England and Jiang, 2007), see
figure 11 illustrated additional tool of inert gas for copper wire bonding comparing
with gold wire bonding.




      EFO assembly for gold wire                     EFO assembly with forming gas supply
                                                     for copper wire

Figure 11 EFO assembly for gold wire and EFO with forming gas supply for copper
          wire

       Copper wires have much higher hardness and stiffness than gold wires.
Copper wire bonding needs more ultrasonic energy and higher bonding force, which
can damage the Si substrate, form die cratering (Hong et al., 2005) and induce
cracking and peeling of the bonding pad (Tian et al., 2005).

       A stage temperature of 150-2008C is also needed for bonding copper wire
(Chen et al., 2006). As-drawn copper wire possesses higher strength and hardness, but
its lower ductility reduces the reliability of bonding. The lower strength of the
10


annealed wire results in breakage (Hung et al., 2006). There is also a need to
investigate the effects of the process parameters on the hardness of Cu FABs (Zhong
et al., 2007), because Cu exhibits a larger strain-hardening effect at a higher strain rate
Bhattacharyya et al., 2005).

        Since copper wire is harder than gold wire, to improve stitch Bond ability,
higher parameter settings have to be used, causing heavy cap marks and potential
short tails or wire open. Cu/Au stitch bonds are weak, and thus copper wire bonding
has wire open and short tail defects, poor process control, and low stitch pull readings
according to weak stitch neck strength from the improper bond parameters, see Figure
12 (weak stitch neck strength and wire pull test schematic used for stitch neck
strength measurement) (Goh and Zhong, 2007).




       Weak and Crack stitch neck                      Wire pull test Schematic
       effect to low pull test reading

                                         Figure 12


       Weak stitch neck is the severing of the wire from its wedge or crescent bond
due to a fracture in the neck. The stitch neck is the portion of the wire where the
wire tapers off into the wedge or crescent bond. It is equivalent to the neck of a ball
bond.

        Weak of stitch neck is commonly due to poor wire bonder set-up. Poor set-up
includes improper bonding parameter settings, bond head movement settings, and
worn-out or contaminated tools. Incorrect bonding parameters can deform the bond
excessively, resulting in a very thin and weak heel which can easily fracture.
Improper bond head movements and low loop settings may subject the wires to
excessive stresses that tend to pull them backward and away from the bonds,
resulting in gross heel cracks which may propagate into total fracture. Worn-out and
contaminated tools can also produce mechanical damage or defects in the wires
which can act as starting points for crack propagation.

       The most likely potential cause of weak and crack stitch neck problem in
thermosonic copper wire bonding process that has always been observed is the
improper 2nd bond parameter because the copper wire characteristics is harder than
gold, in order to make the wire stick on the lead surface the bond parameter have to
11


be set at the different or higher level than normal that used for gold wire. Therefore if
these parameters is set at the improper level, they might affect directly to the weak of
stitch neck problem.

        In general, the ways to measure or observe the stitch neck quality are
scanning electron microscope (SEM) inspection, which is the very high power
microscope, it is used to inspect at the neck of each interested wire. Another way is
the stitch pull test (SPT), which is one of several available time-zero tests for wire
bond strength and quality. It consists of applying an upward force under the wire to
be tested, effectively pulling the wire away from the lead surface.

       Stitch pull testing requires a special equipment commonly referred to as a
wire pull tester (or bond pull tester) see Figure 13, which consists of two major parts:
1) a mechanism for applying the upward pulling force on the wire using a tool
known as a pull hook see Figure 14; and 2) a calibrated instrument for measuring the
force at which the wire eventually breaks. This breaking force is usually expressed
in grams-force.




                              Figure 13 Wire pull tester




                                 Figure 14 Pull hook
12


       Design of Experiment

       Design of experiment was started to use in Agriculture, which Montgomery
(1976) indicated that Fisher had applied the Statistical method and data analysis to use
on the experiment result at Agriculture laboratory in London, UK. This method is the
Analysis of Variance (ANOVA), which is the main method for data analysis from
experimental design but Fisher‘s concept could be well applied in researches of other
study areas. Next step of research and analyze the data to find out the factor effect and
constraints in the process as using the advance statistical method is called Response
Surface Methodology, RSM., which Khuri and Cornell (1987) stated that there were
researches in this area since 1930. Response Surface method was achieved and
popular, moreover it was applied in other research area such as Engineering, Food
Sciences, Biology and Industry etc.

        There are many applications of Design of experiment in researches in
semiconductor industry but the mostly found and published by Sheffer and Levine
(1991) is the research for study the stitch neck broken wires problem in wire bonding
process as there was screening experiment to find out the significant factors from 5
factors by Fractional Factorial design of experiment. After that Sheffer and Levine
(1991) stated about the method to find the surface response equation from the
screening significant factors to improve process capability with Central Composite
Design of experiment.

         This research’ s purpose is to study the factors that influence to the response in
thermosonic copper wire bonding process. After finished wire bonding, next steps is
the quality assurance of wire bonding as one important point for roving inspection is
the stitch pull test, which is the procedure to check and ensure the stitch neck strength
that have no any crack or weak condition. If there is any device that stitch pull test is
lower than specification, that device and also the affecting production lot will be
defective and would be scrapped all.


       Screening Experiment

        Experiments, which consist of several interesting factors (Multi-factor
experiments) have been widely used to screen the significant factors that influence to
the response are the following, (http://www.siliconfareast.com/factorial-2k.htm )

       2k Factorial Experiment

        A frequently used Factorial Experiment design in the semiconductor industry
is known as the 2k Factorial design, which is basically an experiment involving k
factors, each of which has two levels ('low' and 'high'). In such a multi-factor two-
level experiment, the number of treatment combinations needed to get complete
results is equal to 2k. Thus, a 2k Factorial Experiment that deals with 3 factors would
require 8 treatment combination, while one that deals with 4 factors would require 16
of them. One can easily see that the number of runs needed to complete a Factorial
Experiment, even if only two levels are explored for each factor, can become very
large.
13


        The first objective of a Factorial Experiment is to be able to determine, or at
least estimate, the factor effects, which indicate how each factor affects the process
output. Factor effects need to be understood so that the factors can be adjusted to
optimize the process output.

        The effect of each factor on the output can be due to it alone (a main effect of
the factor), or a result of the interaction between the factor and one or more of the
other factors (interactive effects). When assessing factor effects (whether main or
interactive effects), one needs to consider not only the magnitudes of the effects, but
their directions as well. The direction of an effect determines the direction in which
the factors need to be adjusted in a process in order to optimize the process output.

        In Factorial designs, the main effects are referred to using single uppercase
letters, e.g., the main effects of factors A and B are referred to simply as 'A' and 'B',
respectively. An interactive effect, on the other hand, is referred to by a group of
letters denoting which factors are interacting to produce the effect, e.g., the
interactive effect produced by factors A and B is referred to as 'AB'.

        Each treatment combination in the experiment is denoted by the lower case
letter(s) of the factor(s) that are at 'high' level (or '+' level). Thus, in a 2-Factorial
Experiment, the treatment combinations are: 1) 'a' for the combination wherein factor
A = 'high' and factor B = 'low'; 2) 'b' for factor A = 'low' and factor B = 'high'; 3) 'ab'
for the combination wherein both A and B = 'high'; and 4) '(1)', which denotes the
treatment combination wherein both factors A and B are 'low'.

       Based on Factorial Experiments, the main effect of a factor A in a two-level
two-factor design is the change in the level of the output produced by a change in the
level of A (from 'low' to 'high'), averaged over the two levels of the other factor B.
On the other hand, the interaction effect of A and B is the average difference
between the effect of A when B is 'high' and the effect of A when B is 'low.' This is
also the average difference between the effect of B when A is 'high' and the effect of
B when A is 'low.'

        The magnitude and polarity (or direction) of the numerical values of main and
interaction effects indicate how these effects influence the process output. A higher
absolute value for an effect means that the factor responsible for it affects the output
significantly. A negative value means that increasing the level(s) of the factor(s)
responsible for that effect will decrease the output of the process.

       2k Fractional Factorial Experiment

       This experiment has same characteristic as 2k Factorial Experiment but it will
be used when there are many factors to study in the experiment. Due to the
experiment would be high cost and also waste much time in order to perform the
experiment until complete all treatment combination. Therefore they might perform
the experiment as half replication or quarter replication or less.
14


        Response Surface Methodology

         In statistics, response surface methodology (RSM) explores the
relationships between several explanatory variables and one or more response
variables. The method was introduced by G. E. P. Box and K. B. Wilson in 1951. The
main idea of RSM is to use a set of designed experiments to obtain an optimal
response. Box and Wilson suggest using a first-degree polynomial model to do this.
They acknowledge that this model is only an approximation, but use it because such a
model is easy to estimate and apply, even when little is known about the process.

        An easy way to estimate a first-degree polynomial model is to use a Factorial
Experiment or a fractional Factorial designs. This is sufficient to determine which
explanatory variables have an impact on the response variable(s) of interest. Once it is
suspected that only significant explanatory variables are left, then a more complicated
design, such as a central composite design can be implemented to estimate a second-
degree polynomial model, which is still only an approximation at best. However, the
second-degree model can be used to optimize (maximize, minimize, or attain a
specific target for) a response.

       To estimate the second-degree polynomial model, popular and widely used
design of experiments are 2k Central Composite design and Box-Behnken Design

        Regarding to this research considers in second-degree polynomial model as

        Y = β0 +          i   Xi +      i   Xi 2 +                ij   Xi Xj + ε
                                                            i
15


   (X 1 , X 2 ,…, X k ) = (0,0,…,0)

3. Star points number is equal to 2k as each point is far from the center points
   with same distance, which is α as α = (2k)1/4 will be the rotatable design.
   Star points experiment is written as

   (±α,0,0,…,0), (0,±α,0,.. , ), …., (0,0,…,±α)

Therefore 2k Central Composite design will have total points equal to 2k + 2k +
n 0. This experiment can be illustrated in Figure 15, and matrixes of 2k Central
Composite design is illustrated in table 3.




       Figure 15 Total points in 23 Central Composite design

Table 3 Matrix of 23 Central Composite design

                X1           X2         X3         Points
                -1           -1         -1
                 1           -1         -1
                -1            1         -1
                 1            1         -1
                                                  Factorial
                -1           -1          1
                 1           -1          1
                -1            1          1
                 1            1          1
              -1.682          0          0
              1.682           0          0
                 0         -1.682        0
                                                    Star
                 0         1.682         0
                 0            0       -1.682
                 0            0       1.682
                 0            0          0        Center
16


        In order to make the design of experiment to be Rotatable design, which is
   variance of estimated response are constant at every point of experiment that is far
   from the center point in same distance, it have to be defined α and n 0 properly as
   below,

               α = (2k)1/4

               n 0 = 0.8386 ((2k)1/2 +2) 2 – 2k -2k

        From many researches (Box and Draper (1987) found that Central
   Composite design is flexible to use and has the most efficiency when compare
   to the other design to estimate the second-degree polynomial model.

       Table 4 Show α and n 0 for experiment that have various factors


                k                 2           3         4           5          6
         Factorial Points         4           8         16          32         64
           Star Points            4           6         8           10         12
          Center Points           5           6         7           10         15
          No.of Runs              13          20        31          52         91
                α               1.414       1.682       2         2.378      2.828

       Box-Behnken design

       Box-Behnken design is developed by Box and Behnken (1960) to estimate the
second-degree polynomial model, which combines 2k Factorial and Randomized
Incomplete block and it has the property of Rotatable as each block are orthogonal to
each other.

        This experiment has efficiency when is used to study in 3-level design, it is
better than 3k Full Factorial.

        Significant criticisms of RSM include the fact that the optimization is almost
always done with a model for which the coefficients are estimated, not known. That
is, an optimum value may only look optimal, but be far from the truth because of
variability in the coefficients. A contour plot is frequently used to find the responses
of two variables to find these coefficients by including a large number of trials in each
and combinations of them, and using some sort of interpolation to find potentially
better intermediate values between them. But since experimental runs often cost a lot
of time and money, it can also be difficult to pinpoint the ideal coefficients, as well;
there are frequently strategies used to find those values with minimal runs.
Experimental designs used in RSM must make tradeoffs between reducing variability
and reducing the negative impact that can be caused by bias.
17


       Therefore, this research proposes method for optimization of a response in
thermosonic copper wire-bonding process, which is average stitch pull test level using
Response surface method (2k Central Composite design) to estimate the second-
degree polynomial model.

       Lack of Fit Test

        Lack of Fit Test is used to test the model whether is fitting to the experiment
result or not. The model would be used to estimate the response as set up the
hypothesis below,
                      H 0 : Model is adequate or there is no Lack of fit.

                      H a : Model is not adequate or there is Lack of fit.

       However Lack of Fit test would be done under 3 constraints, which are

       1. Number of run must be greater than number of parameter that are shown in
          the model, N>P

       2. There are at least 2 replications on 1 run or more runs but it can ignore the
          replications, if there is estimation on the variance of error from the analysis
          in previous experiment.

       3. Error is assumed as below,

                           ε ~ NID (0,σ ε 2)

       Lack of Fit Test is done under the 1st and 2nd constraint as separating SSE to
be 2 parts, which are Lack of Fit and Pure Error. It can be calculated as the following,

                                     n     rl        _
               SS Pure Error =      ∑∑ (Ylu − Y l ) 2
                                    l =1 u =1


               SS Lack of Fit = SSE – SS Pure Error

                                     n           _
                                =   ∑ rl (Yl − Y l ) 2 ,
                                    l =1


               While l = order of runs, l =1, 2,…, n
                     n = number of non-repeat runs
                     u = order of replication in each run, u =1, 2,…, rl
                      rl = number of replications from order of run l
                       _
                       Y l = mean of run order l
18


       Lack of Fit test uses F-test from formula,

              F = SS Lack of Fit/ (n-p)
                  SS Pure Error/ (N-n)

       While (n-p) = degree of freedom of lack of Fit
             (N-n) = degree of freedom of Pure Error


       Response Surface Analysis

        We can estimate the second-degree polynomial model as determining levels of
factors in order to get the optimum response by 2 methods,

       Method 1 ; Contour Plot analysis, which is illustrated in figure 16




              Figure 16 Contour plot of response surface of 2 factors

       Method 2 ; Canonical Analysis

                           k              k
               Yˆ = βˆ0 + ∑ βˆi X i + ∑ βˆii X i + ∑∑ βˆij X i X j
                                                2
       From
                          i =1           i =1       i   j
                                                   i< j
       Or      Yˆ = βˆ0 + X ′ b + X ′ B X
                           ~     ~   ~    ~
19


       While
            X1        βˆ1      βˆ11     βˆ12 / 2               . . . βˆ1k / 2 
           X                                                                    
                       β 2      β 21 / 2    βˆ 22                . . . βˆ 2 k / 2 
                           ˆ        ˆ
            2
            .         .       .             .                  . . .       . 
       X =   b =   and B =                                                     .
       ~
            . 
                     ~
                        .       .             .                  . . .       . 
            .         .       .             .                  . . .       . 
                                                                                
            X k     β k 
                          ˆ       β k1 / 2 β k 2 / 2
                                    ˆ         ˆ                     . . . βˆ kk 


               The point that consists of the level of factors that give the optimum
response is called Stationary Point, which might be the point that give the minimum
or the maximum level of response. Stationary Point could be calculated as

                                      1
                               X 0 = − B −1 b
                                ~     2     ~



                                 1
       Therefore      Yˆ0 = βˆ0 + Xˆ b            is the optimum estimated response
                                 2 ~0~

       Canonical Analysis can test the optimum response whether it is the maximum
or minimum or saddle point from Eigenvalue consideration as below,


                               B−λI          = 0
                                    ~




       While {λi } is Eigenvalue or Characteristic Roots of Matrix B

       This Optimum point could be tested by solving the above equation and
considering the sign of {λi } that are illustrated in figure 17, 18 and 19.

       Moreover Canonical Analysis can transform the second-degree polynomial
form to be Canonical form as there is the center point at X 0 as below,
                                                              ~



                      Yˆ = Yˆ0 + λ1W1 + ... + λ k Wk
                                     2               2




       While Canonical variable relates to the polynomial variable as

                              W = M ′( X − X )
                               ~         ~   ~   ~ 0


       While M is the orthogonal matrix from the relation below,

                               (B − λ I ) M = 0
                                     ~       ~
20




Figure 17 Response surface of second-degree polynomial of 2 and 3 factors that
     optimum point is maximum point, example λi sign of 2 factors is (-,-)




Figure 18 Response surface of second-degree polynomial of 2 and 3 factors that
     optimum point is minimum point, example λi sign of 2 factors is (+,+)
21




Figure 19 Response surface of second-degree polynomial of 2 and 3 factors that
        optimum point is saddle point, λi sign is (-,+), (+,-) and (+,-,0)
22


                                    Materials and Method

   Materials

   Materials that are used in this research consist of

   1. Devices that passed Die attaching process as no any defects and ready for wire
      bonding process.
   2. Materials used in Thermosonic copper wire bonding process.
   3. Wire pull test machine that would be used for perform the stitch pull test after
      device samples have already been bonded.
   4. Personal Computer in laboratory at IGP Industrial engineering, Kasetsart
      University.
   5. Minitab software version 15 that is used for data analysis.


   Method

   Method that is used in this research are

   1. Perform the screening experiment the significant factors that influence to the
      average stitch pull test level as there are total 6 factors that illustrated in table
      5. 26-1 Factorial design 1 replication was selected, there are total 32 runs as each
      run has 105 wires that are used to calculate the average stitch pull test level for
      each run.

Table 5 Process parameters with different operating levels

-------------------------------------------------------------------------------------------------------
Factor                     Unit           Symbol               Level -1                   Level +1
-------------------------------------------------------------------------------------------------------
Contact Time                ms               CT                   5                 15
Contact Power              DAC               CP                  20                 40
Contact Force              gf                CF                  200               250
Base Time                   ms               BT                  25                 35
Base Power                  DAC              BP                   85               100
Base Force                  gf               BF                  250               300
-------------------------------------------------------------------------------------------------------

   2. Perform the stitch pull test on testing devices and record the stitch pull test
      level of each run and then calculate the average value in order to use for factors
      effect analysis from effect plot.

   3. Use Minitab software to do effect analysis from Pareto effect plot to find out
      the significant factors that influence to the average stitch pull test level, show
      the interaction plot of 2 factors and also test the error assumption in stitch pull
      test data by Normal Probability plot and Residual plot.

   4. Perform response surface method as using the 2k Central Composite design on
      the significant factors from (3.)
23



5. Use Minitab to analyze the data as using ANOVA and testing lack of fit and
   show the response surface figure and optimize the optimum point of response
   surface as using Contour plot and Canonical analysis.
24


                             Result and Discussion

       Design of Experiment (screening experiment)

        Experiment is conducted as 26-1 Factorial design on six factors to study their
effects to the response, average stitch pull test level as shown in table 6,

Table 6 26-1 Factorial Design of Experiment




       26-1 Factorial Experiment Result

                After performing 26-1 Factorial Experiment, which has total 32 runs,
testing and collecting average Stitch pull test data, the result is shown in Table 7
25


        Table 7 Result of response from 26-1 Factorial Experiment

  StdOrder RunOrder CenterPt Blocks       CT        CP        CF         BT        BP         BF         Average STP
         17       1         1         1         5        20        200        25        100        300         21.758
         15       2         1         1         5        40        250        35         85        300         22.701
          1       3         1         1         5        20        200        25         85        250         26.243
         14       4         1         1        15        20        250        35         85        300         23.186
         12       5         1         1        15        40        200        35         85        300         24.669
          6       6         1         1        15        20        250        25         85        250         25.884
         28       7         1         1        15        40        200        35        100        250         23.706
         21       8         1         1         5        20        250        25        100        250         21.519
          3       9         1         1         5        40        200        25         85        300         25.755
         22      10         1         1        15        20        250        25        100        300         20.106
         10      11         1         1        15        20        200        35         85        250         27.462
         13      12         1         1         5        20        250        35         85        250         25.407
          9      13         1         1         5        20        200        35         85        300         25.829
         19      14         1         1         5        40        200        25        100        250         24.360
         18      15         1         1        15        20        200        25        100        250         23.990
          5      16         1         1         5        20        250        25         85        300         23.386
         20      17         1         1        15        40        200        25        100        300         22.068
          7      18         1         1         5        40        250        25         85        250         25.927
         23      19         1         1         5        40        250        25        100        300         21.113
         27      20         1         1         5        40        200        35        100        300         21.676
         16      21         1         1        15        40        250        35         85        250         24.108
         26      22         1         1        15        20        200        35        100        300         22.642
         32      23         1         1        15        40        250        35        100        300         22.551
          2      24         1         1        15        20        200        25         85        300         25.305
          4      25         1         1        15        40        200        25         85        250         26.871
         30      26         1         1        15        20        250        35        100        250         21.929
         31      27         1         1         5        40        250        35        100        250         22.732
         29      28         1         1         5        20        250        35        100        300         21.179
         11      29         1         1         5        40        200        35         85        250         26.475
          8      30         1         1        15        40        250        25         85        300         23.640
         24      31         1         1        15        40        250        25        100        250         22.045
         25      32         1         1         5        20        200        35        100        250         23.829



                From the average stitch pull test result from each run, testing to screen
factors that influence to the average stitch pull was performed as using Pareto effect
plot as shown in figure 20 and also Normal Probability plot and Residual plot were
used to test the error assumption in stitch pull test data as shown in Figure 20 and 21.
26




Figure 20 Pareto effect plot on factors that influence the average stitch pull test




      Figure 21 Normality Probability Plot of average stitch pull test
27




       Normality Probability plot is shown as linear and Residual plot show


               Figure 22 Residual Plot of average stitch pull test

        Independence and equivalence of error distribution are around 0.0 along the
observation order. Therefore we can conclude that stitch pull test error has normality
distribution as independent and mean of error equals to zero and has the constant
variance.

        From Testing effect of factors as using Pareto effect plot that is shown in
Figure 20 found that there are only 3 main factors that has effect to the average stitch
pull test level while no any interaction effects such two or higher order interaction.
Regarding to the result 3 factors that are significant are the following,

       1. Contact force (CF), figure 22 shows contact force parameter that is set at
          200 gf bring about to the average stitch pull test level higher than setting at
          250 gf.

       2. Base Power (BP), figure 23 shows base power parameter that is set at 85
          DAC bring about to the average stitch pull test level higher than setting at
          100 DAC.

       3. Base Force (BF), figure 24 shows base force parameter that is set at 250 gf
          bring about to the average stitch pull test level higher than setting at 300
          gf.
28




Figure 23 Main Effects Plot for average stitch pull test, contact force




Figure 24 Main Effects Plot for average stitch pull test, base power
29




       Figure 25 Main Effects Plot for average stitch pull test, base force


       26-1 Factorial Experiment (Screening) Conclusion

                From the screening experiment of 26-1 Factorial design, found that the
significant factors that have influence on the average stitch pull test level are contact
force, base power and base force parameter. Other factors, which are contact time,
contact power and base time has no effect to the average stitch pull test level both
main effect and interaction.
30


         Design of Experiment (Response Surface Method)

       Experiment is conducted to find the response surface equation. Three
considered factors are contact force (CF), base power (BP) and base force (BF) as the
response still is the average stitch pull test level. The design experiment is 23 Central
Composite design with 6 center points and 1 replication, total runs is 20 runs.
Regarding to the result of screening experiment, contact time (CT), contact power
(CP) and base time (BT) are not significant factors. Therefore, in Central Composite
design of experiment we would control them as fixing their levels during experiment
conducted while levels of 3 non-significant factors are still in the range of the
previous screening as CT = 5 ms, CP = 30 DAC, BT = 25 ms. Factor level that are
used in the experiment is shown in Table 8. After performed the experiment, the
average stitch pull test is shown in table 9.

Table 8 Show level of factors for 23 Central Composite Design experiment

-------------------------------------------------------------------------------------------------------
                  Factor                                                Factor level
                                              ----------------------------------------------------------
                                             -1.682        -1            0           1            1.682
 -------------------------------------------------------------------------------------------------------
CF -- Contact Force (gf)                      183         200          225          250            267

BP -- Base Power (DAC)                          79         85          92          100            105

BF -- Base Force (gf)                          232        250          275         300            317
-------------------------------------------------------------------------------------------------------

Table 9 Result of response from 23 Central Composite design

 StdOrder RunOrder        PtType       Blocks        CF          BP          BF       Average STP
     1       1               1            1          200          85         250        26.571
     4       2               1            1          250         100         250        21.726
     8       3               1            1          250         100         300        20.985
    15       4               0            1          225          92         275         26.56
    10        5             -1            1          267          92         275        22.147
     3        6              1            1          200         100         250        24.019
    18        7              0            1          225          92         275        27.589
     5        8              1            1          200          85         300        25.246
    17        9              0            1          225          92         275        28.221
     7       10              1            1          200         100         300        21.821
    11       11             -1            1          225          79         275        26.685
     2       12              1            1          250          85         250        25.644
    14       13             -1            1          225          92         317        23.384
    13       14             -1            1          225          92         232        24.319
    16       15              0            1          225          92         275        26.402
    19       16              0            1          225          92         275        27.733
    20       17              0            1          225          92         275         28.05
     9       18             -1            1          183          92         275        24.845
     6       19              1            1          250          85         300        22.847
    12       20             -1            1          225         105         275        24.574
31


        From average stitch pull test analysis, found that the response surface equation
of average stitch pull test contains both first and second-degree polynomial as
significant in statistics and also Lack of Fit test result is not significant at 0.05
significant level as Minitab output showed the analysis result below,

       Analysis of Variance for Average STP

       Source               DF    Seq SS     Adj SS      Adj MS         F        P
       Regression            9   89.5027    89.5027      9.9447     11.74    0.000
         Linear              3   31.4629    31.4629     10.4876     12.38    0.001
         Square              3   57.8600    57.8600     19.2867     22.77    0.000
         Interaction         3    0.1798     0.1798      0.0599      0.07    0.974
       Residual Error       10    8.4720     8.4720      0.8472
         Lack-of-Fit         5    5.5313     5.5313      1.1063      1.88    0.252
         Pure Error          5    2.9408     2.9408      0.5882
       Total                19   97.9747

         Normal Probability plot and Residual plot that were used to test the error
assumption in stitch pull test data showed independence and equivalence of error
distribution are around 0.0 along the observation order. Therefore we can conclude
that stitch pull test error has normality distribution, see figure 25, as independent and
mean of error equals to zero and has the constant variance, see figure 26.




       Figure 26 Normality Probability Plot of average stitch pull test
32




              Figure 27 Residual Plot of average stitch pull test

        Therefore we can use this response surface equation to estimate the average
stitch pull test level from the Estimated Regression Coefficients for Average STP that
are given from Minitab as below,
       Estimated Regression Coefficients for Average STP

       Term           Coef     SE Coef         T         P
       Constant    27.4430      0.3754    73.104     0.000
       CF          -0.8049      0.2491    -3.232     0.009
       BP          -1.1208      0.2491    -4.500     0.001
       BF          -0.6322      0.2491    -2.538     0.029
       CF*CF       -1.5013      0.2425    -6.192     0.000
       BP*BP       -0.7470      0.2425    -3.081     0.012
       BF*BF       -1.3756      0.2425    -5.674     0.000
       CF*BP        0.0246      0.3254     0.076     0.941
       CF*BF       -0.0019      0.3254    -0.006     0.996
       BP*BF        0.1479      0.3254     0.454     0.659


       S = 0.920436       PRESS = 47.8935
       R-Sq = 91.35%      R-Sq(pred) = 51.12%        R-Sq(adj) = 83.57%


       The response surface equation of average stitch pull test is

       Yˆ = 27.4430 − 0.8049CF − 1.1208 BP − 0.6322 BF − 1.5013CF 2 − 0.7470 BP 2
       − 1.3756 BF 2 + 0.0246CF * BP − 0.0019CF * BF + 0.1479 BP * BF
33


        From Canonical analysis, found that Eigenvalues are negative, which are
 λ1 = −2.088009, λ2 = −3.914927, λ3 = −4.246973 . Therefore response surface
equation of average stitch pull test form is maximum as polynomial equation could be
transformed to the Canonical equation as

       Yˆ = 28.0764 − 2.088009W1 − 3.914927W2 − 4.246973W3
                                2            2             2




        Contour plot and surface plot of contact force, base power and base force
factor that are illustrated in Figure 27, 28, 29, 30, 31 and 32 are used to optimize the
maximum average stitch pull test level as using Minitab software. We found that the
level of factors that influence to the maximum average stitch pull test, which is
28.0764 grams-force are contact force at 218 grams-force, base power at 86 DAC and
base force at 268 grams-force.




Figure 28 Contour plot of response surface equation of the average stitch pull test that
consists of base power and contact force factor.
34




Figure 29 Surface plot of response surface equation of the average stitch pull test that
consists of base power and contact force factor.




Figure 30 Contour plot of response surface equation of the average stitch pull test that
consists of base force and contact force factor.
35




Figure 31 Surface plot of response surface equation of the average stitch pull test that
consists of contact force and base force factor.




Figure 32 Contour plot of response surface equation of the average stitch pull test that
consists of base force and base power factor.
36




Figure 33 Surface plot of response surface equation of the average stitch pull test that
consists of base power and base force factor.


        From the analysis of response surface equation of average stitch pull test,
found that the equation is in maximum form, which equation gives only one optimum
point that gives the maximum response while other points from other levels of factors
cannot give the optimum. The optimum average stitch pull test level is 28.0764
grams-force, which is given from setting level of factors as the following,

       -   Contact force at 218 grams-force
       -   Base power at 86 DAC
       -   Base force at 268 grams-force

        After we have got the proper level of control factors that give the optimum
level of average stitch pull test, we would have confirmed the result of the analysis by
performing the experiment on these proper levels of bond parameters and observing
the process capabilities from samples 30 units, total 1,050 wires as the result is shown
in figure 33.
37




               Figure 34 Process Capability of stitch pull test

       The confirmation experiment on 30 units (1,050 wires) sample size from the
optimized bond parameters level from the response surface analysis showed that the
average stitch pull test is increased from 21.1389 (Current parameters level setting) to
be 28.0162 (Optimized bond parameters level) and also Cpk is improved from 0.69
(Current parameters level setting) to be 1.62 (Optimized bond parameters level).
Therefore the optimized bond parameters could improve the process capability.


        However, in thermosonic copper wire bonding process there are other
variations involved such as materials, man, machine and method. Therefore after we
had already chosen the level of factors and got the optimum response, people that are
concern in the process have to control these level of factors, which might apply the
control chart.
38


                                       Conclusion

        Regarding to the selection of factors that might influence to the stitch pull test
level in thermosonic copper wire bonding process by the expertise engineer and also
the constraint of factors, there are 6 factors that are contact time, contact power,
contact force, base time, base power and base force. The 26-1 Factorial Experiment
was conducted to screen the significant factors as the result was showed that there are
3 factors that affect to the stitch pull test as the following,

               1. Contact Force (grams-force)

               2. Base Power (DAC)

               3. Base Force (grams-force)

       And after taking all 3 factors to perform the experiment and analysis by
response surface method as using 23 Central Composite design to find the response
surface equation of average stitch pull test, we have got the result as the following,

       Response surface equation of average stitch pull test


        Yˆ = 27.4430 − 0.8049CF − 1.1208 BP − 0.6322 BF − 1.5013CF 2 − 0.7470 BP 2
        − 1.3756 BF 2 + 0.0246CF * BP − 0.0019CF * BF + 0.1479 BP * BF

       As Yˆ is the average stitch pull test.

        The equation is in maximum form of second-degree polynomial, which
equation gives only one optimum point that gives the maximum response while other
points from other levels of factors cannot give the optimum. The optimum average
stitch pull test level is 28.0764 grams-force, which is given from setting level of
factors as the following,

       -   Contact force at 218 grams-force
       -   Base power at 86 DAC
       -   Base force at 268 grams-force

        The optimized level of factors above has improved the Cpk from 0.69 from
current parameters level setting to be 1.62 from the optimized bond parameters level.
Therefore the optimized bond parameters could improve the process capability.
39


                             Recommendations
       Central Composite design is the experiment that is applied frequently in
researches to find the response surface equation that is second-degree polynomial
form but there are other experimental design that are used also such as ,

       Experimental design to find the response surface of first-degree polynomial

       -   2k Factorial
       -   2k Fractional Factorial
       -   Simplex Design
       -   Plackett-Burman Design

       Experimental design to find the response surface of second-degree polynomial

       -   3k Factorial
       -   Non-Central Composite Design
       -   Orthogonal Blocking of Central Composite
       -   Box-Behnken Design

       Currently there is design that was proposed from Japanese industrial engineer
named Genichi Taguchi in order to improve the product quality, which is popular and
widely used in the researches but it has the different method to find the surface
response. Taguchi proposed Orthogonal Array method.

       However selection of the design of experiment depends on the constraints of
researcher and the consideration of proper design on each experiment.
40


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17. Wire bonder Process training manual “ASM Eagle60AP” Rev. A 2005. 2
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18. Zhong, Z.W., Ho, H.M., Tan, Y.C., Tan, W.C., Goh, H.M., Toh, B.H. and
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19. en.wikipedia.org/wiki/Response_surface_methodology


20. ieeexplore.ieee.org/iel1/33/2278/00062577.pdf?arnumber=62577



21. http://www.emeraldinsight.com/10.1108/13565360910923115        1




22. http://www.siliconfareast.com/wirebond-copper.htm
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