｢材料｣ (Journal of the Society of Materials Science, Japan), Vol. 66, No. 6, pp. 427-434, June 2017

Original Papers

Technique for Efficiently Selecting Metal Film with Strong Adhesion to Resin with the
Combination of Orthogonal Array and Response-Surface Method
byTomio IWASAKI *A technique for efficiently selecting a metal film with strong adhesion to a resin with the combination of an orthogonalarray and a response-surface method was developed to select appropriate materials for electronics devices. In this technique,at the first step, important factors that significantly influence the adhesion strength were selected from various factors thatcharacterize metal films by use of an orthogonal array with molecular simulations. As a result, the short-side and long-side
lattice constants a and b were selected from four metal-film factors (a, b, the electronegativity, E, and the surface energy
density, S). At the second step, the adhesion strength was described as a function of the selected important factors by using a
response-surface method. From this function, the most appropriate values for a and b that made the adhesion strength
maximum were obtained. The values for a and b were obtained as 0.244 nm and 0.423 nm, respectively. At the third step, themost appropriate metal film whose lattice constants were close to a =0.244 nm and b=0.423 nm was selected by use of thedata base of lattice constants. As a result, a copper/manganese/nickel-laminated film whose lattice constants were a =0.242
nm and b=0.419 nm was selected as the most appropriate metal film with the strongest adhesion to a resin.
Key words:
Adhesion strength, Metal film, Resin, Response-surface method, Molecular simulation, Orthogonal array

1 Introduction

from metal-film factors such as lattice constants and surface

Following the trend toward increased integration density

energy density that characterize metal films by using an

in multifunctional electronics devices such as biomechanics

orthogonal array2) and molecular simulations4)-9). At thedevices, semiconductor packages, magnetic recording media,

second step, by using a response-surface method3), theand optical disks, nano-scale thin films made up of various

adhesion strength is described as a function of the selectedfunctional materials are used in the devices. Because theimportant factors, and the most appropriate values of thedevices are expected to be used at places of high temperatures

factors that make the adhesion strength maximum areand high humidity in the upcoming IoT (Internet of Things)

obtained. At the third (final) step, appropriate metal films

era, the interface adhesion between different materials needs

whose factors are close to the most appropriate values areto be strong to realize the efficient device reliability. Whenselected.

the interface between the different materials is not stable,

In this study, the author used a naphthalene-ring-based

adhesive fractures occur at the interface at high temperatures

resin as an example resin because the resin is often used in

or in high humidity. Selecting appropriate materials is one ofelectronics devices for the reason that it has the strong

the keys to preventing these adhesive fractures. In

mechanical strength and the heat resistance. Then, the best

semiconductor packages, for example, it is well known thatmetal film with strong adhesion to this resin was selected.

the adhesion of electro-plated nickel-interconnection films to

2 Material-Selection Technique
2.1 Material-Selection Technique Made of Three Steps

chromium underlayers is very strong. Generally speaking,however, it is difficult to select an appropriate material that

The basic idea of material selection in this technique ishas strong adhesion to another material by using a

to select a material whose factors A, B, C, ･･･ are close toconventional trial-and-error approach. So, recently many

the most appropriate values Ao, Bo, Co, ･･･ that optimize an

1)

objective material property, F by describing the property as atechniques, which can select an appropriate material by using

function of material factors, that is, F(A, B, C,･･･). In thisresearchers have paid attention to materials-informatics

andstudy, the objective material property, F that the author wants

experimental data. However, they sometimes need a longto optimize is the adhesion to a resin, and the factors A, B,

time to obtain results because they usually use a lot of data.

C, ･･･ that the author focus on are the lattice constants, theSo, the author has developed a technology for efficiently

electronegativity, and the surface energy density of a metal

information

sciencewithcomputersimulation

selecting a metal film with strong adhesion to a resin byfilm. To describe the material property F as a function of

combining an orthogonal array2) with a response-surface

material factors A, B, C, ･ ･ ･ , a number of data of

method3) and by using molecular simulations4)-9).

experiments or simulations to interpolate are needed. If the

In this technology, at the first step, the important factors

number of factors are too large, many data are needed forthat significantly influence the adhesion strength are selectedinterpolation and it takes too much time to obtain the function+

Received Aug. 19, 2016 ©2017 The Society of Materials Science, Japan*

Member: Research and Development Group, Hitachi, Ltd., Omika, Hitachi, Ibaraki 319-1292, Japan

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T. Iwasaki

F(A, B, C,･･･). So the author uses orthogonal-array analysis2)
to select the important factors.
The overview of the material-selection technique isshown in Fig. 1. This figure shows that the method consists ofthree steps. At the first step, by using the orthogonal-arraysensitivity analysis2) with molecular simulations4)-9), theimportant material factors that significantly influence an
objective material property are selected from material factors(the lattice constants, the electronegativity, and the surface
energy density) that characterize metal films. In thesensitivity analysis, the results of molecular simulations of
the objective material property that is paid attention to areused as input data. At the second step, the objective material

Fig. 3 Stabilized molecular structure and lattice
constants of naphthalene-based resin.

property, which is the adhesion in this paper, is described as afunction of the selected important factors by using a
response-surface method3) with the molecular-simulation
results that are also used at the second step. By using thisfunction, the most appropriate values of the factors that
optimize the objective material property, which is adhesion
strength in this paper, are determined. At the third (final) step,
the materials (metal films) whose factors are close to the mostappropriate values are selected.

2.2 Simulations Used at the First and the Second Steps
As shown in Fig. 1, molecular simulations are used in
the first and second steps. So the method of the simulations is
explained in this section. In this paper, an example resin that
contains naphthalene rings is used because this resin is often
used in electronics devices for the reason that this has strong
mechanical strength and heat resistance. The simulation
model of this example resin is shown in Figs. 2 and 3. Figure
2 shows a two dimensional schematic structure of the resin,which is not a stabilized structure. Figure 3 shows thestabilized structure of the resin, in which two benzene rings
are in the direction vertical to two naphthalene rings. The
simulation model that author used in this study is an interface
between the resin (Fig. 3) and a metal film, as shown in Fig. 4.
This simulation model was made by using “Materials
Studio®” software from Dassault Systemes BIOVIA. Sixteen
resin molecules (four layers of four molecules), one of whichis shown in Fig 3, were used as the resin film model. Thereare 2,272 atoms in the resin molecules.
Next, the size of the metal-film model shown in Fig. 4 is
explained

in

this

paragraph.

molecular-dynamics simulations
Fig. 1

Overview of material-selection technique.

4)-9)Becausethepast

have found that theadhesion strength between the resin and the metal film wasalmost independent of the total number of metal layers whenthat number was more than seven, the number was set ateight in the z direction. The sizes of the metals in the x and y
directions are set at 15a and 15b, where the short-side lattice
constant, a, and the long-side lattice constant, b, are shown in
Fig. 5. So, the number of atoms in the metal film is 3,600. In
this study, the atoms were kept free to move.
In this study, the adhesion strength was evaluated by
calculating the adhesive fracture energy 4)-9) which was
defined as the difference between the area density of potential

Fig. 2 Schematic structure of a naphthalene-based resin.

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energy of the resin/metal-attached state (Fig. 4) and that of2017/05/26

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Technique for Efficiently Selecting Metal Film with Strong Adhesion to Resin with the Combination of Orthogonal Array and Response-Surface Method

Fig. 4

Attached state of a naphthalene-based resin anda metal film.

Fig. 8

Detached state of429

two metal films.

is determined based on the element, its hybridization, and its
connectivity.

2.3 Material Factors Used at the First Step
In this section, the material factors of the metal film are
explained. The author focused on four factors (the short-side
and long-side lattice constants, a and b, the electronegativity,
E, and the surface energy density, S) of the metal film, andthen investigated which factors significantly influence theadhesion strength. The lattice constants, a and b are defined at
the surface of the metal film, as shown in Fig. 5. In this study,
the xy-plane in Figs. 4 and 5 is set parallel to the crystal
Fig. 5

Lattice structure and lattice constants of the top layerof metal film.

planes of the highest atomic density, which are the (111),(0001), and (110) planes for the face-centered-cubic (fcc),
hexagonal-close-packed (hcp), and body-centered-cubic (bcc)
structure metals, respectively. These crystal planes areenergetically stable and are experimentally found to be most
likely to appear at the surfaces when metal films aredeposited by using physical vapor deposition (PVD). So, theshort-side and long-side lattice constants a and b are definedat the crystal planes of the highest atomic density of the metal
film.
The electronegativity, E, that describes the tendency of

Fig.6

Detached state ofa naphthalene-based resin anda metal film.

an atom to attract electrons, is defined in Ref. 13.
The surface energy density of the metal film, S , whichis the energy density required to create a surface from bulk,
was defined as half of the difference between the area densityof potential energy of the surface-connected state (Fig. 7) andthat of the surface-separated state (Fig. 8). The surface energy
density, S was calculated by using molecular-dynamics

Fig. 7 Attached state of two metal films.
the resin/metal detached state (Fig. 6). This fracture energy

simulations with a universal force field10), 11). As explained inRefs. 10) and 11), the potential energy of this force field isexpressed as a sum of valence or bonded interactions andnonbonded interactions in the following equation.
P=PR+Pθ+Pφ+Pω+Pvdw+Pel(1)

was calculated by using molecular-dynamics simulations withthe universal force field 10), 11) . In the simulations, thetemperature was kept at 20°C by using the velocity-scaling
method12). As described in Refs. 10) and 11), this force field

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Here, bond stretching (P R ), bond angle bending (P θ),dihedral angle torsion (Pφ), and inversion terms (Pω) arevalence interactions. On the other hand, van der Waals (Pvdw)
terms and electrostatic (Pel) terms are nonbonded interactions.

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T. Iwasaki

Table 1

L9 orthogonal array corresponding to four factors.

fans and diaphragms. In this methodology, when there are
four material factors, only nine simulations or experiments
shown in an L9 orthogonal array (see Table 1) are needed toclarify the important factors on which the adhesion strengthstrongly depends2). Here the author set Level 1 (small values),
Level 2 (middle values), and Level 3 (large values) of thefour factors at the regions shown in Table 2. By looking into
the data of the four factors corresponding to 31 metals, theauthor was able to find nine metals that correspond to thenine sets of factors shown in Table 1. These nine metals areshown in Table 3. When it is impossible to set three levels foreach factor, the orthogonal array can not be used. In such case,

Table 2

Factors and levels for metal films.

the first stage in Fig. 1 has to be skipped, and all the factors
have to be dealt with at the second stage, where more data
than those of orthogonal array are needed for interpolation14).
By using the nine metals shown in Table 1, the sensitivity2)
for the adhesive fracture energy4)-9) between the metal film
and

the

resin

was

calculated.

By

applying

sensitivity-analysis2) based on orthogonal arrays to thefracture-energy data calculated for the nine metals, thesensitivity of Level j of the i-th factor, Wij is given by
Table 3Nine metal films corresponding to Table 1 (L9),where Levels 1, 2, and 3 are shown in Table 2.

Wij =10 log[(Pij－Qij)/n],(2)

Pij=(Dij1+Dij2+・・・＋Dijn)2/n

(3)

where
and
Qij=(Dij12+ Dij22+・・・＋Dijn2－Pij)/(n-1).

(4)Here, Dijk is the k-th fracture-energy datum that belongs toLevel j of the i-th factor, and n is the number of the data thatbelongs to Level j of the i-th factor.
According to the sensitivity-analysis method2) based onorthogonal arrays, the factors whose increase from Level 1 toLevel 3 significantly influences the sensitivity Wij areimportant in optimizing the adhesion strength, and they are
selected as important factors at the first step of thematerial-selection technique (Fig. 1). At the second step in
Fig. 1, the adhesion strength is described as a function of theselected factors by interpolating the nine fracture-energy data
corresponding to the L9 orthogonal array in Tables 1 and 3 by

2.4 Orthogonal-Array
Orthogonal Array Used at the First Step
Step
At the first step of the material-selection technique (Fig.
1), the important material factors (metal-film factors) thatsignificantly influence the objective material property(adhesion strength) are selected by clarifying the dependenceof the adhesion strength on the four metal-film factors. When
we investigate the dependence, we usually change the valueof one factor with the other three factors fixed. However, it istime-consuming to clarify the dependence by using thismethod. Consequently, the author used the orthogonal-array
design methodology2), which is known to be effective for
efficiently designing macro-scale structures such as propeller

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use of a response-surface method.

2.5 Response-Surface Method
At the second step of the material-selection technique(Fig. 1), a response-surface method is used to describe theobjective material property (adhesion strength) as a functiono f th e i mpor t ant fa cto r s s e l ec t ed b y us e o f th eorthogonal-array analysis explained in Section 2.4. In thisstudy, the author employed a response-surface method, so
called Kriging method3), which is often used in geostatistics
and mechanical structure design. The schematic view of
one-dimensional data interpolation by use of the Kriging
method is shown in Fig. 9. In this method, the function curveis made so that all the data points used for interpolation are

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Technique for Efficiently Selecting Metal Film with Strong Adhesion to Resin with the Combination of Orthogonal Array and Response-Surface Method

Fig. 9431

Schematic view of interpolation with Kriging method
and comparison with liner- and quadratic-function
approximations.

Table 4

Calculated adhesive fracture energy data
corresponding to Table 1 (L9) .

Fig. 11 Function obtained with a response-surface method(Kriging method).
(metal films) whose factors are close to the most appropriate
values are selected.

3 Material-Selection Results and Discussions
The

calculated

adhesive

fracture

energydata

corresponding to the L9 orthogonal array (Table 3) are shownin Table 4. Figure 10 shows the sensitivity, Wij, calculated byusing the fracture energy data (Table 4) and Eqs. (2), (3), and(4). From Fig. 10 it is found that the adhesive fractureenergy (adhesion strength) strongly depends on the 1st and2nd factors (the short-side and long-side lattice constants),
while the fracture energy does not strongly depend on the 3rd
and 4th factors (the electronegativity and the surface energy
density). Thus, the short-side and long-side lattice constants,
a and b, were selected as important factors at the first step of
the material-selection technique shown in Fig. 1.
At the second step of Fig. 1, the author described theadhesive fracture energy as a function by interpolating thenine data in Table 4 with the Kriging method. The obtained
function is shown in Fig. 11. The most appropriate values of
the important factors (the short-side and long-side lattice
constants, a and b) are obtained as a =0.244 nm and b=0.423
Fig. 10 Results of calculated sensitivity.
on the curve. The basic idea of the Kriging method is topredict the value of a function at a given point by computing
a weighted average of the known values of the function in the3)neighborhood of the point .

The theory derives a best linear

unbiased estimator, based on assumptions on covariances, andis mathematically related to regression analysis. By using the
Kriging method, the adhesion strength is described as afunction of the important material factors (metal-film factors).
By using this function, the most appropriate values ofmaterial factors that maximize the adhesion strength can be
determined. At the third (final) step, appropriate materials

nm by using the gradient of the obtained function. Because
these values are the same values of resin’s lattice constants
shown in Fig. 3, it is found that the lattice matching between
the metal film and the resin is the most important inincreasing the adhesion strength between them.
At the third (final) stage of Fig. 1, the appropriatematerials (metal films) whose factors are close to the mostappropriate values (a =0.244 nm and b=0.423 nm, which areresin’s lattice constants) are selected. The author selected
nickel and cobalt because nickel’s lattice constants (a =0.249
nm and b=0.431 nm) and cobalt’s lattice constants (a =0.251
nm and b=0.435 nm) are close to resin’s lattice constants. By
calculating the adhesive fracture energy defined in Section
2.2, the values for nickel (Ni) and cobalt (Co) are obtained as
0.235 J/m2 and 0.232 J/m2, both of which are larger than any

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T. Iwasaki

application. To clarify the reason that nickel has strong
adhesion to the resin, the author visualized the atomic
configuration of the interface between the resin and the nickel
film, as shown in Fig. 12. Because Fig. 12 shows that nickel
atoms can be seen through near the centers of the naphthalenerings and that the configuration of the nickel atoms are inharmony with naphthalene rings, the integration of atomic
interactions caused by this harmony is considered to lead tothe strong adhesion. Although the figures are not shown inthis paper, the atomic configurations of the interface between
the resin and cobalt (Co), copper (Cu), and zinc (Zn) aresimilar to those of the resin/nickel interface shown in Fig. 12.
Fig. 12

Atomic configuration of attached stateof the resin/Ni interface.

The atomic configurations of the resin/vanadium
interface whose adhesive fracture energy (0.185 J/m2) issmaller than that of the resin/zinc interface are shown in Fig.
13. This figure shows that vanadium atoms can be seen
through at the edge of the naphthalene rings (not at thecenter of the rings). So the integration of atomic interaction
at the resin/vanadium interface is smaller than that at theresin/nickel interface shown in Fig. 12.
The atomic configurations of the resin/platinum
interface whose adhesive fracture energy (0.174 J/m2) issmaller than that of the resin/vanadium interface are shown in
Fig. 14. This figure shows that platinum atoms can not beseen through the naphthalene rings. So the integration of
atomic interaction at the resin/platinum interface is smaller

Fig. 13

Atomic configuration of attached state.
of the resin/V interface.

than that at the resin/vanadium interface shown in Fig. 13.
Thus, the integration of atomic interactions caused by thelattice matching is confirmed to lead to the strong adhesion.

4 Further Improvement by Use of Atomic Multilayer
To further improve the adhesion strength, the author
tried to control the lattice constants by using multilayer
metal films made up of atomic-scale thin films shown in Fig.
15, instead of using a single metal. Because the thicknessesof Metals 1, 2 and 3 in Fig. 15 are only two, three, and three
atomic layers, respectively, misfit dislocations are notformed in the metal films. As a result, by using acopper/manganese/nickel-laminated multilayer film, thehigher adhesive fracture energy (0.243 J/m2) was realized.

Fig. 14

Atomic configuration of attached stateof the resin/Pt interface.

value shown in Table 4. They agree well with the values(0.237 J/m2 and 0.230 J/m2 for cobalt and nickel) obtained
from Fig. 11. The obtained function (Fig. 11) has someprediction errors because it is obtained from only nine data
and because 3rd and 4th factors (E and S) are neglected. The
author will report in the next paper, which focuses on themethodology and accuracy rather than materials-selection

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Fig. 15 Attached state of naphthalene-based resin andmultilayer metal film (Metal 1/Metal 2/Metal 3).

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Technique for Efficiently Selecting Metal Film with Strong Adhesion to Resin with the Combination of Orthogonal Array and Response-Surface Method433

5 Comparison between Simulations and Experiments

Fig. 16 Atomic configuration of attached stateof the resin/metal (Cu/Mn/Ni) interface.

Fig. 17

Schematic view of scratch testing.

Fig. 18 Adhesive fracture energy calculated from molecular
dynamics (MD) and determined critical load
measured by scratch testing (experiment).

The atomic configurations of the interface between the resin
and this multilayer film are shown in Fig. 16. This figure
shows that copper atoms can be seen through just at thecenters of the naphthalene rings and that the configurationof the copper atoms are in best harmony with naphthalenerings. Thus, the integration of atomic interactions caused by
the lattice matching is confirmed to lead to the strong
adhesion, again.

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To confirm the effectiveness of the molecular-dynamics
simulation technique described in Chapters 2 and 3, theauthor conducted a scratch test on the film-laminatedstructure (scratch tester: CSR-02 made by Rhesca Co., Ltd.)and compared the test results with the simulation results.
Recently, more advanced methods for measuring adhesion
strength have been proposed in a number of research
papers15)-17). However, these advanced methods were very
difficult to apply to fairly strong interfaces such as thenaphthalene-based-resin/nickel interface. Accordingly, asimple scratch-testing method that was applicable to thenaphthalene-based-resin/nickel interface was employed. A
schematic view of the scratch testing apparatus is shown in
Fig. 17. A diamond indenter with a tip radius of 5 µm makes
the dynamic indentations. During the measurement, load is
gradually increased and when it reaches a critical load,
adhesive fracture occurs at the interface. The adhesion
strength is determined by measuring the critical load, L, atwhich the adhesive fracture occurs.
The author used 0.01-mm-thick naphthalene-based resin
films deposited on the metal films for the scratch test. The
molecular structure of the resin films is the same as that inFig 3. For the metal films, the author used the six metal films(Ni, V, Pt, Mo, Nb, and Cu/Mn/Ni), five of which are listed inTable 4. These films were deposited on silicon substrates byusing physical vapor deposition (PVD), and the thickness ofeach film was set at the same as that used in the simulations
by controlling the deposition time so that misfit dislocations
were not formed. By using the θ-2θ scheme of the X-ray
diffraction (XRD) analysis, the author selected the specimensthat have significant diffraction peaks corresponding only tothe planes of the highest atomic density.
The adhesive fracture energy, D, obtained frommolecular simulations and the critical load, L, obtained fromthe scratch test of the interfaces between resin films andmetal films are compared in Fig. 18. The ordered molecularorientation of the resin caused by naphthalene and benzene
rings is considered to be one of the reasons for the small
deviation and the good agreement between the simulations
and experiments. Because the linear relationship can be seen
betweensimulations
andexperiments,
theadhesion-calculation method is found to be effective fordetermining the adhesion strength. Furthermore, from theresults shown in Fig. 18, it is experimentally confirmed thatthe copper/manganese/nickel-laminated film and the nickel
film, which were selected by using our material-selection
technique (Fig. 1), have strong adhesion to the resin. Thus,
our technique for selecting appropriate materials with the
combination of an orthogonal array and a response-surface
method is considered to be effective for selecting a metal filmthat has strong adhesion to the resin.

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T. Iwasaki

adhesion strength of interfaces between thin films”,

6 Summary

Journal of Materials Research, Vol. 16, No. 6, pp.

A technology for efficiently selecting a metal film withstrong adhesion to a resin with the combination of an
orthogonal array with a response-surface method wasdeveloped to select appropriate materials for electronics
devices. In this technique, at the first step, important factorsthat significantly influence the adhesion strength to the resin
were selected from various factors that characterize metal
films by use of an orthogonal array with molecularsimulations. At the second step, the adhesion strength was
described as a function of the selected important factors byusing a response-surface method (Kriging method). From thisfunction, the most appropriate values of the important factorsthat made the adhesion strength maximum were obtained. At

1789-1794 (2001).
6)

T.

Iwasaki,“Applicationofmolecular-dynamics

simulation to interface stabilization in thin-film devices”,
International Journal of the Japan Society of MechanicalEngineers, Series B, Vol. 47, No. 3, pp. 470-476 (2004).
7) T. Iwasaki, “Molecular dynamics study of diffusion andatomic configuration in layered structures for Al circuit
interconnects”, Computational Mechanics, Vol. 24, No. 2,
pp. 148-154 (1999).
8) T. Iwasaki, “Molecular dynamics study on the effect oflattice mismatch on adhesion strength between organic
materials and metals”, Journal of the Society of Materials
Science, Japan, Vol. 58, No. 3, pp. 257-261 (2009).

the third step, the most appropriate metal film whose

9) T. Iwasaki, “Molecular dynamics study on the effect ofimportant factors were close to the most appropriate values

lattice mismatch on adhesion strength between ceramics

was selected. By carrying out these procedures, the following

and organic materials”, Journal of the Society ofMaterials Science, Japan, Vol. 59, No. 2, pp. 165-170

results were obtained.
(1) By using the sensitivity analysis based on an orthogonalarray, the short-side and long-side lattice constants, a and b
were selected as the important factors from four metal-film
factors (the lattice constants, a, b, the electronegativity, E, andthe surface energy density, S).
(2) By describing the adhesive fracture energy as a functionof the important factors (the short-side and long-side lattice
constants, a and b), the most appropriate values for a and bthat made the adhesion strength maximum were obtained as
0.244 nm and 0.423 nm, respectively.
(3) The most appropriate metal film whose lattice constants
were close to a =0.244 nm and b=0.423 nm was selected. As
a result, a copper/manganese/nickel-laminated film whose
lattice constants were a =0.242 nm and b=0.419 nm wasselected as the most appropriate metal film with the strongest
adhesion to an example resin (naphthalene-based resin).

1) K. Rajan, C. Suh and P. F. Mendez, “Principal component
anddimensional10) A. K. Rappe, C. J. Casewit, K. S. Colwell, W. A. Goddard
Ⅲ and W. M. Skiff,“UFF, a full periodic table force fieldformolecular

mechanics

andmolecular

dynamics

simulations”, Journal
Journal ofof American
American Chemical
Chemical Society, Vol.
simulations,

114, No. 25, pp. 10024-10035 (1992).
11) C. J. Casewit, K. S. Colwell and A. K. Rappe,“Application ofof a universal
universal force
force field
field toto organicorganicmolecules”,
molecules,
Journal of American Chemical Society, Vol. 114, No. 25,
pp. 10035-10046 (1992).
velocity12) K. Hermansson, G. C. Lie and E. Clementi, “On Velocity

Scaling
Journal of
scaling in Molecularmolecular Dynamics
dynamics Simulations”,
simulations”, Journal
Computational Chemistry, Vol. 9, No.3, pp. 200-203(1988).
13)

A.

L.

Allred,“Electronegativity

valuesfrom

thermochemical data”, Journal of Inorganic and Nuclear
Chemistry, Vol. 17, Issues 3–4, pp. 215–221 (1961)
14) S. Jeong and M. Murayama, “Efficient optimization
design method using Kriging model”, Journal of Aircraft,

References
analysis(2010).

analysisasmaterials

informatics tools to reduce dimensionality in materials
science and engineering”, Statistical Analysis and Data
Mining, Vol. 1, Issue 6, pp. 361–371 (2009).
2) G. Taguchi, “System of Experimental Design”, Edited by
Don Clausing, New York: UNIPUB/Krous International
Publications, Vol. 1 and 2, (1987).

Vol. 42, No. 2, pp. 413-420 (2005).
15) T. Kitamura, H. Hirakata and H. Itsuji, “Effect ofresidual stress on delamination from interface edge
between nano-films”, Engineering Fracture Mechanics,
Vol. 70, pp. 2089-2101 (2003).
16) T. Kitamura, H. Hirakata and Y. Satake, “Applicabilityoffracturemechanics

onbrittledelaminationofnanoscale film edge”, International Journal of the Japan3) N. Nonaka and T. Iwasaki, “Development of material

Society of Mechanical Engineers, Series A, Vol. 47, No. 2,

search technology using response-surface method”,
Transactions of JSCES, Paper No.20120009, (2012).

17) H. Hirakata, T. Kitamura and H. Yamamoto, “Direct

4) T. Iwasaki, “Molecular dynamics study of adhesion
strength and diffusion at interfaces between interconnect
materials

andunderlaymaterials”,

Computational

Mechanics, Vol. 25, No. 1, pp. 76-86 (2000).

pp. 106-112 (2004).
measurement of interface strength between copper
submicron-dot

andsilicondioxidesubstrate”,

International Journal of the Japan Society of MechanicalEngineers, Series A, Vol. 47, No. 3, pp. 324-330 (2004).

5) T. Iwasaki and H. Miura, “Molecular dynamics analysis of

09-2016-0099-(p.427-434).indd434

2017/05/26

10:06:41