Journal of The Electrochemical Society, 150 共12兲 G751-G757 共2003兲
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0013-4651/2003/150共12兲/G751/7/$7.00 © The Electrochemical Society, Inc.
Effects of Mechanical Parameters on CMP Characteristics
Analyzed by Two-Dimensional Frictional-Force Measurement
Yoshio Homma,*,z Kikuo Fukushima, Seiichi Kondo, and Noriyuki Sakuma
Central Research Laboratory, Hitachi Limited, Kokubunji, Tokyo 185-8601, Japan
The effects of mechanical parameters on the characteristics of chemical mechanical polishing 共CMP兲 were evaluated by directly
measuring frictional force acting on a wafer in terms of two components, i.e., the tangential and axial components of the platen’s
rotation. It was found that, when the platen and the wafer were rotated at the same speed, the tangential component of the frictional
force was dominant. Also, frictional force was in linear proportion with removal rate. Though frictional force increased in linear
proportion to down force when mechanical-effect-dominant CMP for silicon 共Si兲 or silicon dioxide (SiO2 ) was carried out, it
decreased gradually as platen rotational speed was increased. Copper 共Cu兲 polishing using abrasive-free polishing solutions, a
typical example of chemical-effect-dominant CMP, showed much more complex behavior. Namely, dependence of frictional force
on down force and on platen rotational speed showed nonlinear characteristics. Even when a nonlinear characteristic slurry was
used, it was found that removal rate and frictional force were almost linearly correlated. It can thus be considered that frictional
force is a basic parameter to determine CMP characteristics. From these results, an experimental equation was proposed to
describe CMP characteristics by modifying Preston’s empirical equation.
© 2003 The Electrochemical Society. 关DOI: 10.1149/1.1619990兴 All rights reserved.
Manuscript received October 23, 2002. Available electronically October 10, 2003.
Chemical mechanical polishing 共CMP兲 has come to be widely
used in manufacturing ultralarge scale integrated circuits 共ULSIs兲
for both insulator planarization and damascene processes.1,2 Compared with other LSI manufacturing processes, CMP is unique in
that the film removal utilizes mechanical energy as well as chemical
reaction. The contribution of mechanical energy to CMP can be well
understood by comparing CMP with dry etching, a typical manufacturing process, as shown in Table I. Though the analogy is not strict,
the slurry used in CMP has, for example, a role similar to the process gas in dry etching. Moreover, the frictional force corresponds to
plasma energy. The frictional force in CMP is thus an essential parameter for analyzing the CMP mechanism. To describe the contribution of mechanical parameters to CMP characteristics, Preston’s
empirical equation has mainly been used, while various models on
chemical aspects have been proposed for glasses and metal
polishing.3-5 Discussions on the equation have been made, because
the equation is not considered to be sufficient for describing the
detail of the CMP mechanism.
Mahajan et al. tried to measure frictional force during CMP by
Si and tungsten square tips with water or diluted nitric acids.6 They
observed a constant or monotonous decrease in frictional force over
time. Philipossian further investigated the effects of mechanical parameters on polishing, and they applied the results to a CMP simulation model.7
Following these works, we have developed a new CMP system
that can measure the frictional force accurately under actual CMP
conditions.8,9 This system is equipped with a stage to support the
rotating wafer, which is mobile in two orthogonal directions, and
detects all the forces acting on the wafer during polishing.
Experimental
Dynamic frictional coefficient in Preston’s empirical
equation.—The following empirical equation by Preston has long
been used to describe CMP performance in terms of removal rate
(RR)
RR ⫽ kp v
关1兴
where k is a constant, p is down force, and v is sliding speed or
linear velocity, i.e., the product of the platen rotational speed and the
distance between the platen center and the wafer center. It is clear
from Eq. 1 that the contribution of down force p to removal rate RR
* Electrochemical Society Active Member.
z
E-mail: [email protected]
is equal to that of the sliding speed v . If either down force p or
sliding speed v is doubled, RR also will be doubled.5
Tseng and Wang re-examined the equation and gave a generalized equation10
RR ⫽ M 共 p, v 兲 p ␣ v ␤
关2兴
where coefficients ␣ and ␤ were estimated to be 5/6 and 1/2, respectively, by fitting with experimental results. Equation 2 is different
from Eq. 1; namely the dependence of RR on down force and that of
v are not linear and different. Coefficient M (p, v ), however, also
changed according to both p and v , but the physical meaning of
M (p, v ) has not been investigated. We found that an equation which
describes the relationship can be deduced directly from the energyconservation law, as shown in Eq. 3
RR ⬀ amount of energy consumed between the wafer
and the polishing pad
⫽ h 共frictional force兲 共moving distance per unit of time)
⫽ hnp v ⫹ c
关3兴
where h is a proportional coefficient corresponding to removal efficiency, and n is a dynamic frictional coefficient. Constant c is introduced to generalize the equation. Equation 3 is very similar to Eq. 1,
while it is different from Eq. 2. Equation 3 shows that RR is proportional to both frictional force, i.e., the product (np), and v , if
dynamic frictional coefficient n and coefficient h remain constant.
Frictional force (np) is thus a fundamental parameter for describing
the CMP mechanism. The role of the mechanical parameters on
CMP characteristics was, accordingly, investigated by measuring the
frictional force under actual CMP conditions for dielectrics and Cu.
Measurement of two dimensional frictional force.—A deadweight-type CMP apparatus with a 50 cm diam platen was used, as
shown in Fig. 1. The wafer was supported by pulleys and rotated
spontaneously or was driven by a motor mounted on a stage, which
was free to move in two orthogonal directions, i.e., x and y directions, as shown in Fig. 1a. Frictional forces acting on the wafer were
measured by load cells 共Kyowa Electronic Inst.兲, which supported
the stage, aligned in the x and y directions.8,9
The platen’s rotational speed, i.e., sliding speed, was varied from
30 to 120 rpm 共30 to 120 m/min兲. Down force was varied from 4.9
k to 39 k Pa 共50 to 400 g/cm2兲. Dressing was carried out in situ by
using a ring-type diamond dresser 共D-60/80, Engis Co.兲 with a down
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Table II. Abrasive free polishing solutions. „Products from
Hitachi Chemical Co.…
Table I. Process analogy.
Dry etching
Process gas
gas flow rate
pressure
Plasma
power
frequency
Temperature
CMP
Slurry
flow rate
concentration
Polishing pad
Friction
down force
rotational speed
polishing pad
Temperature
force of 7.8 kPa 共80 g/cm2兲. A polishing pad made of polyurethane
foam was used with 15 mm pitch, grid-patterned grooves on the
surface 共IC1000, Rodel Co.兲.
Four kinds of slurries were used. As a mechanical-effectdominant slurry, the alkaline silica-based slurry SS-225 共Cabot Co.;
silica-abrasive concentration: 25 wt %兲, diluted either with deionized 共DI兲 water or ammonia solution 共pH 10.5兲 to the abrasive concentration of 12.5 wt % was used for Si and SiO2 polishing. In the
experiments using various concentrations of SS-225, the ammonia
solution was used for dilution. As chemical-effect-dominant slurries,
abrasive-free polishing solutions HS-C430 and HS-C430-A3 共properties listed in Table II; Hitachi Chemical Co.; mixed with 30%
H2 O2 solution兲 were used for Cu polishing.11,12 Alumina abrasive
slurry QCTT1010 共Rodel Co., mixed with H2 O2 solution兲 was also
used.
Si wafers and thermally oxidized SiO2 films on Si wafers 共4 in.
diam兲 were used for evaluating the performance of Si or SiO2 polishing. High-purity Cu plate and sputtered or electrochemically
plated Cu films on oxidized Si wafers 共4 in. diam兲 were used for
evaluating the performance of Cu polishing. Either TaN or TiN were
Figure 1. Two-dimensional frictional-force measurement system. 共a兲 Bird’s
eye view. 共b兲 Top view.
Typical
removal
rate
共nm/min兲
Static etching rate
for Cu
共nm/min兲
Ratio of mixing with
H2 O2 solution 共30%兲
HS-400
HS-C430
Cu
Barrier
metals
SiO2
160-200
400-600
共negligible兲
⬍1.0
共negligible兲
⬍1.0
HS:H2 O2 ⫽ 7:3
used as the barrier and adhesion layer. The dependence of removal
rate and frictional force on polishing conditions, such as down force
and rotational speed, was evaluated. The obtained dependences were
compared with those predicted by Eq. 1, 2, and 3.
Elimination of measurement errors.—In order to realize accurate
measurement, components of frictional force due to other factors
than that due to the wafer itself have to be eliminated. Customarily,
frictional force has been mainly measured by detecting the change
of the motor torque rotating the platen. The method, however, suffers significant problems resulting in insufficient accuracy and sensitivity. One is that the effect of the frictional force generated by in
situ dressing which is used in actual polishing, is contained in the
motor torque. The newly developed measurement system can eliminate completely the influence of the in situ dressing.
The second problem is the component due to the friction between
the retainer ring and the polishing pad. Conventionally, two types of
the retainer ring have been used to prevent slip-out of the wafer
during polishing. One employs a so-called mechanical supporting
system, in which a retainer ring is fixed on a soft backing pad such
as NF-200 共Rodel Co.兲, as shown in Fig. 2a. Value d, the height
Figure 2. Comparison of retainer ring structures. 共a兲 Retainer ring fixed on
a soft backing pad. 共b兲 Retainer ring for an air-supporting-type carrier. 共c兲
Experimental retainer ring with low frictional characteristics.
Journal of The Electrochemical Society, 150 共12兲 G751-G757 共2003兲
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Figure 4. Dependence of frictional force on carrier rotational speed.
tional force was measured by arranging the x direction in the
tangential direction and the y direction to the axial direction of the
platen’s rotation.
Figure 3. Frictional force dependence on tilting angle ␣.
difference between the wafer and the retainer ring surface, has been
determined empirically. When total down force F was very small,
the frictional force due to the retainer ring and the polishing pad was
negligible. The retainer ring touched the polishing pad surface with
a partial down force f r , when F was increased. The ratio between
the f r to the wafer, f w , and to the retainer ring, f r changed with the
change of total F. Recently, a so-called air-bag supporting system, as
shown in Fig. 2b, has come to be widely used. In this system, down
forces f w and f r can be applied independently. A large f r was needed
to prevent the slip-out of the wafer, resulting in large frictional
force. These surplus frictional forces are generally larger than the
net frictional force due to the wafer and the polishing pad and vary
with CMP conditions. It has not been possible to accurately evaluate
the frictional force by using conventional method, since the frictional force due to wafer polishing has not been extracted from the
other parameters.
To solve the problem due to the influence of the retainer ring, we
employed a low friction retainer ring as shown in Fig. 2c. A low
friction fluorocarbon polymer was employed. In addition, the f r was
kept at about 0.98 kPa 共10 g/cm2兲 regardless of f w . Owing to these,
the frictional force due to the retainer ring was kept within the range
of 0.49 to 0.98 kPa 共5 to 10 g/cm2兲.
Results and Discussion
Influence of measuring direction.—The intention was to measure
the whole frictional force as two orthogonal components, i.e., in the
of x and y directions of the stage movement. The dependence of
frictional force on tilting angle ␣, is shown in Fig. 1b. Tilting angle
␣ is defined as the angle between the line O-O⬘ 共connecting the
centers of the platen and the wafer兲 and the y direction of the stage.
The platen rotated at 60 rpm 共sliding speed was also 60 m/min兲,
while the carrier rotated spontaneously.
As shown in Fig. 3, the x direction component of the force was
dominant when ␣ was zero, i.e., when the x direction was parallel to
the tangential direction of the platen rotation. As ␣ increased, the y
direction component also increased and became equal to the x direction component when ␣ reached 45 degrees. Throughout the measurement, the resultant force remained almost constant. The fric-
Influence of rotational speed of the carrier.—To investigate the
polishing conditions, it is necessary to determine a physically reasonable relationship between the rotational speed of the wafer and
that of the platen. Patrick et al. found mathematically that a uniform
removal rate distribution within a wafer should be obtained when
the wafer is rotated at the same rotational speed as the platen.13
However, the actual effect of the relationship between wafer rotational speed and that of platen rotational speed on CMP performance
has not been clarified yet.
The influence of carrier rotational speed on frictional force was
measured for a fixed platen rotational speed. The platen’s rotational
speed and the down force were fixed at 60 rpm and 19.6 kPa 共200
g/cm2兲. An alumina abrasive slurry, QCTT1010 共QCTT1010 suspension mixed at the volume ratio of 2:1 with H2 O2 ) was used to polish
a Cu plate. As shown in Fig. 4, when the carrier’s rotational speed
was lower than that of the platen, the axial component of frictional
force acted toward the outside direction. However, when the carrier’s rotational speed was larger than that of the platen, the axial
component changed toward the center. When the rotational speed of
the carrier was almost equal to that of the platen, only the tangential
component was observed. This result suggests that the polishing
condition under the same rotational speed for the platen and the
carrier represents an energetically minimum state. After that, the
experiments were carried out using the same rotational speed for the
platen and the carrier. Although depending on the kind of slurry, the
axial component sometimes was not zero when rotational speeds
were same. In such a case, carrier rotational speed was adjusted to
make the axial component to zero.
Dependence of frictional force on down force.—Figure 5 shows
dependence of frictional force on down force when DI water, SS225 diluted with DI water (SS-225:DI water ⫽ 1:1; abrasive concentration 12.5%兲 were used to polish Si and SiO2 . This figure
shows that frictional force increased in almost linear proportion to
the down force in both cases. This result suggests that dynamic
frictional coefficient n in Eq. 3 is constant when down force
changes. The frictional force in the case of the diluted SS-225 slurry
was about two times larger than that in the case of DI water. The
abrasive powder or chemical components in the slurry may have
been the cause of this increase.
Frictional
characteristics
of
silica-abrasive-based
slurries.—Experiments were carried out to investigate the dependence of the frictional force on the platen’s rotational speed and the
abrasive concentration in the slurry. SS-225 slurries diluted to vari-
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Journal of The Electrochemical Society, 150 共12兲 G751-G757 共2003兲
Figure 5. Dependence of frictional force on down force.
ous abrasive concentrations were prepared by using an ammonia
solution 共pH 10.5兲, so as not to change pH even under extreme
dilution. Figure 6 shows that frictional force decreased with increasing platen rotational speed for various abrasive concentrations.
Figure 6. Dependence of frictional force on rotational speed.
Figure 7. Frictional force dependence on abrasive concentration in SS-225
slurry diluted with ammonia solution.
Comparison of the results in Fig. 6 with the dependence given by
Eq. 3 revealed that the dynamic frictional coefficient n was not
constant. Moreover, the dependence of frictional force on v can be
simulated well by a fourth order of polynomials within the range of
experimental conditions. The dependence of frictional force on abrasive concentration under various sliding speeds is shown in Fig. 7.
Comparing the results using ammonia solution (abrasive
concentration ⫽ 0) with that of diluted slurries containing abrasive
powder, it is seen that a very small amount of abrasive addition,
0.1%, increased the frictional force significantly. After the frictional
force reached the maximum value, at around 5 to 10%, it decreased
again as abrasive concentration increased.
Relationship between frictional force and removal
characteristics.—As shown in Eq. 3, when coefficient h was independent of down force, removal rate varied in linear proportion to
frictional force under a fixed v . The relationship between frictional
force and removal rate was measured, using thermally oxidized SiO2
films with diluted SS-225 slurry 共1:1兲 with DI water or the ammonia
solution, as shown in Fig. 8a. First, it can be seen that removal rate
was linearly proportional to down force, but the removal rate for the
slurry diluted with ammonia solution is only about 25% of that for
the slurry diluted with DI water. The relationship between down
force and frictional force is shown in Fig. 8b. It is clear that the
frictional force also had a linear relationship with down force, and
the frictional force produced by the diluted slurry with ammonia
solution was significantly smaller than that produced by the diluted
slurry with DI water. The relationship between frictional force and
removal rate is shown in Fig. 9; the slope of the lines in both cases
are quite similar. This result suggests that the removal mechanism
and the coefficient value of h are almost the same in both cases. The
major difference between the two slurries is the change of the frictional force, probably caused by the addition of ammonia.
To summarize this section, it was shown that frictional force
measurement is a very effective way to analyze the CMP mechanism. It can be concluded from the results above that coefficient h in
Journal of The Electrochemical Society, 150 共12兲 G751-G757 共2003兲
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Figure 9. Correlation between removal rate and frictional force.
rotational speed: 60 rpm兲. The initial low frictional force indicates
that effective polishing did not occur at a down force below 9.8 kPa.
After polishing at 24.5 k Pa 共250 g/cm2兲 and then decreasing the
down force, however, the frictional force did not return to its initial
value; instead, it showed hysterisis-like characteristics. Under elevated temperature, the nonlinear and hysterisis-like characteristics
disappeared at around 30°C, as shown in the same figure. This result
suggests that the removal characteristics of HS-C430 are temperature sensitive. On the other hand, when HS-C430-A3 was used, the
nonlinear characteristics changed little with temperature, as shown
in Fig. 11. This means that the CMP characteristics were stable
when the solution C430-A3 was used for Cu polishing. It agrees
with that demonstrated by Ohashi et al., i.e., the stable nonlinear
characteristics are suitable for achieving better Cu surface planarity
by the Damascene process.12
Figure 8. Dependence of removal rate and frictional force on down force.
共a兲 Dependence of the removal rate on down force. 共b兲 Dependence of the
frictional force on down force.
Eq. 3 is constant regardless of variation in down force, and the
dependence of RR on down force p is linear, under a fixed sliding
speed.
Characteristics of abrasive-free polishing solutions.—As has
been already reported, abrasive-free polishing solutions have a good
enough performance for the Cu damascene process, as shown in
Table II. Since such solutions show perfect stop-on-barrier characteristics, they enable extremely accurate fabrication.11,12 Frictional
force was measured, first, by increasing down force and, then, by
decreasing it in the case of HS-C430, as shown in Fig. 10. The
arrows in the figures show the measurement order, i.e., by increasing
or decreasing down fore. As seen in the figure, frictional force was
very low when the down force was below 9.8 kPa 共100 g/cm2兲, and
it increased steeply under larger down forces at around 20°C 共the
Figure 10. Influence of polishing temperature on frictional force dependence on the down force. 共abrasive-free polishing solution HS-C430.兲
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Journal of The Electrochemical Society, 150 共12兲 G751-G757 共2003兲
for a chemical-effect dominant solution. The slopes, i.e., the values
of h, suggests that the reaction speed or mechanism involved in
CMP might change with temperature. As we previously reported, a
linear correlation between removal rate and frictional force was also
found in the case of QCTT1010 slurry.8,9
Figure 11. Dependence of frictional force on down force and temperature.
共abrasive-free polishing solution HS-C430-A3.兲
Correlation for Cu polishing.—The HS-C430 solution showed
significantly different dependence on polishing conditions than the
SS-225 slurry, suggesting that it is strongly chemical-effect dominant. To confirm the role of frictional force in Eq. 3 in CMP characteristics, the correlation between frictional force and removal was
evaluated. The relationship between frictional force and removal
rate for Cu polishing using HS-C430 solution at around 20 and 30°C
is shown in Fig. 12. HS-C430 solution was chosen because it exhibited significant change in the characteristics with the temperature
change in Fig. 10. It was found that frictional force and removal rate
had a linear relationship, even at different polishing temperatures, as
shown in Fig. 12.
From Fig. 12, it can be concluded that coefficient h in Eq. 2 is
constant, regardless of down force under a fixed sliding speed, even
Mechanical aspects of CMP mechanism.—The original empirical
equation by Preston is very simple, i.e., Eq. 1. On the other hand,
several discussions on the limits of this equation have been made,
and the modified model has been proposed10 in Eq. 2. Equation 2
was devised by taking into account the contribution of the shear and
normal components of the down force in Eq. 1. The values of ␣, ␤,
and M (p, v ) were determined by parameter fitting with experimental results for a certain slurry, while the physical meaning of M (p, v )
was not examined. Our experimental equation 共Eq. 3兲 is given from
the energy conservation law where h corresponds to removal efficiency. As can be seen, Eq. 3 is very similar to Eq. 1. Because no
assumption is contained in Eq. 3, it is clear that frictional force
increased in proportion to increase in down force p, while it should
have remained constant despite variations in the wafer’s sliding
speed v , if the dynamic frictional coefficient n remained constant. In
addition, Eq. 3 gives more information on the CMP mechanism.
If the dependences of removal rate on either p or on v are different, they should be due to the change in the coefficient n or h,
rather than due to the difference between dependence on p and v .
RR should change in linear proportion to frictional force and to
sliding speed, if coefficient h is independent of down force p and
sliding speed v . An important difference between Eq. 3 and Eq. 2,
thus exists on the dependence of removal rate on down force p and
sliding speed v .
Equation 3 was verified by the experiments using various slurries
and temperatures, that removal rate depends linearly on the frictional force, i.e., coefficient h is constant under a fixed sliding speed.
Regarding the change of dynamic frictional coefficient n, detailed
evaluation of the slurries, especially hydrodynamic characteristics,
is still required. Similar evaluation on the polishing pad would also
be required, since the removal characteristics change significantly
according to the method of slurry dilution, as shown in Fig. 9. In
Fig. 9, the significant change in the removal rate was presumed to be
due to the change in the surface characteristics of the polishing pad,
because the pH of the two diluted slurries did not change. Constant
c can be determined by chemical or mechanical characteristics of
CMP, such as a threshold energy necessary to initiate polishing or
chemical etching rate.
Conclusions
Figure 12. Relationship between frictional force and removal rate.
共abrasive-free polishing solution HS-C430.兲
The effects of mechanical parameters on the characteristics of
CMP were evaluated quantitatively by directly measuring the frictional force acting on a wafer by using a newly developed system
for measuring frictional force. The whole frictional force acting on
the wafer was precisely measured in terms of two components, i.e.,
the tangential and axial components of the platen’s rotation. It was
found that, when the platen and the wafer were rotated at the same
rotational speed, in most cases only the tangential component of the
frictional force was detected. The frictional force was also found to
have a linear relationship with removal rate. Frictional force increased nearly in linear proportion to down force when mechanicaleffect-dominant CMP 共Si or SiO2 polishing兲 was carried out, while
it gradually decreased as the platen’s rotational speed increased.
Copper polishing using abrasive-free polishing solutions showed
much more complex behavior. That is, the dependence of frictional
force on down force showed nonlinear characteristics. Even when a
nonlinear characteristic slurry was used, it was found that removal
rate and frictional force also had a linear relationship. According to
the results, an experimental equation was thus proposed by taking
into account the dynamic frictional coefficient and a new coefficient
corresponding to removal efficiency.
Hitachi, Ltd., assisted in meeting the publication costs of this article.
Journal of The Electrochemical Society, 150 共12兲 G751-G757 共2003兲
References
1. R. R. Uttecht and R. M. Geffken, in Proceedings of the International VLSI Multilevel Interconnection Conference, VMIC, IEEE, p. 20 共1991兲.
2. K. Konishi, U.S. Pat. 3,895,391 共1975兲, Japanese Pat., P879423.
3. T. Izumitani and S. Adachi, in Technical Digest of the Topical Meeting on the
Science of Polishing, The Optical Society of America, p. Tub-Al-1 共1984兲.
4. F. B. Kaufman, D. B. Thompson, R. E. Broodie, M. A. Jaso, and W. L. Gutherie, J.
Electrochem. Soc., 138, 3460 共1991兲.
5. F. W. Preston, J. Soc. Glass Technol., 11, 214 共1927兲.
6. U. Mahajan, M. Bielmann, and R. K. Singh, Electrochem. Solid-State Lett., 2, 46
共1999兲.
7. A. Philipossian, S. Olsen, and E. Mitchell, Spring Meeting Abstracts of Japan
Society of Precision Engineering, JSPE, p. 504 共2002兲.
G757
8. Y. Homma, K. Fukushima, S. I. Kondo, and N. Sakuma, Abstract 655, The Electrochemical Society Meeting Abstracts, Vol. 2000-2, Phoenix, A2, Oct 22-27, 2000.
9. Y. Homma, S. Kondo, N. Sakuma, and K. Fukushima, Spring Meeting Abstracts of
the Japan Society for Precision Engineering, JSPE, p. 492 共2001兲.
10. W.-T. Tseng and Y.-L. Wang, J. Electrochem. Soc., 144, L15 共1997兲.
11. S. Kondo, N. Sakuma, Y. Homma, Y. Goto, N. Ohashi, H. Yamaguchi, and N.
Owada, in Proceedings of the International Interconnect Technology Conference,
IITC, p. 253 共2000兲.
12. N. Ohashi, Y. Yamada, N. Konishi, H. Maruyama, T. Oshima, H. Yamaguchi, and
A. Satoh, in Proceedings of the International Interconnect Technology Conference,
IITC, p. 140 共2001兲.
13. W. J. Patrick, W. L. Guthrie, C. L. Standley, and P. M. Schiable, J. Electrochem.
Soc., 138, 1778 共1991兲.