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Thin Solid Films 476
A chemical kinetics model to explain the abrasive size effect on
chemical mechanical polishing
Ping Hsun Chena,b,1, Bing Wei Huanga, Han-C Shiha,*
aDepartment of Materials Science and Engineering of National Tsing Hua University, 101 Kuang Fu Road, Sec. 2, 300 Hsinchu, TaiwanbP.O. BOX 47-19 Taipei, Taiwan
Received 12 February 2004; received in revised form 9 August 2004; accepted 23 September 2004
Available online 26 November 2004
Abstract
A chemical kinetics model was proposed to describe the abrasive size effect on chemical mechanical polishing (CMP). The model is based
on the consideration of a pad as a sort of catalyst and the re-adhering of abrasives due to the large size. Therefore, a general equation was
deduced according the chemical kinetics methodology to give the meanings of the size effect. Finally, according a set of data related to the
abrasive size effect on CMP, a possible form can be PR=aCCCTXACWAn /[b+cXACWA
n ] where a, b, c and n are the parameters in a CMP system.
D 2004 Elsevier B.V. All rights reserved.
PACS: 82.20; 82.30; 77.84.B; 42.86
Keywords: Planarization; Polymers; Oxides
1. Introduction
Since copper was applied to the interconnect in semi-
conductor devices, the technology of CMP, which stands for
bchemical mechanical polishingQ, has jumped to another
generation [1,2]. Among many researches for describing
CMP, the most famous mechanism was proposed by Cook in
1990. Cook [3] used the method of chemical kinetics to
explain the polishing process. Recently, there have been some
papers discussing CMP in the view of chemical reaction
kinetics. Paul [4] considered the first step in CMP is to form a
thin reaction film. Then, a thin reaction film is polished with
the following two parallel reactions. One is the corrosion
process for dissolution. The other is mechanical abrasion step,
which is in terms of a chemical reaction. Thakurta et al. [5]
combined slurry hydrodynamics, mass transport and reaction
kinetics to predict the copper film polishing rate. The steps
include: (i) mass transport of the oxidizer to the wafer surface,
0040-6090/$ - see front matter D 2004 Elsevier B.V. All rights reserved.
doi:10.1016/j.tsf.2004.09.049
* Corresponding author. Tel.: +886 35 715131; fax: +886 35 710290.
E-mail addresses: cstr@young.url.com.tw (P. Hsun Chen)8
hcshih@mse.nthu.edu.tw (H.-C. Shih).1 Fax: +886 2 25935145.
(ii) reaction of oxidizer with copper to form a reacted layer,
(iii) subsequent removal of the reacted layer by mechanical
abrasion. Gutmann et al. [6] have proposed a generic two-step
model for the CMP process. Their model involves a balance
between a chemical reaction of the slurry constituents with the
surface being polished andmechanical removal of the reacted
surface layer by the slurry abrasive particles.
However, as for the effect of particle sizes of slurry
abrasives, the mechanical-based models dominate. Luo and
Dornfeld [7] proposed an abrasive mechanism in solid–solid
contact mode of the CMP. With the assumptions of periodic
roughness of the pad surface, plastic deformation over
wafer–particle and pad–particle interfaces, and normal
distribution of abrasive particle size, they correlated the
polishing rate with the average abrasive size and the
standard deviation of the abrasive size distribution. Fu et
al. [8] provided a plasticity-based model to explore the
effects of various design parameters (e.g., abrasive shape,
size and concentration, and pad stiffness). For spherical
abrasives, the model predicted the decrease of the polishing
rate with increasing abrasive size; however, for sharp
abrasives, the polishing rate is independent of abrasive size
in the stiff pad and high abrasive concentration regime, but
(2005) 130–136
P. Hsun Chen et al. / Thin Solid Films 476 (2005) 130–136 131
the polishing rate increases with abrasive size in the soft pad
and low abrasive concentration.
In this article, a chemical kinetics-basedmodel is presented
to describe the effect of the abrasive size on the polishing rate.
For simplicity, oxide CMP is focused. The model is based on
the concept of considering a pad as a catalyst.
Fig. 1. Illustration of chemical kinetics mechanism for CMP.
2. Chemical kinetics model setup
Chen et al. [9] have proposed the catalytic-pad chemical
kinetics (represented by CPCK) model based on the concept
of Cook [3] who pointed out the role of chemistry in glass
polishing. The advance of the CPCK model is to take the
pad effect into consideration.
Jairath et al. [10] showed out the wafer-to-wafer polish-
ing rate behavior with pad conditioning differs from that
without pad conditioning. With no pad conditioning, the
polishing rate will decay exponentially as the number of
polished wafers increases. Hernandez et al. [11] studied the
pad effects. They showed the scanning electron microscopy
(SEM) pictures of three cases of (i) soaked in slurry only,
(ii) soaked and polished, and (iii) soaked, polished and
dressed. In the cases of (i) and (ii), slurry was adhered in
some pad voids. Although, in the case of (iii), no slurry was
shown; however, it is believed that pad aging happens
during the CMP process. Thus, there should be a role of a
pad in the CMP mechanism. We can treat a pad as some sort
of catalyst. Then, the theories built in the field of catalyst
chemical engineering can be used to explain the behaviors
in the CMP process.
The basic mechanism of the CPCK model has seven
steps: (a) abrasives move into pores at the top pad region
and (b) they are grasped by surface active sites within the
pores before reaching the polishing areas under a wafer; (c)
meanwhile, some chemicals move onto the wafer surface
and (d) they change the surface quality for polishing at the
trench areas of the pad under the polished wafer; then (e)
reactions happen between pad-grasped abrasives and active
sites of wafer surface, and materials at the wafer surface are
polished; (f) reacted abrasives within the pores of a pad will
escape and (g) they move into the bulk slurry flow to leave a
pad [9]. Some assumptions are made. First, the trans-
portation of fresh or reacted abrasives is fast in a certain
time scale such that the mass transfer resistance could be
omitted. Second, this mechanism happens in a certain area
and thus it is not necessary to take the non-uniformity into
consideration. Third, abrasive size is the same in this basic
mechanism. However, the effect of abrasive size will be
concerned later in this article.
Fig. 1(a) shows the illustration of steps (a) and (b).
If abrasives and pores are represented by the symbols A
and P, respectively, a reversible reaction can be written
as
Aþ P XAP4 ð1Þ
In reaction (1), AP* means the pad-grasped abrasives
that can participate in the CMP process. Fig. 1(b) shows
steps (c) and (d). Let C stands for chemicals and M for
P. Hsun Chen et al. / Thin Solid Films 476 (2005) 130–136132
polished materials. Thus, the second reversible reaction
is
CþM X *CM ð2Þ
In reaction (2), *CM means active sites on the wafer
surface. Then, Fig. 1(c) shows step (e). The main step
of CMP happens in the region where *CM can be
abraded by AP*. The removal of the thin film on the
wafer surface results mainly from the mechanical force.
The chemical part of CMP refers to previous steps.
Then, reaction (3), an irreversible reaction is written down
as
*CM�MB þ AP*YMB � ð*CM� AP*ÞYMB
þ ð*CM� AP*Þ ð3Þ
In reaction (3), *CM-MB is used to replace *CM in reaction
(2). MB is added to represent the bulk material.
Fig. 1(d) shows the removed species, *CM-AP*,
gradually leave the pores of a pad. Thus, some active
sites inside the pores become alive for upcoming
adhesion of fresh abrasives. Then, reaction (4) for step
(f) is written as
*CM� AP* X Pþ *CM� A ð4Þ
*CM-A is a species that should leave the pad immediately
as step (g). Then, the primary mechanism is reached.
However, if the abrasive size is large enough, a part of
abrasives of *CM-A could not leave the pad immediately.
The part could be considered as *CM-A1. Moreover, *CM-
A1 is assumed to be different from *CM-A, so reaction (4)
remains.
*CM-A1 adheres inside the pores again and the adhering
side of *CM-A1 will not be the same as the primary
mechanism, as shown in Fig. 1(e). Thus, we further assume
that an abrasive would have several sites to polish or react
with active sites on the wafer surface and that the number of
sites of an abrasive would vary with the size of an abrasive.
For the re-adhering abrasives, a reversible reaction is
written as
*CM� A1 þ P X ð*CMA1Þ � P* ð5Þ
The re-adhering abrasives, (*CMA1)-P*, will polish the
wafer surface as the fresh abrasives, AP*, do. Thus, like
reaction (3), another irreversible reaction is written as
*CM�MB þ ð*CMA1Þ � P*YMB
� ð*CM� ð*CMA1Þ � P*ÞYMB
þ ð*CM� ð*CMA1Þ � P*Þ ð6Þ
Then, the removed species, (*CM-(*CMA1)-P*), gradually
leave the pores of a pad. Thus, reaction (7) is given as
ð*CM� ð*CMA1Þ � P*Þ X Pþ ð*CMÞ2A1 ð7Þ
At this time, (*CM)2A1 would be assumed not to re-adhere
inside the pores.
Moreover, let us consider the situation where (*CM)2A1
could not leave the pad immediately, either. Following the
same steps and assuming that the part of (*CM)2A1
remaining in the pad is shown as (*CM)2A2, we would
have another three reactions such as:
ð*CMÞ2A2 þ P X ½ð*CMÞ2A2� � P*
*CM�Mþ ½ð*CMÞ2A2� � P*Y ð8Þ
M� f*CM� ½ð*CMÞ2A2� � P*gYM
þ *CM-[(*CM)2A2]-P* ð9Þ
f*CM� ½ð*CMÞ2A2� � P*g X Pþ ð*CMÞ3A2 ð10Þ
Here, one another assumption should be added, which is
that each fresh or old abrasive won’t react with each other
during adhering inside the pores. There might be more
than three types of abrasives mentioned above. It will be
taken into consideration while the rate equation is
deduced.
3. Rate equation deduction
Before deducing the rate equation of CMP, another
assumptions should be made. That is, reactions (3), (6), and
(9) are the rate-limiting (rate-controlling) step, and other
reactions are treated as an elementary reaction.
First, the rate equation is deduced under the condition
that the used abrasives leave the pad immediately without
re-adhesion. In reaction (1), if CA, CP and CAP* stand for
the concentration of abrasives in the slurry, active sites
within the pores and occupied sites by pad-grasping, the
equilibrium equation is
K1 ¼ CAP4= CA CPÞð ð11Þ
In Eq. (11), K1 is an equilibrium constant for reaction (1).
In reaction (2), if CC and C*CM stand for the concen-
tration of certain chemical in the slurry and active sites on
the wafer surface, the equilibrium equation is
K2 ¼ C4CM=CC ð12Þ
In Eq. (12), K2 is an equilibrium constant for reaction (2).
In reaction (4), if CP and C*CM-AP* stand for the
concentration of active sites and occupied sites of the
removed species, *CM-AP*, inside the pores of the pad, the
equilibrium equation is
K3 ¼ CP=C4CM�AP4 ð13Þ
P. Hsun Chen et al. / Thin Solid Films 476 (2005) 130–136 133
In Eq. (13), K3 is an equilibrium constant for reaction (4).
The species, *CM-A, is not included because *CM-A is
assumed to leave the pad immediately.
The total sites within the pores is CT, which is equal to
the sum of active sites, occupied sites of abrasives, and
occupied sites of removed species. Then, we can have
CT ¼ Cp þ CAP4 þ C4CM�AP4 ð14Þ
From Eqs. (11) and (14), CAP*=K1(CACP), and C*CM-AP*=
CP/K3. Thus, both CAP* and C*CM-AP* can be replaced by
Cp. Eq. (14) can be rewritten as
CT ¼ Cp þ K1 CA Cp
�þ CP=K3
�ð15Þ
Thus,
Cp ¼ K3 CTÞ= 1þ K3 þ K1K3CAÞðð ð16Þ
CAP4 ¼ K1K3CA CTÞ= 1þ K3 þ K1K3CAÞðð ð17Þ
C4CM�AP4 ¼ K3 CTÞ= K3 þ K23 þ K1K
23CA
���ð18Þ
Reaction (3) is considered as the rate-limiting (rate-control-
ling) step, so the rate equation of reaction (3), is written as
(k4 is a rate constant)
R ¼ k4C4CM CAP4 ð19Þ
From Eq. (12), C*CM=K2CC. And substitute CAP* with Eq.
(17). Thus, Eq. (19) can become
R ¼ K1K2K3k4 CACCCTÞ= 1þ K3 þ K1K3CAÞðð ð20Þ
Further, if the total polished surface is A, the polishing rate
equation (PR) is written as
PR ¼ AK1K2K3k4 CACCCTÞ= 1þ K3 þ K1K3CAÞððð21Þ
Next, the abrasive size effect is included, and the condition
that the abrasive size is large enough such that *CM-A
could not leave the pad immediately is taken into
consideration.
In reaction (5), if C*CM-AV, CP and C(*CMAV)-P* stand for
the concentration of re-adhering abrasives in the slurry,
active sites within the pores and re-adhering abrasives-
occupied sites by pad-grasping, the equilibrium equation is
K11 ¼ Cð4CMA1Þ�P4=�C�CM�A1 CP
�ð22Þ
In Eq. (22), K11 is an equilibrium constant for reaction (5).
In reaction (7), if CP and C*CM-(*CMA1)-P* stand for the
concentration of active sites and occupied sites of the
removed species, *CM-(*CMA1)-P*, inside the pores of the
pad, the equilibrium equation is
K13 ¼ CP=C4CM� 4CMA1ð Þ�P4 ð23Þ
In Eq. (23), K13 is an equilibrium constant for reaction (7).
The species, (*CM)2-A1, is not included because (*CM)2-
A1 is assumed to leave the pad immediately.
Then, the total sites within the pores is CT, which is equal
to the sum of active sites, occupied sites of fresh and re-
adhering abrasives, and occupied sites of removed species.
Then, we can have
CT ¼ Cp þ CAP4 þ C 4CMA1ð Þ�P4 þ C4CM�AP4
þ C4CM� 4CMA1ð Þ�P4 ð24Þ
From Eqs. (11), (14), (22) and (23), CAP*=K1(CACP),
C*CM-AP*=CP/K3, C (*CMA1)-P*=K11(C*CM-A1CP) and
C*CM-(*CMA1)-P*=CP/K13. Thus, CAP*, C(*CMA1)-P*, C*CM-
(*CMA1)-P* and C*CM-AP* can be replaced in the form of Cp.
Eq. (24) can be rewritten as
CT ¼ Cp þ K1ðCA CPÞ þ K11ðC4CM�A1 CPÞþ CP=K3 þ CP=K13 ð25Þ
Thus,
Cp ¼ CT= 1þ 1=K3 þ 1=K13 þ K1CA þ K11C4CM�A1Þðð26Þ
CAP4 ¼ ðK1CA CTÞ=ð1þ1=K3 þ 1=K13 þ K1CA þ K11C�CM�A1Þ ð27Þ
Cð4CMA1Þ�P4 ¼ ðK11C4CM�A1 CTÞ=ð1þ 1=K3 þ 1=K13
þ K1CA þ K11C4CM�A1Þ ð28Þ
Reaction (6) is also considered as a rate-limiting (rate-
controlling) step. The rate equation of reaction (6) is written
as (k14 is a rate constant)
R ¼ k14C4CM C 4CMA1ð Þ�P4 ð29Þ
However, the total reaction rate should combine Eqs. (19)
and (29). Then, it gives to
R ¼ k4C4CM CAP4 þ k14C4CM C 4CMA1ð Þ�P4
¼ k4CAP4 þ k14C 4CMA1ð Þ�P4
�C4CM
�ð30Þ
From Eq. (12), C*CM=K2CC. And substitute CAP* and
C(*CMA1)-P* with Eqs. (27) and (28), respectively. Thus, Eq.
(29) becomes
R ¼ K2CCCTðk4K1CA þ k14K11C�CM�A1Þ=ð1þ 1=K3 þ 1=K13 þ K1CA þ K11C�CM�A1Þ ð31Þ
Following the concept and procedure, we think of for
(*CM)2A1 in reaction (7), if (*CM)2A1 could not leave the
P. Hsun Chen et al. / Thin Solid Films 476 (2005) 130–136134
pad immediately and re-adhere onto the pad as (*CM)2A2,
Eq. (31) should become
R ¼ K2CCCTðk4K1CA þ k14K11C4CM�A1
þ k24K21C 4CMð Þ2�A2Þ=ð1þ 1=K3 þ 1=K13 þ 1=K23
þ K1CA þ K11C4CM�A1 þ K21C 4CMð Þ2�A2Þ ð32Þ
where k24 is a rate constant for reaction (9), and K21 and K23
are a equilibrium constant for reactions (8) and (10),
respectively.
Thus, a general rate equation would be
R ¼ K2CCCTðk4K1CA þ k14K11C4CM�A1
þ k24K21C 4CMð Þ2�A2 þ k34K31C 4CMð Þ3�A3 þ N Þ=ð1þ 1=K3 þ 1=K13 þ 1=K23 þ 1=K33 þ N þ K1CA
þ K11C4CM�A1þK21C 4CMð Þ2�A2þK31C 4CMð Þ3�A3 þ N Þ
ð33Þ
Here, one assumption is added that chemical active
properties on the surface of fresh or re-adhering abrasives
are all the same. Thus,
k ¼ k4 ¼ k14 ¼ k24 ¼ k34 ¼ N ð34Þ
Ka ¼ K1 ¼ K11 ¼ K21 ¼ K31 ¼ N ð35Þ
Kb ¼ K3 ¼ K13 ¼ K23 ¼ K33 ¼ N ð36Þ
Therefore, Eq. (33) becomes
R ¼ kKaK2CCCTðCA þ C4CM�A1 þ C 4CMð Þ2�A2
þ C 4CMð Þ3�A3 þ N Þ=½1þ nþ 1ð Þ=Kb þ KaðCA
þ C4CM�A1 þ C 4CMð Þ2�A2 þ C 4CMð Þ3�A3 þ N Þ� ð37Þ
where n is a limited value because the CMP process is
operated in a certain time and an abrasive will not always
remain to react with the wafer surface.
Now, we face a problem of how to express (CA+
C*CM-A1+C(*CM)2-A2+C(*CM)3-A3+. . .) in a simple form.
The concept, called bresidence-time distributionQ (RTD) andoften used to analyze a reactor, is introduced [12]. A
reacting flow entering into a reactor can be separated into
many elements. Each element does not stay in the reactor for
the same duration. Some elements might by-pass the reactor,
so they enter and leave the reactor at almost the same time.
Some elements might stay in the reactor for certain duration
so as to have the reaction complete. Some elements stay in
the reactor forever, which might be called a dead zone.
Based on this RTD concept, therefore, chemical engineering
workers use bmean residence timeQ (MRT) to represent the
whole phenomenon.
Philipossian and Mitchell [13] have demonstrated the
phenomenon of MRTof slurry. Thus, the concept of RTDwas
applied to our model. First, as mentioned above, some fresh
abrasives, represented as A, do not leave the pad after they
reactwith thewafer surface, and then become *CM-A1 staying
on the pad. It is like the concept of RTD. Secondly, a function,
F, is assumed to represent (CA+C*CM-A1+C(*CM)2-A2+
C(*CM)3-A3+. . .), and F is reasonably related to CA, XA
(represented as the size of abrasives), n (shown in Eq. (37))
and kP (represented as the sum of pad qualities). Therefore,
F=F(CA, XA, n, kP). Eq. (37) becomes
R ¼ kKaK2CCCTFðCA;XA; n; kPÞ=½1þ nþ 1ð Þ=Kb þ KaFðCA;XA; n; kPÞ� ð38Þ
In the present model, the unit of CA is presumed as the
abrasive number per volume. However, the unit of weight
percentage is conventionally used in CMP experiments. If
CWA stands for the concentration in weight percentage for
abrasives in the slurry, then CA can be transformed into CWA
with slurry density (dS), abrasive density (dA), abrasive size
(XA) and a shape factor (S) for adjusting the calculation
based on spherical abrasives. That is, CWA=CA(dASXA3/
dS). Thus, F(CA, XA, n, kP) becomes FV(CWA, XA, n, m),
where m combines the effects of pad qualities, slurry
density, abrasive density and abrasive size.
Again, if the total polished surface is A, the polishing
rate equation (PR) is written as
PR ¼ AkKaK2CCCTFVðCWA;XA; n;mÞ=½1þ nþ 1ð Þ=Kb þ KaFVðCWA;XA; n;mÞ� ð39Þ
4. Discussion
Eq. (39) is similar to Eq. (21). Eq. (39) can be treated as a
general equation for the polishing rate.
In Eq. (39), there should be a theoretical conflict that if
CC is zero. However, it should not be zero theoretically.
This is because water in the slurry can be considered as a
kind of chemical for activating the wafer surface. As
mentioned above, the present mechanism is based on the
mechanism of Cook [3]. Water should hydrate oxide film.
Thus, the polishing rate will be small or quite small, but not
zero even though there is no such bchemicalQ in the slurry.
Eq. (39) is different from some mechanical-based
polishing rate equations such as the Preston equation or
others mentioned above. The down force and relative
velocity are not explicitly shown. If the solid–solid reaction
is concerned, it will be clear that k of each polishing
reaction, such as reactions (3), (6), and (9), should have
some relationship with the down force and relative velocity.
This results from the stress applied on the wafer surface
affecting the polishing rate [14]. The stress is the combi-
nation of normal stress (down force) and shear stress
P. Hsun Chen et al. / Thin Solid Films 476 (2005) 130–136 135
(relative velocity) and therefore should change the thermo-
dynamic value of k.
As for CT, it means the combination of the active and
non-active sites on the pad. Chen et al. [9] theoretically
demonstrated CT should decrease without pad conditioning
as the number of polished wafers increasing. It is reasonable
to believe that CT should decrease during a single wafer
polishing. Thus, CT should be an average value.
As for the function FV(CWA, XA, n, m), it should be
selective for different CMP systems. As mentioned above,
the CPCK model is referred to the oxide CMP. However, it
is very hard to find the oxide CMP data with respect to
different abrasive size in the literatures. Although Jairath et
al. [10] has proposed some CMP polishing rate data with
different abrasive size, the kinds of size were 7 and 30 nm. It
is not proper to use their data to fit our rate equation.
Therefore, we have to dborrowT the result from metal CMP.
Bielmann et al. [15] has studied the effect of particle size
during tungsten CMP. Generally metal CMP involves two
steps. The first step is to oxidize the metal film and the
second is to remove the metal-oxide film. The removal of
the metal-oxide film comprises the CMP and corrosion
effects [16]. If the corrosion effect on the removal rate of
tungsten film is omitted, the chemical kinetics of metal
CMP is similar to that of oxide CMP. This is because metal
film is oxidized before polished. It is like reaction (2). Fig. 2
shows the conceptual chart for the Bielmann et al.’s results.
The removal rate is proportional to CWA as the abrasive size
is relatively large. Then, the abrasive size starts to show its
effect as it decreases. The curve of the removal rate versus
CWA will deviate from the straight line. The slope of the
curve corresponding to CWA decreases gradually as CWA
increases. The removal rate becomes constant finally.
Therefore, it gives a possible form for FV(CWA, XA, n, m)
which is:
FV CWA;XA; n;mÞ ¼ mXACnWA
�ð40Þ
Then, Eq. (39) becomes
PR ¼ AkKaK2CCCTmXACnWA
=½1þ nþ 1ð Þ=Kb þ KamXACnWA� ð41Þ
In Eq. (41), n is a parameter with respect to XA (abrasive
size). For example, n may be 1 for A range of XA or 2 for B
Fig. 2. Conceptual experimental data chart from Bielmann et al. [15].
range, depending on the system. If we assume AkKaK2m=a,1(n+1)/Kb=b and Kam=c, Eq. (41) will be simpler as
PR=aCCCTXACWAn /[b+cXACWA
n ]. The specific values of all
parameters are not calculated because Bielmann et al.’s
results come from metal CMP. Eq. (41) is deduced for
expressing a possible application of Eq. (39).
It should be mentioned that the selection of FV(CWA, XA,
n, m) is state-of-art. FV(CWA, XA, n, m) can be mXAnCWA,
m(XACWA)n or mXA
zCWAn . Therefore, as confronted with a
CMP system of certain consumables and film to polish,
several forms of FV(CWA, XA, n, m) would be tried until a
proper one meets the experimental data.
In the present model, the distinction between abrasive
particles that do and do not leave the pad is not subject to a
critical size of abrasives. The main difference between these
two kinds of abrasives focuses on whether they react with
the wafer surface. Furthermore, one concept of the present
model is that due to the abrasive size effect the used
abrasives will stay in the pad and react with the wafer
surface by another unreacted, active surface of abrasive.
Therefore, the idea of mean residence time is incorporated
because it expresses the dsameT species will not leave a
reactor together. Actually, it is very hard to identify a critical
size due to the lack of experimental data in the literatures
with respect to this topic. At the present stage, the idea of
mean residence time and its relationship with the abrasive
size are lumped into some parameters as n and m. However,
the more detailed mathematical expression should be further
developed in our future work.
5. Conclusion
A new attempt for describing CMP in the view of
chemical kinetics is proposed. It is a semi-theoretical
approach. Based on the consideration of a pad as a catalyst,
a mechanism was illustrated to have a polishing rate
equation combined with the effect of the abrasive size.
However, some empirical terms were introduced. Based on
metal CMP data without the concern of corrosion, a possible
form can be PR=aCCCTXACWAn /[b+cXACWA
n ] where a, b, cand n are the parameters in a CMP system. Although the
model did not include the corrosion effect, the given
possible forms of polishing rate still can be useful practi-
cally for CMP engineers to estimate the abrasive size effect.
It is noted that the equation doesn’t include the size
distribution effect. More complex equations will be deduced
in the future works.
Acknowledgement
The authors would like to acknowledge the support of
this work by the National Science Council of the
Republic of China (Taiwan) under the contract of
NSC90-2218-E-007-003.
P. Hsun Chen et al. / Thin Solid Films 476 (2005) 130–136136
References
[1] X.W. Lin, D. Pramanik, Solid State Technology 41 (1998) 63.
[2] J.W. Hsu, S.Y. Chiu, M.S. Tsai, B.T. Dai, M.S. Feng, H.C. Shih, J.
Vac. Sci. Technol., B 20 (2002) 608.
[3] L.M. Cook, J. Non-Cryst. Solids 120 (1990) 152.
[4] E. Paul, J. Electrochem. Soc. 148 (2001) G355.
[5] D.G. Thakurta, D.W. Schwendeman, R.J. Gutmann, S. Shankar, L.
Jiang, W.N. Gill, Thin Solid Films 414 (2002) 78.
[6] R.J. Gutmann, D.J. Duquette, P.S. Dutta, W.N. Gill, Proceedings of
6th International Chemical-Mechanical Planarization for ULSI Multi-
level Interconnect Conference (2001 CMP-MIC), Santa Clara, U.S.A.,
March 7–9, 2001, p. 81.
[7] J.F. Luo, D.A. Dornfeld, IEEE Trans. Semicond. Manuf. 14
(2001) 112.
[8] G. Fu, A. Chandra, S. Guha, G. Subhash, IEEE Trans. Semicond.
Manuf. 14 (2001) 406.
[9] P.H. Chen, H.C. Han, B.W. Huang, J.W. Hsu, Electrochem. Solid-
State Lett. 6 (2003) G140.
[10] R. Jairath, M. Desai, M. Stell, R. Telles, D. Scherber-Brewer, in: S.P.
Murarka, A. Katz, K.N. Tu, K. Maex (Eds.), Advanced Metallization
for Devices and Circuits-Science, Technology and Manufacturability,
San Francisco, CA, U.S.A, April 4–8, 1994, Materials Research
Society Symposium Proceedings, vol. 337, 1994, p. 121.
[11] J. Hernandez, P. Wrschka, Y. Hsu, T.S. Kuan, G.S. Oehrlein, H.J.
Sun, D.A. Hansen, J. King, M.A. Fury, J. Electrochem. Soc. 146
(1999) 4647.
[12] H.S. Fogler, Elements of Chemical Reaction Engineering (2nd ed.),
Prentice Hall P T R, USA, 1992.
[13] A. Philipossian, E. Mitchell, MICRO 20 (2002) 85.
[14] J. McGrath, C. Davis, J. McGrath, J. Mater. Process. Technol. 132
(2003) 16.
[15] M. Bielmann, U. Mahajan, R.K. Singh, Electrochem. Solid-State Lett.
2 (1999) 401.
[16] J.M. Steigerwald, S.P. Murarka, R.J. Gutmann, Chemical Mechanical
Planarization of Microelectronic Materials, John Wiley and Sons,
New York, USA, 1997.