A chemical kinetics model to explain the abrasive size effect on chemical mechanical polishing

www.elsevier.com/locate/tsf

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: [email protected] (P. Hsun Chen)8

[email protected] (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 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



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 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


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


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


(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.


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.

A chemical kinetics model to explain the abrasive size effect on chemical mechanical polishing

Documents

Transcript of A chemical kinetics model to explain the abrasive size effect on chemical mechanical polishing