International Journal of Machine Tools & Manufacture 42 (2002) 979–984

A material removal model for polishing glass–ceramic andaluminum magnesium storage disks

Chih-Cheng Wang, Shih-Chieh Lin∗, Hong HochenDepartment of Power Mechanical Engineering, National Tsing-Hua University, Hsin-Chu, Taiwan 300, R.O.C.

Received 7 September 2001; received in revised form 18 December 2001; accepted 3 January 2002

Abstract

In this paper, a model is proposed to more closely describe the relationships between polishing parameters and the materialremoval rate for the commonly used storage disks in PC. Experiments were conducted to verify this model. It is shown that theproposed model predicts the material removal rate more accurately than existing models. The proposed model is expected to applyto different materials polished by similar processes. The FEM analysis of the applied polishing pressure well explained the currentempirical results. 2002 Elsevier Science Ltd. All rights reserved.

Keywords:Polishing; Hard disk; Roughness; Waviness; Flatness

1. Introduction

The magnetic rigid disk drive is one of the most popu-lar data-storage systems used today. In disk drives, elec-troless NiP plated Al–Mg alloys (NiP/Al) and glass–cer-amic are the major substrate materials used. The surfacesof a substrate are generally polished to reach surface fin-ish and flatness requirements.

Chemical–mechanical polishing (CMP) is one of thepreferred methods that are currently in use for both plan-arizing and smoothing surfaces. It is crucial to developa model of the CMP process to allow a full exploitationof the power of this technique. However, the physicalmechanisms that control the CMP process are still notfully understood.

During a CMP process, surface is polished to form aplanarization topology based on chemical reaction andmechanical shearing force. Sivaram et al. [1] stated thatmaterial removal rate followed the Preston equation [2]and was proportional to the rate which work was doneon each unit area of the surface to be polished. Cook [3]concluded that the chemical removal rate was functionof the size of polishing particles and the solution PH.Warnock [4] and Runnels and co-workers [5–7]

∗ Corresponding author. Tel.:+886-3-5719034; fax: +886-3-5722840.

0890-6955/02/$ - see front matter 2002 Elsevier Science Ltd. All rights reserved.PII: S0890-6955 (02)00004-4

developed models to predict polishing rates of arrays offeatures with different size and pattern density. Bajaj [8]studied effects of polishing pad material properties onthe CMP process. Wang et al. [9] studied the stress dis-tribution across a wafer. Tseng et al. [10] studied theeffects of as-deposited stress, externally applied stress,hardness, and modulus of various dielectric films onchemical–mechanical polishing removal and post-CMPcleaning process. Liu et al. [11] developed a model basedon a statistical method and elastic theory to describe thewear mechanism of the silicon wafer surface duringchemical–mechanical polishing. Cook [3] proposed adetailed model for the polishing process. Bramono andRacz [12] used computational dynamics code to simulatethe flow of slurry in the process. Wu [13] and Tsai [14]also developed models to predict the material removalrate of the process. It can be seen from the abovedescription that many models have been proposed todescribe material removal mechanisms in the process.Some models attempt to predict the material removalrate of the process. However, there are still differencesbetween the experimental results and the predictedresults.

In this paper, a model to describe the relationshipmore closely between the material removal rate andmajor polishing parameters is proposed. Experimentswere then conducted to verify this model. It was knownthat the material removal rate was highly dependent on

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the pressure applied. Therefore, it was required to knowthe distribution of pressure applied on the work. In thisstudy, the distribution of pressure applied on workpiecewas studied by using the finite element method. Finally,conclusions are made based on these results.

2. Model

Preston [2] conducted experiments and established thewell accepted equation:

RR� KP × P × V,

where RRis the material removal rate; P is the polishingpressure applied; V is the relative velocity between thepad and the workpiece; and KP is a constant. Althoughthe above equation is frequently adopted in simulatingor predicting polishing behavior, there were differencesbetween test results and the results predicted using theequation [13, 15].

In this paper, a new model is proposed to predict pol-ishing the behavior more accurately. In the CMP pro-cess, chemical reaction might happen between slurry andthe workpiece, and the top layer would be treated chemi-cally for material removal by the subsequent mechanicalaction. Mori et al. [16] stated that when two solid phasematerials composed of different chemical elements makecontact with each other, many kinds of interactions aregenerated at the interface and when solids are separatedby some mechanical means, atoms on one surface mightmove onto the other surface.

Based on the above concept, the material removal rateshould be dependent on the probability that the solidsmake contact with each other. As a hypothesis it is sug-gested that the contact probability of solid is dependenton the film thickness between the polishing pad and thework. The increase in the relative motion between thepad and the work will also increase the probability ofmaterial removal. Therefore, it was proposed that thematerial removal rate be represented by the followingequation:

Table 1Levels of polishing parameters used in experiments

Polishing machine Micro Line AC 319

Work materials Al–Mg substrate∗ Ceramic–Glass Substrate (Asahi-AH3)Polishing pad Politex DG-Hi Universal LP-66Slurry Fujimi 3471 (Al2O3) Mirek E30 (CeO2)Loading F (kgw) 140 200 60 120 180Flow rate of slurry 600 900 2000(ml/min)Rotational speed (rpm) 16/-20 24/-20 24/-30 36/-30 20/0 30/0 40/0Location of disk Inner Outer Inner Middle OuterPolishing time (min) 6 80

∗ Experiments of Wu [13].

RR�P(h) × V�h�n × V (1)

where RR is the material removal rate; P(h) is the prob-ability that material removal occurs and it was approxi-mated by an exponential function of the film thickness,h; n is a constant and is dependent on other polishingparameters; and V is the relative speed between the pol-ishing pad and the work.

According to Ref. [5], the film thickness h can beexpressed by the following equation:

h � Kh�mVPA(2)

where µ is the viscosity of the slurry; Kh is a constant;A is the area of the polished surface; P is the polishingpressure applied. It was indicated that an increase in theapplied pressure decreased the film thickness. Anincrease in the viscosity of slurry or the relative speedbetween the polishing pad and the work will increasethe film thickness. Eq. (1) can then be rewritten as:

RR�(�V/P)�n × V (3)

or

RRV

�(�VP

)�n (4)

For convenience, we defined RR/V as the removal rateindexand �V/P as the film thickness index.Eq. (4) showsthat the removal rate index is a function of the film thick-ness index.

3. Experiment design and experimental setup

In order to verify the proposed model, a series ofexperiments over a range of polishing conditions wereconducted. These tests were conducted with three levelsof applied pressure, three levels of disk location, andthree levels of rotational speed. The work material usedin the experiments was glass–ceramic substrate. And the

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Fig. 1. The schematic diagram of the disk locations.

polishing pad was a Universal LP-66. The slurry usedwas Mirek E30 (CeO2). Table 1 shows the levels ofthese parameters.

In addition, the experimental results of Wu [13] werealso adopted to verify the proposed model. These testswere conducted with two levels of applied pressure, twolevels of locations of nozzles for slurry, two levels offlow rate of slurry, and two levels of rotational speed.The work material used in the experiments was alumi-num–magnesium substrate. The slurry and polishingpads used were the Politex DG-Hi provided by Rodeland Fujimi 3471, respectively, which were also differentfrom those used in these studies. Levels of these para-meters are also shown in Table 1.

The tests were conducted on the Micro Line AC 319double side polishing machine. Fig. 1 is the schematicdiagram of the relative positions of the inner, middle andouter disks. It should be noted that the ring gear wasfixed and the sun gear was held still in these tests. Inother words, polished disks will stay at given locationswithout movement during the process. The removal rateof disks placed at different locations might be differentsince the relative velocity between the disk and the pol-

Table 2Specifications and characteristics of materials used in experiments

Work material Al–Mg substrate∗ Ceramic–Glass substrate

Radius (mm) 95 95Young’s modulus (GPa) 71 73.6Poisson’s ratio 0.33 0.22Polishing pad Politex DG-Hi Universal LP-66Young’s modulus (MPa) 4 6Poisson’s ratio 0.15 0.12Slurry/water 1:4 1:10Viscosity of slurry (Pas) 1.87 × 10-3 4 × 10-3

Particles Al2O3 CeO2

∗ Experiments of Wu [13].

ishing pad varies. The thickness of rigid disk was meas-ured before and after the polishing process at severallocations. The difference between the average thicknessof disk before and after polishing was estimated.

4. Pressure distribution on disk

It was well known that the material removal rate ishighly dependent on the pressure applied during the pro-cess. In order to predict material removal rate more accu-rately than can be achieved by existing models, it isrequired to know the distribution of pressure on the workbeforehand. However, it was difficult to measure thepressure distribution during the process directly. In thisstudy, the finite element method was used to simulatethe process and realize the pressure distribution. A com-mercial software ANSYS was used.

The following assumptions were made for this analy-sis:

1. the loading applied during the process was constant;2. the carrier shown in Fig. 1 could be neglected in the

simulation, since the thickness of carrier is smallerthan that of the workpiece.

Table 2 lists the polishing conditions and parametersused in finite element method. Figs. 2 and 3 show typical

Fig. 2. A typical result for pressure (normal stress) distribution onthe aluminum–magnesium substrate (loading=140 kgw).

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Fig. 3. A typical result for pressure (normal stress) distribution onthe glass–ceramic substrate (loading=60 kgw).

results for pressure distribution on the aluminum–mag-nesium substrate and glass–ceramic substrate, respect-ively. It was found that pressure applied on the innerdisk was higher than that on the middle or inner disk.The average applied pressure on the inner disk is about1.4 times that on the outer disk while that on the middledisk is about 1.15 times that of the outer disk. It is alsoshown that the outer rim of the disk sustained a higherpressure than the middle of the disk. Similar phenomenawere also found in other independent experimentalresults [9] and simulation results [17].

In Wu’s experiments [13], it was found that the aver-age material removed for inner disks was (about 25%)higher than that for outer disks when polishing alumi-num–magnesium substrate. Since the inner pin ring wasfixed in these tests, the disks were fixed at givenlocations during the process. It is also to be noted thatthe relative velocity between the disk and polishing padwas proportional to the distance between the locationexamined and the center of the upper working wheel. Ifthe applied pressure was uniform, the removal rates ofpolished disks were then proportional to the distancebetween the location examined and the center of theupper working wheel. Therefore, the material removedfor the outer disks should be 42% higher than that forthe inner disks. However, it is shown experimentally thatthe material removed for outer disks was 25% smallerthan that of inner disks. Figs. 4 and 5 showed the effectsof disk location on the average and the standard devi-ation of normal stress. It is shown that both the averageand standard deviation of the normal stress on the innerdisk was the highest while it was the smallest on theouter disk. This explains why the material removed forthe outer disks was smaller than that of inner disks whenpolishing the aluminum–magnesium substrate.

5. Results and discussion

For each test, the average relative speed between thepad and substrate was calculated. The average applied

Fig. 4. Effects of disk location on the average pressure applied withdifferent loadings F. (a) Al–Mg substrate. (b) Glass–ceramic substrate.

Fig. 5. Effects of disk location on the standard deviation of pressureapplied with different loadings F. (a) Al–Mg substrate. (b) Glass–cer-amic substrate.

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pressure on each disk was calculated based on the simul-ation results using the finite element method. The aver-age removal rate of each disk was estimated based on thethickness of disk measured before and after the polishingprocess. These data were then used to estimate theremoval rate index and the film thickness index.

Fig. 6 shows the relationship between the removal rateindex, RR /V, and the film thickness index, �V /P. It wasfound that the removal rate decreased as the film thick-ness increased. And the removal rate index was stronglycorrelated with the film thickness index. Based on thesedata, it was found that the n-values in Eq. (4) for thealuminum–magnesium substrate and glass–ceramic sub-strate were 1.48 and 1.1, respectively. And the removalrate model can be expressed as

RRAl-Mg � KAl-MgP0.74V0.26 (5)

RRGlass � KGlassP0.55V0.45 (6)

It is shown that the effect of applied pressure on removalrate was higher when polishing the softer aluminum–magnesium substrate than polishing the glass–ceramicsubstrate. This might be due to the hardness of the alumi-

Fig. 6. Material removal index (RR/V) versus film thickness index(�V /P). (a) Al–Mg substrate. (b) Glass–ceramic substrate.

Fig. 7. Comparison of the measured material removal with those esti-mated from models for Al–Mg substrate.

num–magnesium substrate being much lower than thatof the glass–ceramic substrate, and the effect of appliedpressure on removal rate became more significant whenpolishing the aluminum–magnesium substrate. It is alsoshown that the effect of the relative speed on removalrate was higher when polishing the glass–ceramic sub-strate than polishing the aluminum–magnesium sub-strate. It is believed that the increase in the relative speedbetween the polishing pad and the work increases thechemical activity in the interface of the polishing padand the work. The chemical activity became importantwhen polishing glass–ceramic substrate. Therefore, theeffect of the relative velocity on the removal rate washigher when polishing glass–ceramic substrate.

Figs. 7 and 8 showed the measured removal rate ver-sus those estimated based on the proposed model forboth the aluminum–magnesium substrate and glass–cer-amic substrate, respectively. For comparison, theremoval rate estimated based on other existing modelswere also shown in the figure. These models includedPreston’s equation [2], Tseng’s model [10], Wu’s model[13], and Tsai’s model [14]. It is seen that the proposedmodel can more accurately estimate the removal rate.Table 3 lists the coefficients of determination betweenthe measured and the estimated data. The maximum dif-ferences between these data are also listed in the table.

Fig. 8. Comparison of the measured removal rate with those esti-mated from models for glass–ceramic substrate.

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Table 3Comparison of models for the material removal rates

Proposed model Wu’s model Tseng’s model Tsai’s model Preston’s equation

Al–Mg substrateMaximum error (nm) 633 1331 806 934 1469Average error (nm) 228 524 281 346 541Maximum error (%) 25.05 51.57 31.88 41.93 55.11Average error (%) 8.63 19.91 10.62 12.88 20.49Glass substrateMaximum error (nm/min) 141 251 263 145 351Average error (nm/min) 46 105 75 50 125Maximum error (%) 14.75 33.42 28.15 21.67 44.12Average error (%) 7.05 15.82 11.17 7.79 20.15

As shown in the table the proposed model was superiorto other models in describing the relationship betweenthe material removal rates and polishing parameters. Theaverage error for the proposed model was less than 10%while that for most other models was above 10%.

6. Conclusions

In this paper, a model was proposed to describe therelationships between polishing parameters and thematerial removal rate. The finite element method wasadopted to realize the pressure distribution on the disk.Experiments were also conducted to verify this model.Conclusions were made based on the obtained results:

1. It was shown experimentally that the removal rateindex was a function of the film thickness index.

2. The proposed model was superior to other models indescribing the relationship between the materialremoval rates and polishing parameters.

3. The finite element results showed that the averagenormal stress on the inner disk was the highest whilethat was the smallest on the outer disk. This explainedwhy the material removed for outer disks was smallerthan that of inner disks when polishing aluminum–magnesium substrate with fixed inner pin ring.

Acknowledgements

The authors wish to thank National Science Council,R.O.C. for their financial support (NSC90-2212-E-007-067) and Trace Storage Technology Corporation for pro-viding experimental set-up, specimen and technicalassistance.

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