Material removal regions in chemical mechanical ... · of abrasive weight concentration has been...

IEEE TRANSACTIONS ON SEMICONDUCTOR MANUFACTURING, VOL. 16, NO. 1, FEBRUARY 2003 45

Material Removal Regions in Chemical MechanicalPlanarization for Submicron Integrated Circuit

Fabrication: Coupling Effects of SlurryChemicals, Abrasive Size Distribution,

and Wafer-Pad Contact AreaJianfeng Luo and David A. Dornfeld

Abstract—A material removal rate (MRR) model as a functionof abrasive weight concentration has been proposed for chemicalmechanical planarization/polishing (CMP) by extending a mate-rial removal model developed earlier in 2001 and 2002. With anincrease of the weight concentration of abrasives, three regionsof material removal exist: a chemically dominant and rapid in-creasing region, a mechanically dominant linear region, and a me-chanical dominant saturation region. A detailed model is proposedto explain that the transition from the first to the second region isdue to a transition from a wafer surface covered with a single softmaterial to a surface covered with both soft and hard materials.The slope of the linear region is a function of abrasive size distri-bution, and the saturation removal rate is a function of abrasivesize distribution and wafer-pad contact area. The model can helpto clarify the roles of chemicals, wafer-pad contact area, and abra-sive size distribution in CMP.

Index Terms—Abrasive size distribution, abrasive weight con-centration, bilayer property of passive film, chemical mechanicalplanarization/polishing (CMP), film generation rate, wafer-padcontact area.

I. INTRODUCTION

T HE MATERIAL removal rate (MRR) in the solid–solidcontact mode of chemical mechanical planarization/pol-

ishing (CMP) usually increases linearly with the abrasive weightconcentration. This is observed experimentally [3]–[6], [34].However, this linear increase only holds for a limited range ofabrasive weight concentrations, as shown in Fig. 1 fromto

. Two exceptions exist. First, when there are no or few abra-sives in the slurry, the material removal is usually close to zero[8]–[11]. This has been observed for various wafer materials in-cluding copper [8], aluminum [9], tungsten [10] and silicon [11],and slurry recipes. This material removal, mainly due to thechemical erosion and dissolution, is much smaller than that dueto chemical–mechanical removal with abrasives. This is reason-

Manuscript received February 16, 2002; revised September 18, 2002. Thiswork was supported in part by the National Science Foundation under awardNSF DMI-9813039 and by the University of California SMART program underContract 97-01.

The authors are with the Laboratory for Manufacturing Automation,Department of Mechanical Engineering, University of California at Berkeley,Berkeley, CA 94720-1740 USA (e-mail: [email protected];[email protected]).

Digital Object Identifier 10.1109/TSM.2002.807739

Fig. 1. Three regions of MRR with the increase of abrasive weightconcentration.

able. Otherwise, both high and low features on the wafer surfacewill be removed aggressively as that in the isotropic wet etching,and therefore no “planarization” can be realized. A small in-crease of the abrasive concentration in this region usually leadsto a rapid increase of the material removal; see Fig. 1. The ob-served linear increase, however, is much slower than this rapidincrease and usually does not cross zero at zero weight concen-tration; see Fig. 1. Second, when the concentration of abrasivesis larger than a certain value, say,, the material removal ratewill stop increasing but keep constant (Fig. 1) [3], [6], [7]. Thisphenomenon is called material removal saturation. A qualita-tive explanation of this is that the total contact area betweenthe wafer and pad is occupied by theactiveabrasives. A furtherincrease in concentration cannot increase the number ofactiveabrasives on the contact area. This leads to the material removalsaturation since MRR is supposed to be proportional to theac-tive abrasive number [1], [2].

Therefore, there are two transitions of material removal re-gions with the increase of the abrasive weight concentration.

0894-6507/03$17.00 © 2003 IEEE

46 IEEE TRANSACTIONS ON SEMICONDUCTOR MANUFACTURING, VOL. 16, NO. 1, FEBRUARY 2003

First, a transition from a rapid increase region at small abrasiveconcentrations to a slower linear increase region. The secondis a transition from the linear increase region to the saturationregion at large abrasive concentrations. In this paper, we dis-cuss the extension of the material removal model proposed byLuo and Dornfeld [1] to explain these transitions quantitatively.Three regions of material removal are proposed. First, we have achemically dominant and rapid increasing region, whose rangeis determined by the generation rate and hardness of the sur-face passivation layer. The second is a mechanically dominantlinear region, where material removal increases proportionallywith the weight concentration of abrasives. The material re-moval in both of the above regions increases linearly with abra-sive weight concentrations, although with different slopes. It isproposed that this transition is due to a transition from a wafersurface covered with a single softer material to a surface cov-ered with both softer and harder materials. And, third, we havea mechanically dominant saturation region, where the materialremoval saturates because the contact area is fully occupied bythe abrasives. The range of the first region, slopes of the rapid in-creasing and slower linear increasing region, and the two transi-tion concentrations and the saturation material removal rate areproposed to be functions of the slurry chemicals, abrasive sizedistribution, and wafer-pad contact area. Formulations of mate-rial removal rate as a function of the abrasive weight concen-tration are proposed for the above three regions. Experimentalevidences supporting these regions are presented. The under-standing of the proposed coupling effects of slurry chemicals,abrasive weight concentration, abrasive size distribution, andwafer-pad contact area may help to understand the fundamentalmechanism in CMP and optimize the process in the future.

II. TRANSITION FROM THE FIRST REGION TO THESECOND

REGION: EFFECTS OFBILAYER PROPERTY OF THEPASSIVE FILM

Slurry chemicals play an important role in the materialremoval behavior in the first region and may be attributedto a wear-accelerated corrosion [12] or a combined corro-sion-wear [13] depending on the polished materials, slurrycomposition/environment, and the applied mechanical load.If this understanding is correct, CMP is basically a chemicalprocess, which is enhanced by mechanical elements includingabrasion. Another understanding of the roles of chemicals,however, is based on Kaufman’s model for tungsten CMP [10].Kaufman proposed that a passive film is formed over the wafersurface and this film is continuously formed and removed byslurry abrasives. This model implies that CMP is basicallya mechanical process enhanced by chemical actions, whoseeffects on MRR are attributed to the material and mechanicalproperties of a passive surface layer and its generation rate.This passivation-abrasive removal-repassivation mechanismhas also been applied to explain the metal removal and pla-narization in copper and aluminum CMP [14], [15]. For siliconand silicon oxide CMP, a near surface change was observed[11], [16], [17]. Cook [18] proposed that a surface hydratedsofter layer SiOH is formed under chemical attack forsilica CMP and it is this layer that is removed. Therefore, asimilar mechanism of surface modification, abrasion, and then

Fig. 2. Different layer removed with increase of abrasive weightconcentration/material removal rate: (a) smallMRR < GR of upperlayer (removed material is upper layer), (b)MRR = GR of upper layer (upperlayer is removed as formed), and (c)MRR > GR (part of removed materialsgive the upper softer layer which is removed as formed, and part of removedmaterials give the bottom harder layer).

remodification seems to be at work for silicon and siliconoxide CMP as well. In this paper, we extend Kaufman’s modelto explain that the rapid increase of material removal in theregion of small abrasive weight concentrations is due to abilayer property of the passive films. It is noteworthy thatbased on different slurry chemicals used, both dissolution-typechemistry and passivation-type chemistry may exist in CMP[19], especially in copper CMP. The phenomena that occur inthe dissolution-based CMP may not be able to be explained bythe model proposed here.

Various micrographic and microchemical examinations ofpassive films on many metals and alloys have shown thatthey form as bilayers, consisting of a compact harder barrierlayer underlying a porous, precipitated, hydrated, and softerupper layer [20]; see Fig. 2(a). Recently, X-ray photoelectronspectroscopy (XPS) analysis has demonstrated that in the slurrymodified copper surface a Cu(OH) and CuO bilayer may exist[21]. The formation of the passive layer can be attributed tothe diffusion of the metal cation and oxygen anions throughthe passive films and the generation and annihilation of vacan-cies (chemical reactions) at the metal/bottom film and upperfilm/bottom film interfaces. The growth rate of the bilayeron the metal surface, including the upper and bottom layers,may be either diffusion-controlled when the films are thick orreaction-controlled when the films are thin. This property ofbilayer structure with different microstructures and hardnesshas been observed in near surface modification of the siliconand silica structure as well [16], [17]. Trogolo and Rajan [16]found in silica CMP the existence of a 2-nm surface layer with

LUO AND DORNFELD: MATERIAL REMOVAL REGIONS IN CHEMICAL MECHANICAL PLANARIZATION 47

lower density than the bulk, below which the density increasesto a value greater than the bulk, gradually returning to thebulk density at a depth of 15–20 nm below the silica surface.Although Trogolo and Rajan [16] explain the formation of thebilayer structure from a viewpoint of material science, a similardiffusion and reaction mechanism as that in metal, however,may underlie this phenomenon. The detailed discussion on thedynamical film growth mechanism is beyond the scope of thispaper. Here, a parameter GR is simply introduced to representthe generation/growth rate of the upper and bottom layers. Twohardness parameters and are used to represent thedifferent material properties of the upper and bottom layers,respectively.

Due to the bilayer nature of the metal passive film, two re-gions of materials removal with the increase of abrasive weightconcentrations are proposed as follows. When the weight con-centration is small, the MRR is close to zero as mentioned aboveand probably smaller than the growth rate (GR) of the upperporous layer. This implies that the wafer surface is fully cov-ered with the upper porous softer layer during the polishing, asshown in Fig. 2(a). The material removal rate in this case canbe written as a function of the abrasive size distribution, downpressure, and the hardness of the upper layer based on thematerial removal model developed by Luo and Dornfeld [1], [2].This model is based on the assumptions of a periodic rough-ness of polishing pad, normal distribution of abrasive size, andplastic deformations over the wafer-abrasive and pad-abrasiveinterfaces [1]. The number of activeabrasives and the mate-rial removed by a singleactiveabrasive [1], [2] are included inthe model. It is noteworthy that similar material removal modelshave been proposed by different researchers [31], [35], [36] re-cently after [1]. Considering that theactiveabrasive size is ap-proximately equal to [1], [2], the following simplifiedmaterial removal rate formulation can be obtained:

(1)

where accounts for the number of activeabrasives ( includes the portion of theactiveabrasives repre-sented by a normal distribution density function[1], [2]) and

accounts for the material removed by a singleactiveabrasive. Note that if is approximately con-stant, the portion ofactiveabrasive number represented byis almost independent of abrasive size distribution, which is thecase for the experimental data from [3] to be used in Sections IIIand IV. (Details can be found in [2].) From (1), the slope of thematerial removal as a function of abrasive weight concentrationis inversely proportional to the hardness of the upper film.Therefore, the material removal increases rapidly with abrasiveweight concentration when the upper layer composed of softerhydrated materials is removed.

With the increase of the weight concentrationof abra-sives, the material removal rate increases. At a certain concen-tration (see Fig. 1), the material removal rate willbe equal to the generation rate of the upper softer layer.Then the softer upper layer will be removed as soon as it is gen-erated; see Fig. 2(b). This soft layer is thin and its generation

Fig. 3. The transition from rapid increase region 1 to a slower linear increaseregion.

is expected to be reaction controlled. With a continued increaseof the abrasive weight concentration, the MRR becomes largerthan the generation rate of the upper layer materials. Thus,the upper layer material is generated slower than removed andpart of the harder bottom layer is exposed. Instead of a singleupper layer of materials, a layer of bimaterial composed of boththe upper softer materials and the bottom harder materials [seeFig. 2(c)] will be continuously formed and removed. The ratio ofthe area of softer materials to the harder materials is determinedby the ratio of to . Of all theactiveabra-sives, part of the abrasives with a number proportional to

is removing the softer upper layer with anin situgen-eration rate , while the rest with a number proportionalto is removing the exposed harder bottom layer.Therefore, the material removal rate at concentration larger than

can be written as

(2)

This transition of material removal rate from region 1 to region2 is shown in Fig. 3 schematically. is larger than .Therefore, the linear increase of material removal in region 2is slower.

From the above discussion, the chemicals influence the ma-terial removal in region 2 from two aspects: the generation rateof the upper softer layer and the hardness value of the upper andbottom layers. The addition of oxidation reagents increasing thepassivation or growth rate of the upper soft layer will lead to ahigher portion of soft materials on the wafer surface and, there-fore, a larger material removal rate. That the material removalincreases with the addition of oxidization reagents has beenobserved in experiments for various wafer materials including


(a)

(b)

Fig. 4. The transition from rapid increase region 1 to slower linear increaseregion 2 under: (a) different generation rates but the same hardness of upperhydrated softer film and (b) the same generation rates but different hardness ofupper hydrated softer film.

tungsten [4], [10] and copper [5], [14]. Aluminum can be pas-sivated easily even in DI water and ambient air. Therefore, thegeneration rate saturates easily. This explains why MRRin aluminum CMP does not change much with the oxidizerconcentrations [9]. The increases of oxidizer concentrations donot change the basic micrographic structure of passive layers.This implies that the surface hardness values do not changemuch with concentrations. Therefore, the lines in the second re-gion should move up and down parallel with each other onlywith changes of the oxidizer concentration. This idea is shownschematically in Fig. 4(a). Changing the type of oxidizers, how-ever, may lead to a hardness change. If the metal oxide is toohard, MRR may be small even with a high generation rate. Thisidea is shown schematically in Fig. 4(b). Therefore, a proper ox-idizer should satisfy two conditions simultaneously: first, highoxidization rate and, second, soft enough metal oxide after thepassivation. The hydration of the passive film might be indis-pensable in consideration of the softness requirement.

However, it is noteworthy that in the first region the chem-icals contribute to the material removal through the hardnessvalue of the upper softer layer only. The passivation rate doesnot contribute to the material removal rate. This implies that un-like that in the second region, increasing oxidizer concentrationwill not yield an increase of material removal rate in the firstregion. Gutmann [37] noted that in copper CMP when the ma-terial removal rate is large, an increase of oxidizer concentra-tion yields an apparent increase of material removal rate. When

the material removal is small, however, it does not cause an ap-parent change. An explanation of this is that in the first case, thematerial removal is in the second region, where the passivationrate contributes to the overall material removal. In the secondcase, however, the material removal is in the first region, wherethe passivation rate does not contribute to the overall materialremoval. This idea can be seen schematically from Fig. 4(a) aswell.

Better understanding of the generation mechanism of the pas-sive films is needed to evaluate the transition concentration andgrowth rate exactly. An exact evaluation of this value is beyondthe scope of this paper. Here, we propose only that the value oftransition concentration is independent of the abrasive sizedistribution and down pressure applied on the wafer top sur-face. This could be based on the following understanding on thecoupling effects of mechanical and chemical elements. At thetransition concentration , the material removal rate is equalto the generation rate of the upper porous film, therefore, from(1)

(3)

The abrasives are indented into the upper layer under force; see Fig. 2. (The details on the indentation model can be

found in [1] and [2].) The polishing consists of the passageof abrasive particles under load across the wafer surface.The area of the leading edge between a single abrasive andthe surface layer is equal to the radius of the projectedindentation circle times the indentation depth (Fig. 2 and[1]) and is proportional to [1]. The activeabrasive number is . Therefore, the total areaof leading edge at transition concentration is proportionalto . Cook [18] proposed that thetemperature at the leading edge is much higher due to thebonding breakage. Therefore, the chemical reactions there aremore intensive than those on the other areas. Furthermore, dueto the high-energy state of the stressed metal, a higher intensityof broken bonds in the neighborhood of the leading edge maylower the energy barrier to oxidation [22]. Therefore, it isreasonable to assume that the generation rate of the upper layeris proportional to this direct contact-leading edge area. Thisrelationship can be simply written as

(4)

This function decouples the effects of the mechanical elementsincluding down pressure and abrasive size distribution fromother elements. The function is introduced here toaccount for the effects of other chemical and mechanical factors

such as the applied potential, chemical concentration, iondiffusion constant, slurry PH values, and temperatures. The

may influence the generation rate through other elementsexcept the leading edge area and this is accounted for in func-tion as well. An assumption in (4) is that the abrasivesize distribution and down pressure affect the generation ratethrough the leading edge area only, or is independentof abrasive size distribution and down pressure.


Fig. 5. The transition from rapid increase region 1 to slower linear increaseregion 2 under different abrasive size distribution.

Substitution of (3) into (4) yields

independent of abrasive size distribution and down pressuretransition concentration independent of abrasivesize distribution and down pressure.

For convenience, (2) can be written in another form asfollows:

(5)

where is the intercept of the MRR line with the concentra-tion axis (Fig. 3), representing the effects of passivation rate ofthe upper softer layer on the overall material removal rate. Itis easily determined that from Fig. 3.Since is independent of the abrasive size distribution anddown pressure, should be independent of the abrasive sizedistribution and down pressure as well. The prediction of thetransition under different abrasive size distribution based on thismodel is shown in Fig. 5. Separating the portion of active abra-sive from , we obtain the material removal as a function ofslurry chemicals, abrasive size distribution, and down pressure

(6)

where is a constant accounting for factors including relativevelocity , and other consumable parameters,the probabilitydensity functions and a function of the pad hardness and padtopography [1], [2]. and in (6) are taking the place of

and in (1). can be taken as aneffectiveconcentra-tion, and the wafer surface can be taken as covered with a singlematerial with aneffectivehardness . The independence of

on the down pressure guarantees the validity of the previous

model [1] on the down pressure dependency of material removalrate in the range of , which can be written as

(7a)

where

(7b)

is dependent on the chemicals, abrasives and pad, and

(7c)

is dependent on the pad topography , pad materials ,and abrasive size distribution but independent of chemicals.Note that reflects the sensitivity of material removal onthe pressure distribution and can be used to optimize thenonuniformity from the viewpoint of consumable effects [23].

In summary, the first transition is due to a transition from a re-gion where a single softer material is removed to a region wheresofter and harder materials are removed simultaneously. Thistransition may not be a function only of the abrasive weight con-centration. Based on the same reasoning, it may be a function ofother mechanical elements such as down pressure and velocity.At small down pressures and velocities, the material removalincrease may be much faster since the material removed is thesofter upper layer. This is supported by experimental data fromOuma [24].

III. T RANSITION FROM THE SECOND TO THETHIRD REGION:EFFECTS OFABRASIVE SIZE DISTRIBUTION

AND WAFER-PAD CONTACT AREA

The second transition is the transition of the material removalrate from the linear slower increase region 2 to a saturation re-gion 3. It is proposed that this transition is because the con-tact area between wafer and pad is totally occupied byactiveabrasives.

Before the material removal saturates, the material removalformulation as a function of abrasive size distribution in region2 was developed in last section; see (5). The value of

is proportional to the number of abra-sives on the contact area. When the weight concentration issmall, most of the contact is direct contact between the waferand pad asperities. The contact areais dependent on the downpressure, pad material, and pad topography but independent ofthe abrasive geometry and abrasive size [1]. When the area istotally occupied by abrasives, however, the abrasives behave asan interfacial layer between the wafer and pad asperities. In thiscase, the pad asperities are considered to have a highereffectiveYoung’s modulus and larger radius. With larger abrasives, theeffectiveYoung’s modulus of the pad is larger. This changes thecontact area . When saturation occurs, this contact area willbe totally occupied byactiveabrasives and therefore the number

of abrasives will not increase with concentration any more.At the material removal saturation, the relationship between

the contact area and the abrasive size distribution can be esti-mated as follows. As shown in Fig. 6, the abrasives, which areclosely packed together, are taken as an interfacial layer between


Fig. 6. Schematic of wafer-abrasive-pad contact in the situation of materialremoval saturation: (a) before down pressure applied to the wafer and (b) afterdown pressure applied to the wafer.

the wafer and pad asperities with effective Young’s modulusand thickness , which is theactiveabrasive size and ap-proximately equal to . The pad asperities are assumedto have a spherical tip with radius and Young’s modulus ,as used in [1]. The pad asperity and the interfacial layer are mod-eled as two springs in series, so the effective Young’s modulusof the pad asperity , considering the interfacial abrasive layer,can be approximated as

(8)

Since not all of the interfacial space between the dashed curvein Fig. 6(b) and the pad asperity is occupied by abrasives, the ef-fective Young’s modulus of the interfacial layer of abrasivesis much smaller than the real Young’s modulusof the abra-sive materials. This can be estimated aswhere is the real contact area between the abrasives andthe wafer and the contact area occupied by the abrasives,as shown in Fig. 6(b). The is equal to the number ofac-tive abrasives times the projected area of the indentation of asingle abrasive into the wafer. is equal to the number of abra-sives times the area occupied by a single abrasive. Therefore,the ratio of and can be estimated asbased on (4) in [1], where is the contact pressure and theeffectivewafer hardness. Therefore, . Sincethe contact pressure (around 10 Pa[1]) is much smaller thanthe wafer hardness (around 10Pa for tungsten and 10 Pafor silicon oxide and silicon [26]), the effective is much

smaller than the real . For alumina abrasives, the realis around 500 GPa [26]. Therefore, the effective is around

GPa GPa.The effective radius of the asperity considering the inter-

facial abrasive layer is ; see Fig. 6. Based on contactmechanics ([25], [1, Eq. (2)]), an approximate relationship be-tween the abrasive size and the contact area underdown pressure can be obtained as

(9)

where is a constant related to the pad topog-raphy, pad material, and abrasive material. Polymers used hereusually have Young’s modulus around 1 GPa [26]. The value of

has been estimated earlier as 0.05–0.5 GPa. The radiusofthe pad asperity should be around 10–100m. Therefore,can be estimated to be around 0.02–2m .

Once the contact area is known, the relationship between thecontact pressure and theactiveabrasive size can beestimated as

(10)

The force applied on a singleactiveabrasive is

(11)

It is noteworthy that the contact area at saturation increases withthe abrasive size while the contact pressure decreases with theabrasive size.

From [1, Eq. (11)]

where is theeffectivehardness of the wafer and the rel-ative velocity of the wafer, and (10), the material removed by asingle active abrasive in the situation of saturation, satisfies

(12)

The abrasive size dependence of material removed by a singleabrasive in the situation of saturation is different from thatwithout saturation. This is because the contact pressure andcontact area are dependent on theactiveabrasive size.

The number of activeabrasives in the situation of satura-tion is

(13)

Therefore, the material removal rate at saturation shouldsatisfy

(14a)The saturation material removal rate decreases with the increaseof the abrasive size. It is noted that in (8) may be approxi-mately equal to when is much larger than . Fol-


(a)

(b)

Fig. 7. Material removal rate of tungsten CMP as a function of oxidizerconcentration and: (a) silica and (b) alumina abrasive concentration.

lowing similar steps as above by substituting andinto (9), a simplified relationship between

and the active abrasive size can be obtained as

(14b)Based on the above discussions, the MRR can be written as a

function of abrasive size distribution and concentration

(15)

when , which is a function of weight concentration and

(16)

when , which is independent of weight concentration.If the slope of the linear region is, which satisfies

(17)

as shown in (15), the relationship betweenand abrasive sizecan be written as

(18)

In summary, when , the contact area is in-dependent of the abrasive size. A linear relationship betweenthe concentration and the material removal rate exists. When

, the contact area is dependent on theactiveabrasivesize. The material removal saturates since the contact area hasbeen fully occupied by the abrasives. It is noteworthy that thissecond transition of material removal regions was also modeledby Fu.et al.[31] and Paul [32], [33] using different approaches.

IV. EXPERIMENTAL VERIFICATION

A. Two Transitions

Fig. 7 shows tungsten (W) CMP MRR experimental resultsby Jairathet al. [4]. They proposed that the passivation/oxida-tion of the tungsten surface occurs as: WOx WOOx , where Ox is the oxidant used in the slurry. It is proposed inour model that this passive film is composed of two layers, one,a hydrated softer layer, the other, a compact harder layer. Bothsilica and alumina abrasives are used for the polishing experi-ments. The abrasives and oxidizer concentrations are changedfrom 1% to 8% and 1 to 5 . It is seen that the material re-moval increases proportionally with the abrasive weight concen-trations. Higher oxidizer concentration yields higher materialremoval rate. This is due to the higher growth rate of the uppersofter layers. The hardness value of the bottom layer WO,however, may not change since the micrographic structure doesnot change. Therefore, for different oxidizer concentrations, theslopes of material removal in Fig. 7(a) and (b) remain constant.This agrees with the model prediction in Fig. 4. Jairath [4] didnot measure the material removal rate in the absence of abra-sives, however, experimental data from other sources [10] showsthat it is minimal. This is also a requirement for industry-stan-dard slurries to avoid isotropic etching. Therefore, the increaseof material removal in the first region must be much more rapidthan that in the second region. The dashed line in Fig. 7(a) repre-sents a conservative estimation of the material removal increasein the first region. Based on this estimation, the hardness ratio ofthe bottom layer to the upper layer should be at least 5.4. Moreexperimental data in the first region in the future will be helpful.It is noted that the increase of material removal in the second re-gion is more rapid for alumina abrasives than that for silica abra-sives. This indicates that the effect of the abrasive morphologycannot be neglected. A more detailed model to account for thiseffect, and probably the chemical durability of the abrasives, canbe developed in the future. This transition of material removalregions has been observed in copper and tantalum CMP [34] as


Fig. 8. Material removal rate of copper and tantalum CMP as a function ofalumina abrasive concentration (from [34]).

well, as shown in Fig. 8. Note that the material removal in theabsence of abrasives is almost zero.

Jairathet al. [4] did not change the abrasive size distribution.Therefore, their experimental results are not sufficient to verifythe proposed material removal formulation as a couplingfunction of abrasive size distribution, slurry chemicals, andwafer-pad contact area. Bielmannet al. [3] did tungsten CMPexperiments using five different distributions of abrasive sizesand slurry chemicals including 0.1 M KFe(CN) , the sameoxidizer as that used by Kaufman [10], and nitric acidHNO ,a chemical to adjust the slurry PH value. Table I lists theaverage sizes and the standard deviations of the five kinds ofabrasives [3]. The abrasive weight concentrations are changedfrom 2% to 15%. The material removal rate as a function ofabrasive concentration is shown schematically in Fig. 9.

First, it can be seen that there is a transition from the first re-gion to the second region, as in Jairth’s experiments. The linearincrease of material removal rate with the abrasive weight con-centration does not cross zero at zero concentration. Dashedlines in Fig. 9 are used to approximate the first regions. Thematerial removal increases in the second region are not parallelto each other as in Fig. 7. This is because the slopes are a func-tion of the abrasive size distribution; see (5). The slopeis thesmallest for abrasive size 2 m, increasing to largervalues with the decrease of the abrasive sizes. Fig. 10 shows thegood correlation between the slopesfrom experimental resultsand those from model predictions. In Section II, it was proposedthat the transition concentration is independent of the abra-sive size distribution. This is demonstrated by the independenceof the value of , the intersect of the MRR lines in region 2 withthe concentration axis, on the abrasive size distribution. A con-stant value of 10 is obtained by fitting the experimental results.This good correlation of model prediction (see Fig. 5) and ex-perimental results is shown schematically in Fig. 11.

The second transition can be seen from Bielmann’s experi-mental results as well. The material removal saturation occurswhen the concentration is larger than 10% for abrasive sizes

TABLE IMEAN SIZE AND STANDARD DEVIATION OF THE

ABRASIVE SIZE DISTRIBUTIONS USED IN [3]

Fig. 9. Material removal rate as function of weight concentrations under fivedifferent abrasive size distributions (from [3]).

Fig. 10. Experimental slope values versus predictions.

0.29 m, 0.38 m, and 0.60 m, while the linear relationshipholds for abrasive sizes 0.88m and 2 m; see Fig. 9. Basedon (14a), the saturation MRR for an abrasive size of 0.29mshould be larger than that for abrasive size 0.6m. This can beseen from the data in Fig. 9 as well. Based on the model, theratio of saturation MRR for abrasive sizes 0.29m and 0.6 mshould be equal to the ratio of the contact areas


Fig. 11. Prediction of material removal rate as a function of weight concentration for five different abrasive size distributions (usingx = 0:6�m as reference).

for these two abrasive sizes; see Fig. 9. Theactiveabra-sive size for and 0.6 m can be obtainedapproximately as 0.495 and 1.22m, respectively. Using (14a),

is obtained as 3m . In the earlier section, is estimatedto be 0.02–2. Considering the estimation and experimental er-rors, the fitted value m is reasonable. Using (14b)with the assumption that , the fitted asperity tip radius

is equal to 3 m. This range of value is quite reasonable.Moreover, it is noted that the material removal saturates earlierfor smaller abrasives. This agrees with (18), which indicates thatthe saturation concentration is smaller when abrasive sizes aresmaller.

Substituting m into (16), we can predict theratio of the saturation for and 0.38 m as1.077, indicating that they are close to each other. This corre-lates with the experimental results in Fig. 9. Using (18), the sat-uration concentrations, , for and mcan be calculated. The predicted slopes in the linear region are41.573, 39.03, 5 and 28.614, respectively, for the above threeabrasive sizes. The value ofis equal to 10. The ,

, and nm/min. So the values of arepredicted as 8.23%, 8.16%, and 11.73%, respectively.

Based on the above discussion, the saturation material re-moval rate and saturation concentration for and2 m can be approximately estimated. Using (16), the ratio ofsaturation material removal rate for abrasive size and0.88 m can be obtained as 1.11. Similarly, the ratio for abra-sive size and 2 m is approximately 1.5. Therefore,the saturation MRRs for and 2 m are predictedas 560 nm/min and 416 nm/min, respectively. Using (18) andthe slope data, the saturation concentration for and2 m can be predicted as 21.9% and 23.5%, respectively. How-ever, more experimental data is needed to verify this.

Fig. 12. Model prediction versus experimental data for silicon oxide CMPusing three kinds of abrasives.

In summary, using the material removal curve atm as a reference, the material removal as a function of con-

centration for other abrasive sizes can be predicted and these areplotted schematically in Fig. 11.

B. Coupling Effects of Abrasive Sizes, Polishing Pad, andChemicals on Down Pressure Dependency of MRR

Most of the time CMP works in the second region. It is worthyto see experimental results supporting the down pressure depen-dence of MRR predicted by (7a). This can be seen from the fol-lowing three aspects: 1) the correlation between (7a) and the


(a)

(b)

Fig. 13. Model prediction versus experimental data for silicon oxide CMPusing different abrasives and pads.

experimental down pressure dependence; 2) the dependence ofin (7a) on polishing pads and abrasives, as indicated by (7c);

and 3) the independence of on slurry chemicals. Jairathetal. [4] did silica CMP experiments using three different abra-sives, while other parameters including slurry chemicals werekept the same. Fig. 12 shows the good correlation between themodel predictions and Jairath’s experimental results. The valueof changes apparently with the abrasives. The down pressuredependence of material removal using two different polishingpads (one grooved IC1000 pad, and the other perforated IC1000pad) and two different slurry abrasives (one colloidal abrasives,and the other fumed abrasives) has been investigated by Clarket al. [27]. Again, the model prediction correlates with the ex-perimental results; see Fig. 13(a) and (b). It is also found that

changes with the polishing pads and abrasives. This is

Fig. 14. Model prediction versus experimental data for copper CMP usingdifferent passivation chemicals.

reasonable considering that is a function of abrasive sizedistribution, pad materials, and pad topography. It is found inFig. 13(a) that when using colloidal abrasives, the ratio offor the two different polishing pads is 2. This ratio does notchange when using the same two polishing pads for fumed abra-sives, Fig. 13(b). This requires that was a product of ,a parameter related to pad topography and pad material, and

, the abrasive size distribution, as described by(7c). Passivation dominant copper CMP was done by Ramarajanet al.[28] using DI water and different chemicals. It is seen fromFig. 14 that the model correlates with the experimental resultsquite well. All do not change with the slurry chemi-cals, agreeing with the conclusion that is independent of thechemicals. Note that when compared with experimental data,the values of model parameters used include the proportionalconstants ; see (7b). For simplicity, they are not put in thefigures. The readers are referred to [1] to see what consumableparameters are included in and how to obtain them.

From the experimental data, it is seen that the pressure de-pendency of material removal can be approximated by a linearrelationship

where is the intercept of the linear line with the MRRaxis and , its slope. This is the famous experimental Pre-ston’s equation. Based on the model, the and Preston’scoefficient are functions of consumable parametersand

, in (7b) and (7c). A change of the and implies achange of the consumable parameters.


Fig. 15. Down pressure dependency of material removal rate under differentslurry temperatures.

Moreover, a possible transition of down pressure dependencyfrom region 1

(19)

to region 2

(20)

is supported by experimental results from Liet al. [29]. Theymeasured the down pressure dependency of material removalrate under three different slurry temperatures. When the tem-perature is small, the generation is small. For all of thedown pressures in the range of the experiment, the material re-moval occurs in the second region. One single (19) can be usedto fit the experimental data, as shown in Fig. 15 by line 5. Withthe increase of the slurry temperature, the generation rateincreases. When the down pressure is small, the material re-moval is smaller than the generation rate , and thereforethe material removal occurs in the first region, where the softerupper layer with hardness is removed. When the materialremoval is larger than the generation rate, the material removaloccurs in the second region, where the bottom harder and uppersofter layers are removed simultaneously. Therefore, (19) and(20) have to be used to fit the experimental data in the lowerdown pressure region and higher down pressure region respec-tively, as shown by lines 1–3 and lines 2–4 in Fig. 15.

V. CONCLUSION

A material removal rate model as a function of the abrasiveweight concentration has been developed for CMP by extendingan MRR model developed earlier [1], [2]. With an increase ofthe abrasive weight concentrations, three regions of material re-moval exist: first, a chemically dominant and rapidly increasingregion, whose range is determined by the generation rate and

hardness of the surface passivation layer, second, a mechani-cally dominant linear region, where the material removal is pro-portional to the weight concentration, and third, a mechanicaldominant saturation region, where the material removal satu-rates because the total contact area is fully occupied by the abra-sives. The passive layer of the wafer surface is proposed to bea bilayer structure. A detailed model is proposed to explain thatthe transition from the first to the second region is due to a tran-sition from a wafer surface covered with a single soft material toa surface covered with both soft and hard materials. The chemi-cals contribute to the material removal through the generationrate of the upper softer layer of the passive films. The slopeof the linear region is a function of abrasive size distribution,and the saturation removal rate is a function of abrasive sizedistribution and wafer-pad contact area. These model predic-tions and relationships are verified by experimental results. Themodel can help to clarify the roles of chemicals, wafer-pad con-tact area, and abrasive size distribution in CMP. An integratedCMP model [30] considering the proposed roles and interac-tions of above factors may be developed in the future.

ACKNOWLEDGMENT

The authors would like to thank Prof. R. Gutmann in the De-partment of Electrical Engineering at R.P.I, S. Aksu in the De-partment of Material Science, R. Chang in the Department ofElectrical Engineering, and Z. Mao in the Laboratory for Man-ufacturing Automation at the University of California, Berkeley,for useful discussions. The authors also appreciate the detailedhelpful comments of the reviewers.

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Jianfeng Luo received dual B.S. degrees in both me-chanical engineering and electrical engineering fromTsinghua Univeristy, Beijing, China, in July 1997. Hereceived the M.S. degree in mechanical engineeringfrom the University of Cincinnati, OH, in September,1998 in the area of computational mechanics. He iscurrently working toward the Ph.D. degree from theUniversity of California, Berkeley, in the area of pre-cision manufacturing.

His research interests include process developmentand optimization for semiconductor manufacturing,

precision manufacturing, mechanical modeling, and computational mechanics.

David A. Dornfeld received the B.S., M.S., andPh.D. degrees, all in mechanical engineering, fromthe University of Wisconsin, Madison, in the area ofproduction engineering.

He joined the faculty of the University of Cal-ifornia, Berkeley, in the Mechanical EngineeringDepartment in 1977 and is presently the Will C.Hall Family Professor of Engineering. He is apast-Director of the Engineering System ResearchCenter in the College of Engineering. In 1982 and1992, he was Directeur de Recherche Associe, Ecole

Nationale Superieure des Mines de Paris, Paris, France, and Invited Professorat Ecole Nationale Superieure d’Arts et Metiers-ENSAM, Paris, respectively.

Dr. Dornfeld is a Fellow and an active member of the American Societyof Mechanical Engineers (ASME), contributing to the technical programs andjournals of the society. He is the past Technical Editor of theTrans. ASME,Journal of Engineering for Industry. He was the recipient of the ASME BlackallMachine Tool and Gage Award in 1986. He is a Fellow and past-Director of theSociety of Manufacturing Engineers (SME) and a member of the Japan Societyof Precision Engineering (JSPE), American Society of Precision Engineering(ASPE), and the U.S. Acoustic Emission Working Group (AEWG). He is thepast-President of the Board of Directors and a member of the Scientific Com-mittee, North American Manufacturing Research Institute (NAMRI/SME). Heis an Active Member of the CIRP (International Institute for Production Engi-neering Research) where he served as Co-Chair of the Working Group on ToolCondition Monitoring and is Chair of the Scientific Technical Committee onCutting.

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