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Brittle and Ductile Fracture Mechanics Analysis of SurfaceDamage Caused During CMPTerry A. Ring,a,z Paul Feeney,b David Boldridge,b Jaishankar Kasthurirangan,b

Shoutian Li,b and James A. Dirksenb

aChemical Engineering Department, University of Utah, Salt Lake City, Utah 84112, USAbCabot Microelectronics Corporation, Aurora, Illinois 60504, USA

This work reviews the mechanical properties and fracture mechanics of materials important in the manufacture of multilayerinterconnects on silicon chips in order to understand surface damage caused during chemical mechanical polishing �CMP�. It givesan explanation for chatter marks, surface flaking in interlayer dielectric material, and rolling indenter and plastic plow lines incopper on the wafer surface during CMP of silicon chips.© 2007 The Electrochemical Society. �DOI: 10.1149/1.2426877� All rights reserved.

Manuscript submitted September 12, 2006; revised manuscript received October 24, 2006.

Chemical mechanical planarization is also called chemical me-chanical polishing �CMP�. These terms evoke the combination ofchemical and mechanical aspects in the polishing and planarizationof silicon chips. There have been several papers over the years thatdiscussed the chemical dissolution,1,2 of surfaces being polished,and there was less work on the mechanical wear,3-5 of a surfacebeing polished until more recently. There have not been many pa-pers that discuss the mechanical aspects of scratching and surfacedamage in CMP.

CMP is used multiple times during the production of today’ssilicon chips as there are multiple layers of wiring required to con-nect the more than one billion transistors per square centimeter in amodern silicon chip to the outside world. CMP uses a suspension ofabrasive particles as the contacting medium between a polymericpad and the wafer surface. In addition to material-selective removalat the wafer surface, CMP is used to produce flat wafer surfaces thatallow small features to be in focus during photolithography. CMPslurries, if not very carefully produced to eliminate impurity par-ticles, have the propensity to cause surface damage to the wafer.Surface damage can be trivial or it can be catastrophic as when awire line or dielectric layer is cut by a scratch. Surface damageduring CMP is a major concern of chip manufacturers. The reasonsthat this is the concern are �i� there are more and more wiring layersneeded for newer generations of chips, �ii� the layers are thinnerwith each new generation of chips, and �iii� the size of the surfacedamage that causes catastrophic wiring failure is smaller with newgenerations of chips.

With each wiring layer there are several CMP steps needed tocreate that layer. At a minimum there is one copper CMP step andone dielectric CMP step. There may also be a step where the barrierlayer is polished. With each CMP step there is a finite probability,PCu or PD, that surface damage will cause a wiring failure in a die.This probability allows the calculation of a process yield given by

yield = �i

N

�1 − PCu�n�1 − PD�m �1�

where n is the number of copper CMP steps and m is the number ofdielectric steps for the construction of a single layer. The wiringlayer is signified by i in the equation, and N is the number of wiringlayers. Assuming that n = 1, m = 1, and N = 8 for a modern chip,small values of PCu and PD, say 0.01 and 0.001, respectively, canlead to a process yield of 91%, which is not uncommon. This lowyield has led to a reliance on inspection after each step and layerreworking if too many surface flaws are observed. Both inspectionand reworking of the surface increase the cost of chip processingsignificantly. To reach six sigma levels for chip manufacturing withchip failure rates of only 3.4 in 1,000,000, the catastrophic flaw

probability, i.e., PCu and PD in this 8-layer metallization example,must be lowered to 1 in 107, an effectively unattainable flaw prob-ability with present CMP technology.

As we move to smaller line sizes and to more layers of wiringrequiring more CMP steps, CMP surface defects will need to belowered significantly in their depth, area of damage, and number percm2 so that they do not destroy the ever smaller components, wiresand insulating layers. This paper is devoted to the understanding ofsurface defects and the fracture mechanics that causes them. Theonset of surface damage is accompanied by the observation of in-creased concentration of large particles.6 These large particles canbe impurities of slurry production, dried crusts that fall into theslurry during production and use or produced during CMP as weardebris.

Model

In CMP processes, surface damage can take place because CMPuses a slurry of abrasive particles. At the wafer surface there areareas of metal �copper� and areas of dielectric insulating materials�borosilicate glass, silicate glass produced by chemical vapor depo-sition, low-K, a carbon-loaded silicate; and barrier layer materials,e.g., various nitrides and silicides�. There are two general types ofmaterials based upon their mechanical properties: ductile materialsand brittle materials. Metals are the classic examples of ductile ma-terials that can be deformed without failure. Glasses are the classicexamples of brittle materials: they shatter. These properties are con-trasted in the stress-strain curves shown in Fig. 1a and b. In Fig. 1a,we see the stress-strain curve for an annealed sample of polycrys-talline copper. At elongations, �, less than 0.0008 corresponding tothe linear portion at the y axis, there is a linear �elastic� region witha slope given by Young’s modulus for the material. Above the linearregion there is a plastic zone where the slope of the curve decreaseswith increasing elongation up to the tensile strength. At elongationsabove the tensile strength there is a decrease in the stress to the pointof rupture at an elongation of 53%, an enormous amount of stretch-ing before failure. In Fig. 1b we see the stress-strain for borosilicateglass. There is a linear �elastic� region up to an elongation of only0.0012, the point of rupture. Thus, we can see from these two figuresthe differences between ductile and brittle materials that are the twomajor components of the metallization layers of today’s chips.

Fracture mechanics.— There are three surface fracture modesshown in Fig. 2. In Irwin’s notation,7 mode I denotes a symmetricopening, the relative displacement between the corresponding sidesof the opening being normal to the fracture surface, while modes IIand III denote antisymmetric separation through relative tangentialdisplacements, normal and parallel to the crack front, respectively.

The focus of fracture mechanics is on the tip of the crack iden-tified by the end of the fracture lines in Fig. 2: any fracture mode.Much effort is expended to identify the stress intensity at the tip ofthe crack and a parameter traditionally calculated is the stress inten-z E-mail: [email protected]

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sity factor, KI, KII or KIII, where the subscript refers to the mode ofloading. In the following discussion, we will use mode I loadingalmost exclusively for fracture toughness �with cracking� and forscratching and wear. When the stress intensity factor is larger than acritical value, e.g., KI � KIc, the crack will enlarge. Before we pro-ceed to this discussion, we need to explain the formation of thecrack or surface flaw. This is best done with a discussion of anindenter that may be considered a hard impurity particle forced intothe surface of the wafer by a normal force provided by the pad asshown in Fig. 3.

Indentation.— During indentation a normal force is applied to anindenter placed at the surface. The indenter, typically made out of avery hard material, can have different shapes including sharp pointsand rounded spherical surfaces. As the force applied is increased, thesurface under load initially deforms elastically under the load, leav-ing behind an undamaged surface when the load is removed. Elasticdeformation is referred to as Hertzian contact, as Hertz developed ananalytical solution for this type of contact, shown in Fig. 3. Elasticdeformation depends upon the elastic modulus of the material, E. Atable of materials properties is given in the Appendix for commonmaterials encountered in CMP. The elastic modulus can be predictedfrom first principles using molecular modeling if the crystal struc-ture is known for the material. The stress distribution under a spheri-cal indenter is shown in Fig. 3. With a larger force, the load is toohigh and slip planes within the material are activated, giving rise toplastic deformation, which leaves behind surface damage in theshape of the indenter’s profile when the load is removed;8 see Fig. 4�without the semicircular crack�.

The normal load, LN, needed to cause plastic deformation �with-out cracking� is a measure of the materials hardness, H. The hard-ness has several definitions depending upon the shape of the in-denter. If the indenter is a sphere HB = LN/��d * ��, where d is the

diameter of the indentation and � is its depth for Brinnell hardnessand HM = LN/��dM

2 � for Meyer hardness, where dM is the diameterof the dent. If the indenter is a square pyramid, the Vicker’s hardnessis HV = 1.8454LN/a2, where a is the corner-to-corner diagonal dis-tance of the square mark in the surface; see Fig. 5a. If the indenter isan elongated pyramid, the Knoop hardness is HK = 14.2LN/D2,where D is the maximum dimension of the indenter mark in thesurface.

With even larger forces applied to the indenter, the surface frac-tures forms a semicircular or radial cracks into the surface directlyunder the point of the indenter; see Fig. 4 and 5. The radial cracks,of size c �also CR in Fig. 4�, have a half-circle shape under theindenter protruding to a distance c away from the point of contactalong the surface of the material in opposite directions.

Figure 1. �a� Normal stress-strain curvefor copper showing the yield stress thatoccurs after the elastic region, the plasticzone, the tensile strength, and elongationat rupture. The Young’s modulus for cop-per is 110 GPa. Data for this figure takenfrom The Physics of Solids, by R. Turton.�b� Normal stress-strain curve for BSGshowing that there is only a linear �elastic�region up to the tensile strength. TheYoung’s modulus for BSG is 62 GPa.

Figure 2. Surface fracture modes.

Figure 3. Normal stress distribution under a spherical indenter �Ref. 30�.The surface of the indenter is deformed so that it makes contact with the flatsurface. The normal stress is given in the contours as the stress, �/Po, wherePo is the applied pressure acting on the spherical indenter.

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A crack at the surface intensifies any stress, �, placed upon thesample. The stress intensity factor, KI, for a small surface flaw ofsize c is given by

KI = Y��c �2�

where Y�=1.12 � �� is a purely geometric constant. After indenta-tion with very high load, LN, resulting in cracking, the stress inten-sity factor associated with the residual stress field can be written as9

KI =�LN

c3/2 �3�

where LN is the normal load, c is the crack size, and ��=��E/H�1/2� is a constant associated with the material’s properties,the elastic modulus E of the material, the hardness, H, of the mate-rial given in the Appendix , and the indenter shape characterized by��0.016�. The final size of the crack, co, loaded to its criticalpoint, Lc, is determined by the fracture toughness, KIc, of the mate-rial, a material property also given in the Appendix .

KIc =�Lc

co3/2 �4�

When there is an additional stress, �, applied with mode I loading,there will be two contributions to the total stress intensity factor,given by10

KI =�LN

c3/2 + Y�c1/2 �5�

The crack of size, c, will enlarge when KI � KIc.Measuring the crack size associated with this additional load

applied with an indenter allows the fracture toughness, KIc, to bedetermined experimentally. At loadings below the point of crackingand within the zone where only plastic damage occurs on the surfaceallows the hardness of a material to be determined experimentally.Microindenters may be used to characterize the mechanical proper-ties of the different materials used to construct silicon chips whenthese mechanical properties have not been measured elsewhere.

Scratching.— With CMP scratching, a hard object of a givenshape is both forced into the surface and dragged across the surfaceof a material. This is the same geometry as that of an indenter shownin Fig. 5, but an additional lateral force is used to drag the indenteralong the surface of the material. Multiple hard objects simulta-neously being forced into the surface and being dragged across thesurface of a material is referred to as mechanical wear.

The resulting failure can be predicted by various mechanicalwear �or scratching� equations depending upon the assumption ofplastic deformation or brittle fracture; see Fig. 6a and b. For a givenmaterial, the wear rate goes from reasonably low rates for plasticwear to orders of magnitude higher with brittle fracture. The wearrate transition occurs at a threshold normal load given by11

LNc � 2 � 105KIc4 /H3 �6�

where H is the hardness of the surface being damaged and KIc is itsfracture toughness. The plastic and brittle fracture wear rates arediscussed in the next two paragraphs.

Plastic deformation.— The differential volume, dV, of material re-moved per unit length, dx, of the scratch depends upon the load ofthe abrasive point normal to the surface, LN, and the mechanicalproperties of the materials comprising the surface12,13

dV/dx � �LN/H� �7�

where H is the hardness of the surface being damaged. This equationassumes that the abrasive point is harder than the material compris-

Figure 4. Schematic of a semicircular indentation crack of length c underthe action of residual and applied tensile stress, �.

Figure 5. �a� Surface and �b� subsurface structure of a Vicker’s indentationcrack. The radial cracks protrude to the surface and are observed in �a� atfour locations. The lateral cracks are observed in �a� as the gray zone sur-rounding the indenter’s depression. The surface of a copper pattern with �c�rolling indenter surface damage. In the bar equals 10 m.

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ing the surface. The volume removed is plowed into a furrow ontothe material’s surface; see Fig. 6a.

Brittle fracture.— The differential volume, dV, of material removedper unit length, dx, of the scratch depends upon the load of theabrasive point normal to the surface, LN, and the mechanical prop-erties of the materials comprising the surface14

dV/dx � �E/H�4/5K1c−1/2H−5/8LN

9/8 �8�

where E is Young’s modulus of elasticity, H is the hardness, K1c�=2E f� is the fracture toughness, and f is the surface energy forfracture. All of these material properties are for the surface beingdamaged, as this equation assumes that the abrasive point is harderthan the material comprising the surface. The volume removed inthis case consists of the surface furrow as well as large pieces of thesurface material being dislodged from the surface out to the pointwhere the lateral cracks reach the surface; see Fig. 6b. The aboveequations are consistent with experimental measurements forscratching wear and particle erosion within the limits of experimen-tal accuracy15 and can be used to determine �i� the plastic wear rateof the pad during both pad conditioning and CMP, �ii� the mechani-cal wear �plastic wear� rate of the copper surface in CMP, and �iii�the mechanical wear �brittle wear� rate of the ILD surface in CMP.These mechanical types of wear are not always desirable processesin CMP as they lead to surface defects.

Scratch depth.— To determine the depth distribution of thescratches due to both abrasive and impurity particles, we considereach of these scratching particles to be attached to the tip of anasperity or, if larger than an asperity, to be pressed into the pad.Because we have a distribution of particle sizes for both the abrasiveparticles and the impurity particles, and we have a distribution offorces caused by the height distribution of asperities on which theparticles will reside, this gives a complicated scratch depth distribu-tion. If, in addition, the impurity particles are not spherical but an-gular, we will also have an additional distribution to consider: thedistribution of radii of curvature for the point of the impurity par-ticle in contact with the wafer surface. The depth of the scratch foran indenter of radius, a, depends upon the type of failure takingplace at the wafer surface. Either plastic deformation or brittle frac-ture at the wafer surface can lead to scratching, as shown in Fig. 6aand b. The plastic deformation scratch depth shown in Fig. 5 and 6is given by16

b = �LNE�

H2 1/2

�cot ��1/3 �9�

where LN is the normal load applied to the indenter, E�=��1− �1

2�/E1� + �1 − �22�/E2��−1� is the relative modulus of elasticity �or

relative Young’s modulus� for the materials in contact, 1 and 2, H isthe hardness of the surface of the wafer, material 1, and 2� is theangle between opposite edges of the indenter, material 2. Note thereis load enhancement due to the hardness of the particles at the as-perity tip compared to the polyurethane asperity itself. Its effect isfelt in the E� term as E2 is increased.

The depth of the radial cracks �see Fig. 5b�, gives the scratchdepth for brittle fracture17

c = CR = � r�E�

H1/2� LN

KIc�cot��2/3 2/3

�10�

where KIc is the fracture toughness of the surface of the wafer,material 1, and r is a dimensionless constant with the value 0.037,18

or 0.016.19

There is a transition between plastic and brittle fracture scratch-ing that takes place as the load is increased. The critical load atwhich this transition takes place is given by20 Eq. 6. Therefore,when the load on an impurity particle is less than LNc, plastic defor-mation will take place. When the load on an impurity particle isgreater than LNc, brittle fracture will take place. Brittle fracture is byfar the most destructive to the wafer surface as the lateral and radialcracks penetrate more deeply than the plastic deformation damage.

The impurity particle is forced by one �or more� of the pad as-perities to be in contact with the wafer surface. There is a distribu-tion of pad asperities onto which the impurity particles can be at-tached and still be in contact with the wafer. Depending upon thelength of the pad asperity that the impurity particle is attached to andthe size of the impurity particle, the load, L, acting on the impurityparticle-wafer contact point can be determined. Greenwood andWilliamson,21,22 have used exponential distribution functions to de-scribe the rough surfaces. The contact area, Acon, and load, L, overthe wafer is obtained by integration of the asperity height from thedistance between the wafer and the plane of reference in the pad, �to infinity given below. An asperity will contact the wafer if itslength, z, is greater than �

Acon = �asperitiesAwafer��

��0

�

��z − ��g��g�z�d�dz �11�

LN = �asperitiesAwafer��

��0

�4

3E��z − d�3/2g��g�z�d� �12�

In the above equations, Awafer is the surface area of the wafer as-suming a flat surface, g�x� is the distribution function for the asper-ity height, z, or the radius of curvature of the asperity, �, and E’ isthe effective Young’s modulus defined below. The applied pressureis LN/Awafer and the average contact pressure is LN/Acon.

Equation 11 and 12 can be used to predict the size distribution ofsurface damage produced during CMP. In this analysis, the Green-wood et al. exponential distribution of pad asperities was character-ized by the mean and standard deviation of the length of the asperi-ties, and an area density of asperities with all asperities assumed tohave the same radius of curvature at their tips. The pad asperityparameters used in this analysis were those measured by Yu et al.23

for a conditioned pad. The asperities press the impurity particles intothe wafer surface, creating a normal load that allows the depth of thesurface damage to be predicted using Eq. 10 for a brittle materiallike the interlayer dielectric �ILD� and Eq. 6 for a ductile materiallike copper. Putting this all together, we find that the size distribu-tion of scratches produced by the impurity particles is given in Fig.7. Here, we see that the deepest scratches are formed by the largestimpurity particles and the population of scratches decreases as thescratch depth increases for a given size of impurity particles. Brittle

Figure 6. �a� and �b�, Schematic of plastic deformation �left panel, showingerosion debris with material plowed up on the wafer surface� and brittlefracture �right panel, showing lateral cracks which will flake off if theyprotrude to the wafer surface�. In �a� and �b� micrographs, the bar is 1 m.


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material does not have a plastic zone where plastic deformationscratching can take place, so the ILD curves are only for brittlefracture surface damage. Because copper is a malleable material itdeforms plastically, so these copper curves are only for plastic de-formation surface damage. Combining the analysis shown in Fig. 7with knowledge of the number and size distribution of impurityparticles in a log-normal size distribution of particles, the scratchesproduced by this distribution of impurity particles can easily becalculated by simply integrating over the impurity particle size dis-tribution. The scratch population produced by the single impurityparticle of a particular size is shown in Fig. 7.

Size distribution of scratch debris.— Another important aspectof scratching is the size distribution of debris material produced. InCMP these particles can be a new generation of impurity particlesleading to enhanced scratching. We can determine this by consider-ing the material flaked off the wafer surface due to brittle fracturedamage; see Fig. 8 and 9.

The material flaked from the surface by scratching has a thick-ness corresponding to the depth of the plastic layer, b, defined byEq. 9. The other dimension is related to the lateral crack length, CL,defined by24

CL = 0.096�E/H�2/5Kc−1/2H−1/81 − ��oKc

4/H3�/�LN��1/4�1/2LN5/8

�13�

where �o is an order 1 dimensionless constant. Ideally, the shape ofthe flake is considered a wedge of a circle with the radius of thecircle being CL. Because the abrasive particles will have differentnormal loads and different point shapes �considering impurity par-ticles� the debris particle size distribution will be broad. However,the debris particle size distribution can be predicted if the distribu-

tion of normal loads is known �assuming that the indenter shapes arespherical�. One important point is that the size of the debris due tobrittle fracture scratching is larger than the indenter tip causing thescratching, so that brittle fracture scratching produces new impurityparticles larger than the original indenter that are likely to go on tomake even large scratches, quickly propelling the number and sizeof surface defects to high levels.

Experimental observations of surface damage and comparisonswith predictions.— The surface of the wafer during the fabricationof any of the multiple interconnection layers has areas of metal andareas of dielectric exposed to the CMP slurry. The thickness of thelayer and the width of a region of metal or dielectric are on the orderof 100 nm in size with modern chips. Surface damage during CMPcan cut through the thickness or the width of these features andcause the components that they represent to fail. For this reason,understanding and controlling surface damage during CMP is im-portant.

V-shaped plastic deformation scratches in copper have been ob-served on wafer surfaces in cases with high levels of scratching; seeFig. 9a-c. The size of the V is on the order of hundreds of nanom-eters in width. Because this is larger than the size of the abrasiveparticles, it is assumed to be due to an impurity particle being nor-mally loaded and dragged along the wafer surface. Furthermore, asthe impurity particle is dragged across the surface the depth of the Vis different when the surface changes from tantalum to copper, andvice versa. A plastic deformation scratch will form in a materialwhen the stress imposed by the indenter is greater than the hardnessof the material. In the case of copper this is 0.874 GPa and in thecase for tantalum this is 0.873 GPa, using data from the . Noting thatthe ILD in Fig. 9a and b is borosilicate glass �BSG�, we know thatthe applied stress that caused the scratch in the copper layer but notin the BSG layer is �0.874 GPa �the hardness of copper and�5 GPa the hardness of BSG�.

If a single impurity particle is large, hard, and has multiple pointsof contact with the wafer surface, it can be loaded with sufficientforce by many pad asperities to cause multiple indenter points to bedragged across the surface simultaneously, giving multiple parallelscratches as shown in Fig. 9d. Each of the indenter points can betreated with the scratching equations presented previously �Eq.9-12�; however, to apply these equations we would need to knowhow the load developed by the pad is distributed over the back ofthe impurity particle and the specific geometry of the hard points ofcontact with the wafer surface. This load redistribution will be spe-cific to each of these very large impurity particles. This makes asimple analysis of the resulting scratching difficult. Another possibleexplanation of the multiple parallel scratches shown in Fig. 9d isthat a series of pores, similar in size, has been produced in thedeposited metal layer possibly associated with previous scratches atthe underlying layer surface. During CMP these pores are uncov-ered, leaving them open after a certain amount of removal.

Other types of copper plastic surface damage are shown in Fig.9e and f, where a random pattern of an irregular particle rollingacross the copper surface is shown. In Fig. 9e, the particle makes

Figure 7. Size distribution of scratches produced in �A� ILD and �B� copperby impurity particles of various sizes; solid line�1 m, dotted line�2 m,dashed line�4 m, dot-dash line�8 m. Note load magnification due to thehardness of the impurity particle is not taken into account in this plot.

Figure 8. Elastic-plastic contact damage. Shading represents plastic zone.Extending from the plastic zone in all directions are lateral cracks, whichdelaminate due to stress in the surface, as shown on the right of the figure.


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indentations as the particle rolls but the tips are broken during roll-ing, altering the shape of the indentation marks as it rolls along.Figure 9f shows an example of a plowing-rolling action of an im-purity particle on a copper surface.

Brittle surface damage in the BSG surface is shown in Fig. 9gand h. Here, the brittle fracture lateral cracks are flaked away fromthe surface, leaving behind an irregular surface. The pieces missingin the surface give rise to irregular flakes of BSG in the slurry,impurity particles that can go on to cause more damage on the wafersurface. In addition, there are repeated C patterns where there wasno flaking of the surface along the trajectory of the scratch. Thesewill be discussed later.

Various examples of CMP surface damage can be addressed byfracture mechanics analysis. An example is the series of indentationsmade by a rolling, large, nonsymmetric impurity particle as seen inFig. 10. Here, the particle rolls along the surface of the pad andwhen its sharp edge comes in contact with the wafer on its longeraxis it is normally loaded by the pad with a significantly larger forcecausing an indentation. With the shorter axis in contact with the

Figure 10. Rolling particle surface damage, where sharp edges associatedwith the elongated axis of the particle act as indenters. Arrow indicates thedirection of rolling particle. Photo from Cabot Microelectronics. Bar�10 m.

Figure 9. Examples of surface damage ofmetalization layers. �a� and �b� are ex-amples of plastic deformation surfacedamage showing V-shaped scratches in apatterned copper wafer surface. The widthof the scratch in the copper is 160 nm in�b�. In some cases the scratch occurs inboth the copper and tantalum metal sur-faces with different depths as in �c�. Mul-tiple scratches from a single impurity par-ticle causes multiple-parallel scratches asin �d�. �e� and �f� are meandering surfacedamage marks in copper. �g� and �h� areexamples of brittle fracture surface dam-age in BSG. Photos are from Cabot Mi-croelectronics.


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wafer surface there is not sufficient force to cause indentation. Theindentations will take on the shape of the surface of the longer axisof the particle and be imbedded into the wafer surface according tothe indenter equations, Eq. 9, if the load is below that for brittlefracture and Eq. 10 if the load is above this critical load. Measuringthe depth and shape of the indentation shown in Fig. 10, we candetermine the force that must have been responsible for the inden-tation using Eq. 9 and the mechanical properties of the two surfacesin contact. The larger of the two repetitive spots shown in Fig. 10has a radius of the damage zone of �208 nm. If we assume that an�-alumina particle with a 60° sharp edge on its elongated axis isresponsible for the damage, then the force acting on the particle is�1.76 dynes according to Eq. 9. And, if we assume that a piece ofBSG debris with a 60° sharp edge on its elongated axis is respon-sible for the damage, then the force acting on the particle is �2.65dynes. If we assume that the impurity particle started its surfacedamage in the upper left-hand corner of Fig. 10, we can see that onesharp edge of the impurity particle is damaged after 12 roll events,leaving behind a single surface indentation for roll events 13through 15. We can also determine some sense of at least two di-mensions of the impurity particle by the distances between the re-petitive indentations; the large axis is 4.17 m and the smaller axisis 1.25 m.

A large number of rolling particle indenter scanning electronmicroscope �SEM� images have been analyzed for the length of therepeat distance, on average, and the width of the repeat structure, onaverage. These results have been reduced to distribution functions,which are given in Fig. 11. In this figure we see the surface damagestructures produced during copper CMP using Cabot CMC 5000slurry on 200 mm patterned wafers polished on a Mira CMP tooloperated at a platen rpm of 57 and a wafer rpm of 63. This surfacedamage has a lognormal distribution with a mean of 3 m for thewidth and 4 m for the length. These measurements allow an indi-rect characterization of the hard impurity particles present in CMPslurries or generated during CMP.

Another type of surface defect is shown in Fig. 12. Here, we seethat the surface defect is repetitive and appears to form a C-shapedcrack in the surface of the wafer in the optical image of one of thesechatter cracks in ILD materials. In this image the cracks are larger atone end and smaller at the other end of the repetitive line. Theatomic force microscope �AFM� view of another chatter crackshown in Fig. 12 shows repetitive C-shaped surface damage that istens of nanometers deep, with some individual cracks being deeperthan others. Indeed, the AFM stylus may not be able to completelyprobe the depth of a narrow crack, as it may be too narrow at itsapex. The AFM image in Fig. 12 appears to be of a chatter crack thathas had some CMP polishing done on it after it was made and beforethe AFM image was taken, because the surfaces are rather rounded.

A sectional analysis of the AFM image is given in Fig. 13. Here, wesee that the repetitive chatter cracks are �40 nm deep at they aredeepest and have a repeat distance of 2 m.

A rolling 2 m on-edge angular particle with a C-shaped in-denter tip could be causing these chatter cracks, but it is not likelythat there would be so many impurity particles with C-shaped in-denter tips on them. Another explanation could be an angular in-denter with a stick-slip lateral action, but it is not likely that thesticking would occur regularly; it is more likely to occur randomly.In addition, we have seen that the same indenter that causes theflaking action of brittle fracture sometimes makes the chatter cracks;see Fig. 9h. As a result, an alternative explanation has been soughtfor chatter cracks. This other explanation can be simplisticallyviewed as that of a bouncing particle, where the springiness of thepad causes the particle to bounce against the wafer surface. Bounc-ing may be initiated by an impurity particle that is sliding across thesurface of the wafer entering into either a v-groove or flake in thewafer surface made during a previous scratching incident or a zoneof surface buildup due to deposition that acts like a ramp. After thefirst bounce, the particle can have sufficient force when it hits thewafer surface to indent the surface of the wafer. This force is sup-plied by the elastic properties of the pad when the particle is pushedinto it and then rebounds. Once the wafer surface is indented by animpurity particle, the lateral movement of the pad against the waferforces the indentation to open a mode I crack according to Eq. 5,where the applied force is supplied by the lateral elastic propertiesof the pad and the lateral motion of the wafer relative to the pad.This mode I crack will open up under the indenter but lead to acombination mode II-mode III tear in the surface of the wafer, giv-ing the C-shape of an individual crack in the line of repetitivecracks. The impurity particle will, at a high level of surface loading,

Figure 12. Chatter surface damage showing the repetitive 40 nm deep in-dentations in the copper wafer surface.

Figure 11. Width and length distribution of surface damage traces made by rolling indenter particles in copper CMP. Results for lognormal fits shown as theblue lines with �a� geometric mean repeat spacing�10.85 m, �g = 1.997, �b� geometric mean width 3.52 m, �g = 1.90, upon analysis of 75 surface defectsof this type.


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break free from the torn surface with some debris generated, but tomove laterally it must now be pushed into the pad surface verticallybecause the tear protrudes from the wafer surface. With this verticalmomentum another bounce back to the wafer surface is initiated.The frequency of bounces can be determined not by the size of theramp but by the simple physics of a mass �the particle� on a spring�the pad�. The governing equation is

F = k1x = md2x

dt2 �14�

where k1 is the spring constant of the pad, m is the mass of theparticle, and x is the vertical distance that the particle moves into thepad during rebound. The solution to the above equation is given by

x = A sin��t + �o� �15�

where A is the amplitude given by

A = �xo2 + �vo

�2

�16�

where xo is the initial displacement of the particle in the pad and vois the initial vertical velocity of the particle. The angular frequency,� �and frequency, f� for a mass on a spring are given by25

� =2�

T= 2�f = �k1

m�17�

where T is the period of oscillation. The spring constant, k1, for acubic particle with an edge length, l, being pushed into a porous padis approximated by26

k1 � Erel� l �18�

where Erel� is the relative elastic �Young’s� modulus for the contact ofthe particle, and the pad is given by

Erel� = �1 − �particle2

Eparticle+

1 − �pad2

Epad −1

�19�

where � is Poisson’s ratio and E is the elastic modulus. Because theparticle is a hard material relative to the pad, this equation for therelative elastic modulus can be simplified to27

Erel� �Epad

�1 − �pad2 �

�20�

The period for particle bouncing is given by one-half the period ofoscillation for a mass on a spring because the particle cannot com-plete an oscillation without hitting the wafer halfway through itscycle.

Using an assumed 10 m cubic particle with an impurity densityof 4 gm/cc, a polyurethane pad with a porosity of 70% and boro-silicate wafer surface, the particle bouncing period is 1

2 � 0.5 s= 0.25 s. Assuming that the relative speed of the pad to the waferduring CMP is 1 m/s �it can vary from 0.1 to 3.85 m/s inpractice28,29�, the distance between points of surface cracks is0.25 m, which is the correct order of magnitude for what wasobserved in Fig. 13, e.g., 0.33 m. This result is encouraging be-cause we did not know either the size of the bouncing indenterparticle the relative velocity of the pad to the wafer in this example.

In addition, we need to verify that there is sufficient force or loadgenerated to indent the wafer surface when the impurity particlecollides with the wafer. Using the governing equation 4, there issufficient force when the particle hits the wafer surface to indent theBSG surface and to open up a radial crack 10 nm, deep, assumingan indenter tip on the impurity particle of 100 nm diameter and amaximum displacement of 50 nm for the particle above the wafersurface. The depth of the crack observed in Fig. 12 is 45 nm. Toexplain this extra length we must either assume a maximum dis-placement larger than 50 nm or add a lateral stress, �, to the openingand use Eq. 5. When this is done, we can approximate the lateral �orshear� stress that would be necessary to crack the wafer to a depth of45 nm to be 5.3 GPa. The lateral shear would open up a combina-tion mode II-mode III tear in the surface, giving the C-shape to thistype of crack.

The total length of the crack from tip to tip of the C-shape ob-served in Fig. 13 is 0.61 m. The observed length and the observeddepth �45 nm� of the chatter cracks shown in Fig. 13 can be used todetermine the amount of energy required in creating these cracksbecause the fracture surface energy of BSG in known to be45.3 J/m2. The energy required to create one of these individualchatter cracks is 1.2 � 10−12 J.

In some cases the rebound force can be sufficiently large to em-bed the particle into the surface of the wafer; see Fig. 14. This mostoften occurs when the rebound happens over a metal that can un-dergo plastic deformation and absorb the impact with surface dam-age. The damage is in the form of a crater that is molded to theparticle’s shape, thereby detaching it from the pad and fixing it intothe surface of the wafer.

Finally, it is necessary to get some sense of typical results forsurface damage when scratching is prevalent during CMP. The fol-lowing observations come from Cabot Microelectronics upon char-acterizing the scratches on thousands of wafers:

ILD wafer surfaces show only one type of surface damage chat-ter scratches that are referred to as brittle fracture scratches in thisreport.

Copper wafer surfaces show

Figure 13. Sectional analysis of chattersurface damage shown in Fig. 12.

Figure 14. Hard impurity particle embedded in �a� copper pattern of wafersurface after CMP with �b� EDAX of particle showing Cu, SiO2, and a traceof Al2O3.


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1. Irregular pattern skipping scratches corresponding to 60–80%of total.

2. Line scratches also called razor scratches or plastic plowscratches in this document corresponding to 5–25% of the total ex-cept in the case of some Ta polishing colloidal SiO2 slurry formu-lations with a hard pad when line scratches are the dominant modeof surface damage.

3. Rolling particle surface damage corresponding to 0–20% ofthe total.

These observations are consistent with what would be predictedfor the scratching of a brittle material like silicate produced byplasma enhanced chemical vapor deposition of tetraethyl orthosili-cate �PETEOS�. Because the material is elastic up to the point ofrupture as shown in Fig. 1b, PETEOS should not show any indentermarks; because this material is brittle it cannot fail by plastic defor-mation. PETEOS, however, can and does fail by brittle fracture.These observations are also consistent with what would be predictedfor the scratching of a ductile material, copper, as the material isplastic for most of its deformation range after an initial elastic limit

is reached at a very small amount of deformation as is shown Fig.1a. As polycrystalline copper is highly plastic up to a strain �orelongation� of 53%, it is nearly impossible to cause it to undergobrittle fracture and rupture in CMP.

Conclusions

Hard impurity particles present in the CMP slurry are responsiblefor surface damage in both ductile �e.g., copper� and brittle �e.g.,ILD� materials at the wafer surface. The shapes of the ILD surfacedamage consistently show only brittle fracture failure. When theload is sufficiently high, lateral cracks are formed which form chipsthat become debris particles that are swept away from the wafersurface and into the CMP slurry, potentially causing further surfacedamage. Surface damage in copper is plastic plow damage and roll-ing particle indenter damage, typical of a ductile material. Examplesof both of these surface damage mechanisms, including several vari-ances unique to CMP, are shown in this paper and explained interms of fracture mechanics and impurity particle dynamics.

Table A-I. Mechanical properties of IC materials encountered in CMP process (Ref. 31).

Material

MolecularWeight

gm/moleDensitygm/cm3

Poisson’sRatio,

�

KnoopHardness,

HGPa

Modulus atRupture or

TensileStrength,

MPa

Young’sModulus,

E GPa

FractureToughness,

KcMPa m1/2

Si 28.086 2.329 1 98.74 0.6Metals that form the wires and viasMo 95.94 10.22 - 278 10–100a

W 183.84 19.3 0.28 3–3.4 398 20Cu 63.546 8.96 0.34 �0.874,

Brinell�220 130 50–100

Al 26.982 2.71 0.33 1.4 55 72 35–45Ag 107.87 10.49 0.37 125 76Ta 180.95 16.69 0.34 �0.873,

Vickers�186

Ti 47.86 4.51 0.32 �0.97,Vickers�

330 116 30–100a

Oxides, dielectrics, and CMP abrasivesWO3 231.84 7.2 100–300? 3–10a

Cu2O 143.09 6.0 1.7 100–300? 3–10a

CuO 79.545 6.3 1.5 100–300? 3–10a

Al2O3 101.96 3.97 0.27 21 275–550 393 3.5–4.5TiO2 79.90 4.04

Anatase4.26

Rutile

6–108–10

100–300?100–300?

3–10a

3–10a

Fe3O4Fe2O3

231.54159.69

5.20Magentite

5.26Hematite

6–104–8

100–300?100–300?

3–10a

3–10a

ZrO2 123.22 5.68 0.32 12 138–240 138 8.4SiO2 60.085 2.2 0.16 5.5 110 72 0.7–0.9BSG - 2.23 0.20 3–5 69 69 2.5Polish stop materials and other hard IC materialsSiC 40.10 3.22 0.19 25 450–520 414 3–5a

Si3N4 140.28 3.17 0.24 22 414–580 304 5.6–11BN 24.82 2.27 20.5 83 -TiC 59.91 4.93 26 462 -TiN 61.91 5.22AlN 40.989 3.26 12 331 3–7a

WC 195.86 15.63 450–650 -Diamond 12.011 3.51 78–100 1035 2.5a

Pad materials and polymersPolyurethane - �1 0.25 5–10? 0.2? 1–3a

PolymerLDPE

- 0.96 5–10? 8.3–31 0.172 1–3a

a values from Ref. 32.


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Acknowledgment

University of Utah assisted in meeting the publication costs of this ar-ticle.

AppendixMechanical Properties of Materials

Table A-I collects the mechanical properties of the materials that are important inCMP.

References1. S. Sundararajan, D. G. Thakurta, D. W. Schwendeman, S. P. Murarka, and W. N.

Gill, J. Electrochem. Soc., 146, 761 �1999�.2. R. S. Subramanian, L. Zhang, and S. V. Babu, J. Electrochem. Soc., 146, 4263

�1999�.3. J. J. Vlassak, Mater. Res. Soc. Symp. Proc., 671, M4.6.1 �2000�.4. G. Ahmadi and X. Xia, J. Electrochem. Soc., 148, G99 �2001�.5. J. J. Vlassak, Mater. Res. Soc. Symp. Proc., 671, M4.6.1 �2001�.6. E. E. Remsen, S. P. Anjur, D. Boldridge, M. Kamiti, S. Li, T. Johns, C. Dowell, J.

Kasthurirangan, and P. Feeney, J. Electrochem. Soc., 153, G453 �2006�.7. Linear Fracture Mechanics: Historical Developments and Applications of Linear

Fractur Mechanics Theory, G. C. Sih, R. P. Wei, and F. Erdogan, Editors, p. xii–xviLehigh University, Envo Pub. Co., �1975�.

8. T. J. Bell, J. S. Field, J. F. Lesha, and M. V. Swain, Mater. Res. Soc. Symp. Proc.,522, 15 �1998�.

9. D. J. Green, An Introduction to the Mechanical Properties of Ceramics, p. 243,Cambridge University Press, Cambridge �1998�.

10. D. J. Green, An Introduction to the Mechanical Properties of Ceramics, p. 243, Eq.8.63, Cambridge University Press, Cambridge �1998�.

11. A. G. Evans and D. B. Marshall, “Wear Mechanisms in Ceramics,” in Fundamen-tals of Friction and Wear of Materials, D. A. Rigney, Editor, pp. 439–441 Ameri-can Society for Metals, Metals Park, OH �1981�.

12. M. A. Moore, “Abrasive Wear,” in Fundamentals of Friction and Wear of Materi-als, D. A. Rigney, Editor, pp. 73–118 American Society for Metals, Metals Park,OH �1981�.

13. A. G. Evans and D. B. Marshall, “Wear Mechanisms in Ceramics,” in Fundamen-tals of Friction and Wear of Materials, D. A. Rigney, Editor, p. 441 AmericanSociety for Metals, Metals Park, OH �1981�.

14. D. B. Marshall, “Surface Damage in Ceramics: Implications for Strength Degrada-tion, Erosion and Wear,” in Progress in Nitrogen Ceramics, F. L. Riley, Editor, p.635–656 Kluwer, New York �1983�.

15. A. G. Evans and D. B. Marshall, “Wear Mechanisms in Ceramics,” in Fundamen-tals of Friction and Wear of Materials, D. A. Rigney, Editor, pp. 439–452 Ameri-can Society for Metals, Metals Park, OH �1981�.

16. D. B. Marshall, “Surface Damage in Ceramics: Implications for Strength Degrada-

tion, Erosion and Wear,” in Progress in Nitrogen Ceramics, F. L. Riley, Editor, p.440, Martinus Nijhoff Publishers, Boston �1983�.

17. D. B. Marshall, “Surface Damage in Ceramics: Implications for Strength Degrada-tion, Erosion and Wear,” in Progress in Nitrogen Ceramics, F. L. Riley, Editor, p.640 Martinus Nijihoff, Boston �1983�.

18. D. B. Marshall, “Surface Damage in Ceramics: Implications for Strength Degrada-tion, Erosion and Wear,” in Progress in Nitrogen Ceramics, F. L. Riley, Editor, p.642 Martinus Nijihoff, Boston �1983�.

19. D. J. Green, An Introduction to Mechanical Properties of Ceramics, p. 244, Cam-bridge University Press, Cambridge �1998�.

20. A. G. Evans and D. B. Marshall, in Fundamentals of Friction and Wear of Mate-rials, D. A. Rigney, Editor, pp. 441, Eq. 1, 7, and 12, American Society for Metals,Metals Park, OH �1981�.

21. J. A. Greenwood, J. Lubr. Technol., 1967, p. 81–91.22. J. A. Greenwood and J. B. Williamson, Proc. R. Soc. London, Ser. A, 295, 300

�1966�.23. T-K Yu, C. C. Yu, and M. Orlowski, “A Statistical Polishing Pad Model for CMP,”

Transactions of the International Electron Devices Meeting, 1993, Washington,DC, IEEE, 1993, p. 865–868.

24. D. B. Marshall, “Surface Damage in Ceramics: Implications for Strength Degrada-tion, Erosion and Wear,” in Progress in Nitrogen Ceramics, F. L. Riley, Editor, p.635–656, Martinus Nijhoff, Boston �1983�.

25. F. W. Sears and M. W. Zemansky,University Physics, 3rd ed., Part I, p. 262 Addi-son Wesley, Reading, MA �1963�.

26. Derived from the elastic properties of the pad and particle.27. The pad is often porous and the elastic modulus is given by Epad = Eo�1 − �pad

2 �and Poisson’s ratio for the pad is given by �pad = �o�1 − �pad

2 �, where �pad is the padporosity. �L. J. Gibson and M. F. Ashby, Cellular Solids: Structure and Properties,Oxford University Press, Oxford �1988��.

28. W. J. Patrick, W. L. Guthrie, C. L. Standley, and P. M. Schiable, J. Electrochem.Soc., 138 1778 �1991�.

29. J. M. Steigerwald, S. P. Murarka, and R. J. Gutmann, Chemical Mechanical Pla-narization of Microelectronic Materials, Wiley-Interscience, New York �1997�.

30. Governing equations from K. L. Johnson, Contact Mechanics, p. 90, CambridgeUniversity Press, Cambridge �1985�.

31. Data from various sources including C. Planche, H. Berman, and C. Frandel, TheSystem of Mineralogy of Jams Dwight Dana and Edward Salisbury 1837–1892,Volume 1, Elements, Sulfides, Sulfosalts, Oxides, 7th ed., Wiley, New York �1944�;S. Sengupta, Lattice Theory of Elastic Constants, Zurich, Switzerland �1993�; W.D. Callister, Materials Science and Engineering—An Introduction, 3rd ed., Wiley,New York �1994�; A. G. Evans and D. B. Marshall, “Wear Mechanisms in Ceram-ics,” in Fundamentals of Friction and Wear of Materials, D. A. Rigney, Editor, pp.439–441 American Society for Metals, Metals Park, OH �1981�.

32. M. F. Ashby, Materials Selection in Mechanical Design, p. 36, Pergamon, Oxford�1979�.


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