Effect of rogue particles on the sub-surface damage of fused silica during grinding/polishing

Transcription

1 UCL-JNL Effect of rogue prticles on the sub-surfce dmge of fused silic during grinding/polishing T. I. Surtwl,. Steele, M. D. Feit, L. Wong, P. E. Miller, J. A. Menpce, P. J. Dvis My 10, 007 Journl of Non-Crystlline Solids

2 Disclimer This document ws prepred s n ccount of work sponsored by n gency of the United Sttes Government. Neither the United Sttes Government nor the University of Cliforni nor ny of their employees, mkes ny wrrnty, express or implied, or ssumes ny legl libility or responsibility for the ccurcy, completeness, or usefulness of ny informtion, pprtus, product, or process disclosed, or represents tht its use would not infringe privtely owned rights. eference herein to ny specific commercil product, process, or service by trde nme, trdemrk, mnufcturer, or otherwise, does not necessrily constitute or imply its endorsement, recommendtion, or fvoring by the United Sttes Government or the University of Cliforni. The views nd opinions of uthors expressed herein do not necessrily stte or reflect those of the United Sttes Government or the University of Cliforni, nd shll not be used for dvertising or product endorsement purposes.

3 Mnuscript for submission to Journl of Non-Crystlline Solids Effect of ogue Prticles on the Sub-Surfce Dmge of Fused Silic during Grinding/Polishing T. Surtwl,. Steele, M. D. Feit, L. Wong, P. Miller, J. Menpce, P. Dvis Lwrence Livermore Ntionl Lbortory, P.O. Box 808, Livermore, CA 94551, USA The distribution nd chrcteristics of surfce crcks (i.e., sub-surfce dmge or scrtching) on fused silic formed during grinding/polishing resulting from the ddition of rogue prticles in the bse slurry hs been investigted. Fused silic smples (10 cm dimeter x 1 cm thick) were: 1) ground by loose brsive grinding (lumin prticles 9-30 µm) on glss lp with the ddition of lrger lumin prticles t vrious concentrtions with men sizes rnging from µm, or ) polished (using 0.5 µm cerium oxide slurry) on vrious lps (polyurethnes pds or pitch) with the ddition of lrger rogue prticles (dimond (4-45 µm), pitch, dust, or dried Ceri slurry gglomertes) t vrious concentrtions. For the resulting ground smples, the crck distributions of the s-prepred surfces were determined using polished tper technique. The crck depth ws observed to: 1) increse t smll concentrtions (>10-4 frction) of rogue prticles; nd ) increse with rogue prticle concentrtion to crck depths consistent with tht observed when grinding with prticles the size of the rogue prticles lone. For the polished smples, which were subsequently etched in HF:NH 4 F to expose the surfce dmge, the resulting scrtch properties (type, number density, width, nd length) were chrcterized. The number density of scrtches incresed exponentilly with the size of the rogue dimond t fixed rogue dimond concentrtion suggesting tht lrger prticles re more likely to led to scrtching. The length of the scrtch ws found to increse with rogue prticle size, increse with lp viscosity, nd decrese with pplied lod. At high dimond concentrtions, the type of scrtch trnsitioned from brittle to ductile nd the length of the scrtches drmticlly incresed nd extended to the edge of the optic. The observed trends cn explined semi-quntittively in terms of the time needed for rogue prticle to penetrte into viscoelstic lp. The results of this study provide useful insights nd rules-of-thumb relting scrtch chrcteristics observed on surfces during

4 opticl glss fbriction to the chrcteristics rogue prticles cusing them nd their possible source. *Work performed under the uspices of the US Deprtment of Energy by Lwrence Livermore Ntionl Lbortory under contrct No. W-7405-ENG-48 with the LDD progrm. PACS Codes: b; Np; d Keywords: crck growth C81; fbriction F100; glss surfce G190; mechnicl properties M10 1. INTODUCTION The cretion of sub-surfce mechnicl dmge (SSD) (i.e., surfce micro-crcks) cn be thought of s the repeted indenttion of mechniclly loded hrd indenters (brsives) sliding on the surfce of brittle substrte (workpiece) during vrious cutting, grinding nd polishing processes. These surfce crcks re commonly identified s scrtches nd digs. During grinding opertions, the removl of mteril is governed by the intersection of multiple surfce crcks. In contrst, the mteril removl mechnism responsible for polishing is less strightforwrd. Vrious mechnisms hve been proposed including surfce melting [1], plstic removl or brsion [-3], brittle frcture [4-5], dhesion [6], nd chemicl []. However, the most widely ccepted mechnism involves the removl of mteril by chemicl rection between the polishing prticle nd the substrte resulting in moleculr level removl [,5,7-8]. For sttic indents, the lods needed to initite frcture (lterl, rdil, Hertzin) re finite nd cn be nlyticlly expressed in terms of the size of prticle for blunt indentors nd mteril properties for shrp indentors [4]. The criticl lod for shrp indentor to crete frcture in fused silic is ~ 0.0 N [4]. For sliding indents (i.e., leding to scrtching), the types of fetures (triling indent crcks, medin crcks, lterl crcks, nd plstic deformtion/compction) [4,9,10] re function of the locl shpe of the prticle t contct (shrp vs blunt) nd the pplied lod. At low lods (P < 0.05 N) plstic trench is formed without frctures. At intermedite lods (0.1 N < P < 5 N) well defined rdil (or triling indent) frctures long with lterl crcks re observed. At higher lods (P > 5 N), the plsticlly deformed trck frctures into rubble like ppernce, nd lterl nd triling indent crcks re less pronounced.

5 On spect of the trnsition from grinding to polishing cn be thought in terms of the decrese in prticle size of the slurry nd the subsequent decrese in the lod/prticle. During grinding lrger prticles re used (greter thn ~10 µm), resulting in less loded prticles per unit re between the workpiece nd the lp nd thus, resulting in lods/prticle tht exceed the initition lod for frcture. During polishing smller prticles re used (less thn 3 µm), resulting more loded prticles per unit re nd lods/prticle below the frcture initition lod. For typicl ceri bsed polishing slurry (0.5 µm), ssuming 0.3 fill frction t the interfce nd ll the prticles re lod bering, one estimtes lod/prticle of N. Clerly, the lod on n verge polishing prticle is mny orders of mgnitude lower thn needed to initite frcture. Thus ny scrtch formed on polished surfce implies prticle (i.e. lrger (rogue) prticle) tht is holding much higher lod thn the verge prticle. The presence of rogue (i.e. lrge) prticles in the slurry during grinding or polishing is known to strongly influence surfce properties of the workpiece either in terms of deeper dmge or isolted scrtching [,4,11]. Severl studies for polishing integrted circuits hve investigted the effects of rogue prticles for wfers ground or polished using chemicl mechnicl polishing. Bsim et. l. [1] spiked colloidl silic slurries with rogue silic prticles nd found tht scrtch densities incresed with rogue prticle size nd concentrtion. By chrcterizing the slurry size distribution using dynmic light scttering, Bsim lso illustrted tht rogue prticles present even t very low concentrtion (<1 out 100,000) cn degrde surfce qulity. Ahn et. l. [11] nd Kllingl et. l. [13] compred different colloidl silic nd colloidl lumin bsed slurries of different ph, filtering, or ultrsonic preprtion to reduce micro-scrtches; the results were explined in terms of how the process prmeters ffect the lrge prticles in the distribution. In our previous studies, the chrcteristics nd sttisticl distribution of SSD s function of different grinding processes using polished tper technique hs been mesured nd nlyzed [14-16]. These results suggested tht only smll frction (1 out of tens of thousnds of prticles) of the brsive prticles were prticipting in the mteril removl by compring the mesured crck depth tht with tht expected from sttic indenttion models. Hence only smll frction of the prticles were being mechniclly loded. In the present study, the effects of rogue prticle dditions during both grinding & polishing nd their effect on the SSD depth nd the chrcteristics of scrtching hve been investigted. Understnding the impct of the

6 presence of rogue prticles during grinding & polishing cn ultimtely be used to develop finishing processes resulting in miniml or no SSD. This is importnt in res which require high qulity polished brittle surfces including integrted circuits, high strength windows, nd optics for use in high power lser pplictions [17].. EXPEIMENTAL.1 Ground Smples ound fused silic smples (10 cm dimeter x 1.0 cm thick) were ground or polished using slurries tht were intentionlly contminted with vrious concentrtion nd sizes of rogue prticles. Ground smples were prepred on rotry 8 borosilicte glss lp (0.3 psi, 1 hr, 15 rpm lp) using n lumin brsive prticle (Microgrit 9T or 15T) slurry. ogue prticles (Microgrit 15T or 30T) were dded to the bse slurry t vrious concentrtions. The SSD distributions of the s-prepred surfces were then determined by: 1) creting shllow ( µm) wedge/tper on the surfce by mgneto-rheologicl finishing; ) exposing the SSD by HF/NH 4 F cid etching; nd 3) performing imge nlysis of the observed crcks from opticl microgrphs (Nikon Optiphot, reflectnce) tken long the surfce tper (see Fig. 1). Detils of this chrcteriztion technique to determine SSD depth nd length distributions re provided elsewhere [14-16]. Photogrphs of the grinding setup is shown in Fig. nd the prticle size distributions of the loose brsives used in the rogue prticle experiments re shown in Fig. 3. The mtrix of experiments for the ground smples re shown in Tble 1.. Polished Smples The pitch lp ws prepred by heting 500 gm of Gugolz 73 ground in ~mm sized pieces in n luminum foil covered stinless steel continer (1 cm dim x 16 cm) in convection oven t 76.7 o C for 60 minutes. The pitch ws stirred fter 30 minutes nd 50 minutes. The molten pitch ws then poured immeditely fter removl from the oven onto preheted (76.7 o C) lumimum plte block (0 cm dim) with tpe (3M blck duct) wrpped round the edge on flt, level surfce until the lp formed the desired thickness. After 10 minutes, tht tpe ws removed nd the groove pttern (3.8 cm tringles with 3 mm wide, 3 mm deep, 60 o V-grooves) ws embossed using rubber msk. The embossing ws ccomplished by plcing the msk on the pitch nd rotting the lp upside down on the flt, level surfce for 3 min. The polyurethne lp (Sub

7 550) ws prepred by dhering the lp mteril on glss substrte nd by routing 1 mm grooves in 10 squre pttern. Figs. b&c show photos of the polishing lps. Polished smples were prepred by first removing ll the pre-existing SSD by ceri polishing on n 8 rotry polisher using Hstilite PO ceri slurry on polyurethne pd (0.3 psi, 15 rpm lp) (Sub 550) or on pitch (Gugolz 73). The SSD dmge removl ws verified by HF/NH 4 F etching for 30 minutes nd inspecting the surfce by opticl microscopy for ny observble surfce crcks. The fused silic smples were then repolished for 1 hr with the sme polishing slurry contminted: 1) t vrious brsive sizes of 4, 6, 10, 15, 0 or 45 µm t vrious concentrtions using rogue dimond prticles (Dimond Innovtions DMS Poly 85T) on the polyurethne pd, ) t vrious lods using 6 um dimond on polyurethne pd, 3) on vrious lps using the 6 um dimond, 4) t vrious tempertures using 6 um dimond on pitch, nd 5) with vrious types of rogue prticles (dust, dimond, pitch, dried ceri) on pitch. The mtrix of experiments for the polishing experiments re shown in Tble. The morphology of the dimond prticles ws exmined by scnning electron microscopy. The chrcteristics of the resulting scrtches due to the rogue prticles were then chrcterized by opticl microscopy fter HF/NH 4 F etching to expose ll the SSD. Note ll the crck fetures were observble by opticl microscopy only fter etching. The prticle size distributions of the loose brsives used in the rogue prticle experiments re shown in Fig. 3b. 3. ESULTS 3.1 ogue prticles during grinding Tble 1 shows the bsic experimentl prmeters nd summry of the results for the ground smples (G1-G9). The removl rte, mesured SSD depth, verge crck length, surfce roughness nd the clculted verge lod/prticle, surfce density of crcks, nd the mximum crck length for ech of the smples re listed. The lst three prmeters re clculted using brittle frcture model described in detil in our previous study [14].

8 The number density of crcks on typicl ground surfce is very high, such tht the individul crcks intersect ech other giving rubble-like ppernce. However, few microns below the surfce (i.e. fter polishing through it), one cn now identify distinct individul crcks, ll of common morphology, which decrese in number density with depth. Most of these crcks hve triling indent chrcter [14] (commonly referred to s chtter mrks [18] or stick-dig frctures). Figure 4 shows n opticl microgrph of ground surfce fter the rubble-like surfce hs been removed, illustrting the typicl crcks observed on ground surfce. The length or size of these triling indents crcks hve been found to scle with the size of the brsive prticle used for grinding [14,16]. Figures 5 & c show the SSD depth distributions mesured by the tper polish technique on the series of loose brsive ground surfces with vrious concentrtions of rogue prticle dditions to the slurry. The crck depth distributions re reported in terms of cumultive crck obscurtion (crck re frction) s function of depth into the originl treted glss surfce. Obscurtion ws used insted of crck number density to describe the SSD density becuse the intersection of crcks ner the surfce cuses significnt uncertinty in the crck number density. The shpe of the depth distributions follows single exponentil dependence for the mjority of the distribution except ner the end of the distribution where crck density drops very rpidly, ppering like n symptotic cutoff. The SSD depth ws observed to increse significntly even with smll mount of rogue prticles for both the 9 µm plus 15 µm rogue prticles (Fig. 5) nd 15 µm plus 30 µm rogue prticles (Fig 5c). The corresponding crck cumultive crck length distribution for the sme set of smples re shown in Figs. 5b & d. From our previous studies [14], the length of the triling indent frcture ws found to be correlted directly to the size of the brsive leding to frcture. As shown in Tble 1, the verge crck length for the 15 µm loose brsive (G) ws 3.8 µm nd for the 30 µm loose brsive ws 15. µm. Upon exmintion of Figs. 5b & 5d, the crck length distribution shifted to lrger vlues with n increse in rogue prticle concentrtion nd pproched tht of the size of the triling indent crck expected for the rogue prticle itself. This suggests tht with incresing rogue prticle concentrtions, the rogue prticles were prticipting

9 more in cusing frcture. This is lso consistent with the crck depth distributions dt discussed bove. Figure 6 shows plot of the mximum SSD observed s function of the rogue prticle concentrtion. The horizontl dshed lines illustrte the bounds by which the SSD depth ws observed with the bse prticle slurry lone nd with the rogue prticle slurry lone. The mesured SSD depth with the rogue prticles re bound by these limits which is not surprising result. However, it ppers tht the SSD depth will strt to increse from the depth found with the bse slurry t firly low frction of rogue prticles (<10-4 ) or t n rel density of 10 cm -. Hence only smll mount of rogue prticles is enough to increse the SSD. Interestingly, the removl rte lso strts to noticebly increse with the ddition of rogue prticles somewhere between frction of rogue prticles nd strt to pproch the removl rte of the rogue prticle lone (see Fig. 6b). 3. ogue prticles during polishing Tble shows bsic experimentl prmeters nd summry of the results for the polished smples (P1-P19). The results include the observed scrtch properties (the number density, verge length, verge width, nd the percentge of the types of scrtches observed). Without the ddition of rogue dimond prticles during polishing (i.e., only using slurry mde from Hstilite PO Cerium oxide), our polisher ws ble to repetbly crete surfces tht showed no scrtches or digs fter etching the smple (e.g., smple P1). Note tht before ny of the other polishing smples (P-P19) were prepred, ll the scrtches nd digs were removed from ech substrte using the sme procedure s noted for P1 (i.e., without rogue prticles) to ensure tht the observed scrtches were cused by the rogue prticles tht were dded to the slurry. The vrious types of scrtches tht were observed s result of the ddition of rogue prticles re shown in Fig. 7. These scrtches cn be divided into three bsic ctegories: 1) Plstic which re scrtches tht show no brittle frcture but just plstic modifiction to the surfce (often referred to sleeks); ) Brittle which re scrtches tht hve only crcks (triling indent or lterl); nd 3) Mixed which re scrtches tht contin both plstic modifiction nd crcks. The scrtches cn then be further ctegorized by the types of crck (lterl or triling indent). Plstic type scrtches

10 would be expected from shrp indenters where the locl pressure exceeds the yield stress t the contct zone. Purely brittle type scrtches would be expected from blunt type indenters. Scnning electron microscope imges of the dimond rogue prticles rnging from 4-45 µm re shown in Fig. 8 which show tht the dimond prticles hve both blunt nd shrp chrcter to them; thus, it is not surprising tht both plstic nd brittle scrtches were observed. The scrtch dimensions (length, width), the scrtch number density s functions of rogue prticle size nd rogue prticle dimond concentrtion re summrized in Figs. 9-d. The scrtch number density ws found to increse exponentilly with rogue prticle size t fixed rogue prticle number concentrtion (see Fig 9). This suggests tht the lrger the rogue prticle, the greter the probbility or the more efficient it is in cusing scrtches. The mgnitude of the difference in scrtch number density with prticle size is lso illustrted in the microscope imges shown in Fig. 10. Interestingly, the scrtch number density ws much less sensitive to the rogue prticle concentrtion. For most of the rogue prticle concentrtions exmined (5-500 cm - ) the scrtch concentrtion did not chnge by more thn fctor of 5. However, t very high rogue prticle concentrtion (5000 cm - ), the plstic scrtch number density incresed by fctor of 1000 (see Fig. 9b). The width nd the length of the scrtches were both observed to increse with rogue prticle size nd were reltively insensitive to rogue prticle concentrtion except t very high rogue prticle concentrtion (Fig. 9c-d). The width increse is ttributed to the lrger contct zone expected with lrger rogue prticles; the width of the scrtch ws nominlly 15-30% of the men dimond dimeter dded to the slurry. The scrtch length ws lso noted to increse with dimond prticle size in the rnge of 4 µm to 0 µm (Fig. 9c). Figure 11 illustrtes this trend more definitively by plotting the cumultive scrtch length distribution observed for vrious rogue dimond prticles. A similr plot (Fig. 11b) shows the effect of pitch temperture on the scrtch length distribution, whose results will be discussed in more detil in the Section 4. ogue prticles of different mteril types were shown to cuse scrtches. Whether the rogue prticles were dimond (P1), pitch prticles (P18), or dried ceri gglomertes (P19), scrtches were seen regrdless (See Tble ). The only exception ws orgnic urbn dust (P17) which did

11 not led to ny mesurble SSD. Pitch prticles nd dried ceri gglomertes re common sources of rogue prticles during polishing, nd these results confirm tht clenliness nd the elimintion of pitch prticle sources nd dried slurry round the polisher re criticl to obtin scrtch-free surfces. 4. DISCUSSION 4.1 ogue prticles during grinding nd lod/prticle The chnge in the SSD depth distribution with the ddition of rogue prticles during grinding cn be rtionlized in terms of the chnge in the prticle size distribution which leds to chnge in the lod distribution of prticles in contct with the workpiece. In our previous study [14], brittle frcture model ws used to describe how the prticle size distribution of the grinding prticles led to the crck depth nd length distributions. Some of the key fetures of the model include: 1) only the lrger prticles in the distribution re loded nd led to frctures; nd ) the lod on given prticle scles linerly with the size of the prticle. Using this brittle frcture model s bsis, one cn gin insight to the behvior observed when two prticle size distributions re mixed. For this nlysis, ssume tht the prticles (both the bse nd the rogue) hve log-norml distribution (g(d)) in the form: g (ln( d ) ln( 1 lnσ ( ) d d c )) = e (1) d π lnσ where d is the size of the prticle, σ is prmeter tht describes the width of the distribution, nd d c is the men prticle size. When the two prticles distributions re mixed, the resulting distribution (g t (d)) is simply the geometric sum of the two given by: g ( d) = (1 x ) g ( d) x g ( d) () t r b + where g b (d) is the bse prticle size distribution, g r (d) is the rogue prticle size distribution, nd x r is the number frction of prticles from the rogue prticle size distribution. Then the frction of prticles being loded nd resulting in SSD is given by: d r r mx f = g ( d) d (3) lod d min t Where d min is the minimum prticle size tht is mechniclly loded nd prticiptes in the frcture nd d mx is the lrgest prticle size in the distribution. For simplicity, ssume tht the frction of prticles being loded is the sme regrdless of the mixture of the two distributions.

12 Knowing f lod, one cn determine d min numericlly; in order words, one now knows the distribution of loded prticles. Using n nlysis utilized in the previously described model [14], the loded prticle distribution cn be then converted to frctionl distribution of crck depths (f c (c)) nd cumultive obscurtion or crck density depth distribution (O(c)), which re given by: d fc ( c) = gt ( d) (4) c c mx O( c) = fc ( c) w n L( c) dc (5) c Substituting vlues for d / c nd L(c) s derived in the previous study s: d c 3 1/ K Ic N L dc 1/ 4 = 4 χ P h T c (6) π K N d k P Ic L c T 3/ 4 L( c) = c h P T 3E N L d χ c nd simplifyin, the following expression for the crck depth distribution is obtined: where Q is: c 1/ 1/ 3 O c = mx 1/ ( ) g ( d) c Q dc (8) c t 3π K Ic wn N L dc k Q = 8 (9) χ h PT 3E where K Ic is the frcture toughness of the substrte, N L is the number of brsive prticles being loded, d c is the men brsive prticle size, χ h is the Hertzin indent crck growth constnt, P T is the pplied lod, w is the width of the crck on surfce, n is the number density of crcks on the surfce, nd k is mteril constnt relted to the modulus nd Poisson s rtio of the substrte nd indenter. Using Eqs.1-3, the loded distribution of prticles s function of rogue prticle concentrtion hs been clculted. By tking the simple cse where the frction of prticles being loded (f L ~0.01), the number density of crcks on the surfce (n ~0.05 um - ), nd the lod for the verge loded prticle (P T /N L ~0.5 N) do not chnge with the ddition of rogue prticles, we cn estimte the SSD depth predicted by Eqs The clculted SSD is reported in Fig. 6 / 3 1/ 3 (7)

13 by the solid line. The ssumptions described bove re likely n oversimplifiction of the rel system. However, this simple model predicts SSD depths tht re consistent with mesured dt s function of the rogue prticle concentrtion. This model cn be used to estimte the SSD depth in the presence of rogue prticles or s method to estimte the size or concentrtion of rogue prticles bsed on n observed chnge in SSD depth distribution. 4. Scrtch Chrcteristics nd Viscoelstic Model During n idel polishing process (s opposed to grinding), mteril removl occurs chemiclly t the moleculr level rther thn by mechnicl frcture []. During polishing, the nominl lod per polishing prticle is quite low ( N), well below tht needed to initite frcture []. However, when rogue prticles re present during polishing, the mechnicl lod on the rogue prticle cn be orders of mgnitude higher, resulting in rogue prticle-induced frcture (i.e., scrtching). Lods on the order of N for plstic nd 0.1 N for brittle frcture initition re needed [4,9]. The ddition of rogue dimond prticles led to surfce scrtches whose width, length nd number density depend on the size nd concentrtion of the rogue prticles dded. As discussed in Section 3., there re three mjor trends tht were observed: 1) the propensity of rogue prticles to led to scrtches is strongly dependent on the size of the rogue prticle nd wekly dependent on the concentrtion; ) the length nd width of the scrtches both increse with the size of the rogue prticle nd re essentilly independent of concentrtion; 3) t the highest rogue dimond size (45 µm) nd t the very high rogue dimond concentrtions for the 4 µm dimond, the number density of scrtches increses by orders of mgnitude, the scrtch lengths re the length of the optic (qusi infinite), nd the nture of the scrtches were ll plstic in nture. The discussion below explins the ltter two observtions. The scrtch lengths incresed from ~330 µm to ~1300 µm with rogue prticle size (see Tble nd Fig. 11). For these smples, the scrtch number densities were ~ to 5 cm - or nominlly totl scrtches on 100 mm dimeter round substrte. The verge reltive velocity of the prticle reltive to the optic hs been determined s 80 cm/sec. Hence, for the length of scrtches observed, the time tht ech of the rogue prticles were loded rnged between msec. If we ssume tht the scrtches were creted rndomly during the time of polishing of

14 n hour, then scrtch is creted on verge every sec. The conclusion here is tht the scrtching process occurs spordiclly. A longer scrtch length suggests tht rogue prticle lods to the surfce of the workpiece for longer period of time, ssuming constnt reltive rogue prticle velocity. In the discussion below, mechnism is proposed by which the time for rogue prticle being loded is governed by the size of the rogue prticle nd the viscoelstic properties of the lp. Figure 1 shows schemtic of the proposed mechnism. At some rbitrry time zero, rogue prticle finds its wy t the interfce between the optic nd the lp. Due to the lrge size of the rogue prticle, it will ber much higher lod (P>0.001 N) thn the verge prticle on the lp; this lod is sufficient to initite brittle frcture or plstic deformtion on the optic. While loded nd sttic reltive to the lp, the rogue prticle will penetrte into the viscoelstic lp until: 1) the gp between the lp nd optic is reduced to tht of the polishing ceri prticle (0.5 µm), thus dropping the lod on the rogue prticle to mtch tht of the verge ceri prticle nd ending the scrtch (Fig 1b), or ) the mximum elstic penetrtion hs been reched (function of the elstic modulus of the lp) resulting in incomplete rogue prticle penetrtion, little drop in lod on the rogue prticles, nd indefinite scrtch lengths (cross the length of the optic). To exmine this mechnism more quntittively, consider hrd sphericl brsive under qusi sttic lod (Fig. 13). Using n pproch Lee nd dock [19] which expnded the originl Hertz elstic contct [0] to simple liner viscoelstic substrte, the governing force blnce eqution is given by: E Lp dε P ε + η Lp = (10) dt π where P is the pplied lod on the sphericl prticle, is the contct zone rdius, nd ε is resulting strin. The viscoelstic properties of the lp re described by the elstic modulus (E Lp ) nd viscosity (η Lp ). For given pplied pressure (term on right hnd side of Eq. 1), there is n elstic limit response (first term on left hnd side) nd time dependent response (second term on left hnd side). One problem becomes immeditely evident: most formultions re for smll strin (e.g., smll rdius of contct compred to the rdius of the prticle). However, in this study we re interested

15 in lrge strin. This problem hs been noted by, for exmple, Kumr nd Nrsimhn [0]. elted to this is the possibility of pushing the prticle fr into the pitch (pst rdius ). This leds to more difficult differentil eqution but we never will hve >. The solution to this is to consider the sher strin so the strin vrible is not / but: ε = tn( θ ) = (11) where is the rdius of the prticle nd θ is the ngle between the contct zone edge nd verticl plne running through the center of the prticle. Combining Eq. 10 nd 11 nd rewriting gives: ε + ELp P 1+ ε ε =. (1) t η π η ε Lp Lp It is convenient to rewrite Eq. 1 using: 3 3 χ = ε = 3 / (13) ( Lp ) η Lp τ = (13b) 3E which results in: χ χ 3 P + = t τ π 1 η Lp 3 ( + χ / ). (14) Eq. 14 cn be solved numericlly nd using Eq 13, the contct zone s function of time ((t)) cn be solved. However, the key prmeter needed is the totl penetrtion s function of time. The penetrtion in relity hs two components. The first component is the penetrtion depth (h*) due to the contct zone nd the geometry of the prticle (see Fig. 13) with the result: h* = (15) The second component is due to the fct tht the bseline surfce is lso displced wy from the contct zone (see Fig. 13b). Hunter [] nd Ting [3] hve shown pproches to ccount for the surfce displcement. Ting s pproch provides n nlyticl expression for the totl displcement in terms of the contct zone rdius nd cn be pplied to high strin which is given by:

16 ( ) > < + = r for r t r r t r r t t t r r t t t r for r t t t t r h ) ( ) ( ln 1 ) ( ) ( ln ) ( 1 ) ( sin ) ( ) ( ln ) ( ) ( ln ) ( ), ( 1 π π π (16) where r is rdil distnce wy from the center of the prticle. Now consider rogue prticle penetrting into the lp s described in Fig. 13. The prticle would penetrte until the lod subsides in the prt nd hs essentilly penetrted distnce: ) ( bse f h =. (17) Hence 4 µm rogue prticle will t most penetrte 3.5 µm, becuse the dimeter of the Ceri slurry is 0.5 µm. The totl penetrtion s function of time cn now be clculted using Eqs. 13, 14 nd 16. Using the known properties of the polyurethne pd (E= 100 MP; η= Poise) [4], nd ssuming lod of 1 N (in the rnge needed to cuse brittle scrtches), the penetrtion of the rogue prticle s function of time ws clculted for smples P3, nd P6-P9. The results re shown in Fig. 14. The model predicts penetrtion times tht re longer for lrger rogue prticles. For the rogue prticles in the rnge 4-0 µm penetrtion times of 1-5 msec re clculted. Both of the bove results re consistent with the experimentl dt. Notice in Fig. 14b tht the 45 µm prticle does not completely penetrte t low lods. It is useful to consider figure-of-merit (FOM) which would determine if sphericl prticle would rech n equilibrium depth or penetrte the dimeter of the rogue prticle. Consider the cse where the prticle reches equilibrium, the strin rte in Eqs. 1 or 14 goes to zero. ewriting gives n expression for the equilibrium strin (ε ) s: E P 3 1 π ε ε = + (18) ewriting Eq. 11 gives n expression n expression for the equilibrium contct zone : 1 + = ε ε (19)

17 Similrly, the equilibrium penetrtion (h ) cn then be determined in terms of using Eq. 16 evluted t r=0: 1+ h = ln 1 By combining Eq. 18-0, the equilibrium penetrtion is solely dependent on the stress prmeter P ( α = ) on the right hnd side of Eq. 18. Figure 15 shows plot of equilibrium strin (ε ), π E normlized equilibrium contct zone ( /), nd the normlized equilibrium penetrtion (h /) s function of stress prmeter (α) clculted using Eqs This set of globl curves shows the equilibrium condition t long times. For the specific cse of the rogue prticles, the rogue prticle will ber the lrge lod until is penetrtes roughly the dimeter of the prticle. In other words, this is until h/~ (for cses where the rogue prticle rdius >> bse prticle rdius). This point is reched when the stress prmeter reches vlue of Hence for vlues of the lod prmeter greter thn 3.64, the prticle will rech is mximum penetrtion; for vlues of <3.64, nd equilibrium penetrtion will be reched before full penetrtion of the prticle. In the ltter cse, the scrtch length will lwys be infinite. Another interesting point is tht t n α of 3.64, the strin will be 3.88 nd the normlized contct zone will be (0) The nlysis described bove cn be used to estblish more simple, time dependent solution for the cse of the rogue prticle. ewriting Eq. 14 in terms of τ nd α one finds: χ χ α + = t τ τ 3 ( 1+ χ / ) The solution to Eq. 1, evluted t the mximum strin of 3.88 is shown in Figure 15b. This plot which is portryed s normlized time vs lod prmeter is globl plot to determine the time of penetrtion of rogue prticle for given lod, prticle size, nd lp properties (viscosity, modulus). When α is incresed (higher lods nd/or smller prticles), the time for penetrtion decreses. Although this plot ws determined numericlly, this globl plot cn be described nlyticlly by the following simple expression: ( ) log( α ) (1) log t + ()

18 for vlues of α greter thn 4. ewriting in terms of scrtch length nd mteril prmeters gives: L s v η 8.9 (b) P where <v> is the verge reltive velocity of the prticle reltive to the optic surfce. Using Eq. b or just by performing the numericl clcultion of Eqs. 18-0, the crck lengths were clculted t lods of 1 N nd 5 N (in the rnge needed to cuse scrtches) nd compred to the mesured scrtch lengths in Fig. 16 s function of rogue prticle size. The brs in the mesured dt represent 80% of the distribution of scrtch lengths observed. Note tht the dt is bound within the lod rnge of 1-5 N. Also, the stress prmeter vlue of 3.64 is reched t nominl size of 30 µm for lod of 1 N. Above this size, the model predicts infinitely long scrtches (i.e. scrtch lengths extending to the edge of the workpiece); gin consistent with the experimentl dt where the 45 µm prticles led to infinitely long scrtches. Eq. b is serves s simple expression tht cn be used to determine the length of the scrtch bsed on the size of the rogue prticle, lod, kinemtic nd mteril properties of the lp. The vlidity of the viscoelstic mechnism for scrtch length cn be exmined semiquntittively by plotting the scrtch length not only s function of rogue prticle size, but s function of number of other prmeters such s lp viscosity (determined either by temperture or lp mteril used) or nd pplied pressure. These results re summrized in Fig. 17 nd in Tble. In the cse for the lp mteril (Sub 550, IC1000, or Pitch), the scrtch length ws observed to increse with increse in lp viscosity. Also, the temperture of the lp influenced the scrtch length. As the temperture ws incresed, the lp viscosity decresed nd scrtch length decresed. Finlly, s the pplied pressure ws incresed, the scrtch length ws found to decrese. All of these trends re consistent with the viscoelstic mechnism for explining scrtch lengths. 5. CONCLUSIONS The distribution nd chrcteristics of surfce crcking (i.e., sub-surfce dmge or SSD) formed during grinding & polishing fused silic glss in the presence of rogue prticles (i.e. lrger

19 prticles thn the men size of the nominl grinding/polishing medi) ws investigted. The ddition of rogue prticles during grinding reveled tht smll mount of rogue prticles (>10-4 rogue frction) is enough to noticebly increse both the SSD depth nd the removl rte. The ddition of rogue prticles during polishing reveled tht: 1) the efficiency by which rogue prticles cn led to scrtching is strongly dependent on the size of the rogue prticle nd wekly dependent on the concentrtion for most of the rogue concentrtions; ) the length nd width of the scrtches both increse with the size of the rogue prticle nd re essentilly independent of the rogue prticle concentrtion; 3) t the highest rogue prticle size (45 µm) nd t the very high rogue concentrtions for the 4 µm dimond, the number density of scrtches increses by orders of mgnitude, the scrtch lengths re the length of the optic (qusi infinite) nd the nture of the scrtches re ll plstic in nture. The ltter two effects re well described using simple model which relies on the time needed for rogue prticle penetrtion into viscoelstic lp. A simple reltion resulting from the model (Eq. b) llows one to estimte the scrtch length bsed on the viscoelstic properties of the lp nd size of the rogue prticle. 6. EFEENCES [1] G. Beilby, Aggregtion nd Flow of Solids, Mcmilln & Co. London (191). [] L. Cook, J. Non-Cryt. Solids 10 (1990) 15. [3] L. Smuels, Metllogrphic Polishing by mechnicl methods, nd Ed, Elsevier, New York (1971). [4] B. Lwn, Frcture of Brittle Solids- Second Edition Cmbridge Solid Stte Science Series (1993). [5] I. Hutchings, Tribology: Friction nd Wer of Engineering Mterils, Butterworth/Heinmnn (199). [6] E. binowicz, Polishing Scientific Americn 18 (1968) 91. [7]. Komnduri, D. Lucc, Y. Tni, Technologicl Advnces in Fine Abrsive Processes Annls CIP 46 (1997) 545. [8] Q. Lou, S. mrjn, S. Bbu, Modifiction of Preston Eqution for the Chemicl Mechnicl Polishing of Copper, Thin Solid Films 335 (1998) 160. [9] M. Swin, Proc.. Soc. London A, 366 (1979) 575.

20 [10] K. Li, W. Lio, Surfce/subsurfce dmge nd the frcture strength of ground cermics, Journl of Mterils Processing Technology 57(1996) [11] Y. Ahn, J. Yoon, C. Bek, Y. Kim, Chemicl mechnicl polishing by colloidl silic-bsed slurry for micro-scrtch reduction, Wer 57 (004) 785. [1] G. Bsim, J. Adler,. Singh, B. Moudgil, Effect of prticle size of chemicl mechnicl polishing slurries for enhnced polishing with miniml defects, J. Electrochem. Soc. 147:9 (000) 353. [13] C. Kllingl, D. Duquette, S. Murrk, An investigtion of slurry chemistry used in chemicl mechnicl plnriztion of luminum, J. Electrochem. Soc. 145:6 (1998) 074. [14] T. Surtwl, L. Wong, P. Miller, M. Feit, J. Menpce,. Steele, P. Dvis, D. Wlmer, Subsurfce mechnicl dmge distributions during grinding of fused silic, J. Non-Cryst. Sol. 35 (006) [15] J. Menpce, P. Dvis, L. Wong, W. Steele, T. Surtwl, P. Miller, Mesurement of Process-dependent subsurfce dmge in Opticl Mterils using the MF technique SPIE 5991, Boulder Dmge Symposium XXXVII (005). [16] P. Miller, T. Surtwl, L. Wong, M. Feit, J. Menpce, P. Dvis,. Steele, The distribution of subsurfce dmge in fused silic, SPIE 5991, Boulder Dmge Symposium XXXVII (005). [17] M. Feit, A. ubenchik, Influence of subsurfce crcks on lser induced surfce dmge, SPIE 573 (003) [18] F. Preston, Structure of brded surfce glsses, Trns. Opt. Soc. 3(3) (19). [19] E.H. Lee nd J.. M. dok, Contct problem for viscoelstic bodies, J. Appl. Mech., (Sept. 1960). [0] M. Oyen, Sphericl indenttion creep following rmp loding, J. Mter. es (Aug. 005). [1] M.V. Kumr nd. Nrsimhn, Anlysis of sphericl indenttion of liner viscoelstic mterils, Current Sci. 87, (Oct. 004). [] S.C. Hunter, The Hertz problem for rigid sphericl indenter nd viscoelstic hlf spce, J. Mech. Phys. Solids, 8, (1960). [3] T.C.T. Ting, The contct stresses between rigid indenter nd viscoelstic hlf-spce, Trns. ASME J. Appl. Mech. 33, (1966).

21 [4] Vlues from H. Lu Mterils Chrcteriztion 49 (003). ACKNOWLEDGEMENTS Work performed under the uspices of the US Deprtment of Energy by UC, Lwrence Livermore Ntionl Lbortory under contrct No. W-7405-ENG-48 with the LDD progrm. The uthors would like to thnk Ed Lindsey for SEM imges of the dimond prticles.

22 Tble 1: Summry of results from rogue prticle ddition during Al O 3 loose brsive grinding on glss lp. Smple Bse Prticle Size (µm) ogue Prticle Size (µm) Weight % rogue prticles ogue prticle rel density ogue prticle frction (by number) emovl rte SSD depth Men Crck Length Weighted roughness PV roughness Averge Lod/ Prticle Surfce density (x10 5 ) Mximum crck length (µm) (µm) - (#/cm ) - (µm/hr) (µm) (µm) (µm) (µm) (N) (cm - ) (µm) G G G G * G * G * G * G * G , Tble : Summry of results from rogue prticle ddition during 0.5 CeO polishing on polyurethne pd or pitch. Smple ogue prticle ogue prticle size ogue prticle rel density Pressure Temperture Pd Mteril Scrtch number density Averge scrtch length Averge scrtch width Brittle Scrtch Type Plstic + Brittle Plstic (µm) (#/cm ) (psi) (C) (#/cm ) (µm) (µm) (%) (%) (%) P1 dimond PU P dimond PU P3 dimond PU P4 dimond PU P5 dimond PU 98 Across optic P6 dimond PU P7 dimond PU P8 dimond PU P9 dimond PU P10 dimond PU 3000 Across optic P11 dimond pitch , P1 dimond pitch P13 dimond pitch P14 dimond IC P15 dimond pitch P16 dimond pitch P17 ASTM 13 10, pitch Urbn dust P18 Pitch 0* pitch P19 Dried ceri pitch T = room temperture, uncontrolled; PU= polyurethne pd; *Pitch prticle hs lrge spect rtio mesured verge ws 0 µm x 80 µm

23 Figure 1: Schemtic illustrting the steps in the wedge technique to determine SSD depth distributions. () (b) (c) Figure : Photos of the () grinding nd (b&c) polishing setups.

24 Frctionl distribution (µm -1 ) Microgrit 9T Microgrit 15T Prticle Size (µm) () Microgrit 30T Frctionl Distribution (µm -1 ) µm Ceri Dimond 4 µm 6 µm 10 µm 15 µm 0 µm Prticle Size (µm) (b) 45 µm Figure 3: () Prticle size distributions of the Al O 3 slurry used in the grinding experiments; nd (b) prticle size distributions of the cerium oxide slurry nd rogue dimond prticles dded during the polishing experiments. Dt from mnufcturer literture.

25 G: 15 µm G5: 15 µm µm G7: 15 µm µm 890 µm G8: 15 µm µm G9: 15 µm µm G3: 30 µm Figure 4: Microscope imges of the triling indent crcks observed on the ground smples prepred with 15 µm nd 30 µm loose brsives nd vrious mixtures. The imges were tken long the wedge of the smple (i.e. representtive of the crck density just below the surfce).

26 Obscurtion 10 0 G1: 9 µm G: 15 µm G3: 9 µm + 15 µm Crck Depth (µm) () Cumultive Crck Length Distribution G1: 9 µm G: 15 µm G3: 9 µm + 15 µm Crck Length (µm) (b) Obscurtion G: 15 µm 10 0 G5: 15 µm + 0. cm - 30 µm G6: 15 µm + cm - 30 µm 10-1 G7: 15 µm + 0 cm - 30 µm G8: 15 µm + 00 cm - 30 µm G9: 15 µm cm - 30 µm 10 - G3: 30 µm Crck Depth (µm) Cumultive Crck Length Distribution G: 15 µm G5: 15 µm + 0. cm - 30 µm G6: 15 µm +.0 cm - 30 µm G7: 15 µm + 0 cm - 30 µm G8: 15 µm + 00 cm - 30 µm G9: 15 µm cm - 30 µm G3: 30 µm Crck Length (µm) (c) (d) Figure 5: () SSD depth distribution nd (b) crck length distribution of the fused silic surfce fter loose brsive grinding with 9 µm, 15 µm, nd 9 µm contminted with 15 µm lumin prticles; (c) SSD depth distribution nd (d) crck length distribution of the fused silic surfce fter loose brsive grinding using 15 µm, 30 µm, nd 15 µm contminted with 30 µm lumin prticles. The lines re curve fits using the model described in ref [14].

27 Mesured SSD Depth (µm) µm + 30 µm rogue 9 µm µm rogue 10 SSD of 5 9 µm ogue Prticle Frction () SSD of 30 µm SSD of 15 µm emovl te (µm/min) Frction of rogue prticles (b) Figure 6: () Mximum SSD depth s function of rogue prticle concentrtion (of 15 µm or 30 µm lumin reltive to the SSD observed on the 9 µm nd 15 µm loose brsive grinding without the ddition of rogue prticles. The solid line without dt points represents the model described by Eqs. 8 & 9 in Section 4.1. (b) Mesured removl rte of the 15 µm loose brsive grinding s function of the rogue 30 µm concentrtion.

28 Plstic Abrsive Wer Mixed Brittle frcture / Plstic Abrsive Wer Brittle Frcture Sleek Sleek + lterl frcture Sleek + triling indent frcture Sleek + triling indent + lterl frcture Triling indent frcture Triling indent + lterl frcture 19 µm Figure 7: Ctegories of different type of scrtches observed in smples P1-P19.

29 4 µm dimond 6 µm dimond 10 µm dimond 10 µm 10 µm 10 µm 15 µm dimond 0 µm dimond 45 µm dimond 10 µm 50 µm 40 µm Figure 8: SEM imges of dimond prticles used s the rogue prticles for smples P-P10.

30 Scrtch # density (cm - ) Brittle Mixed Plstic ogue Prticle Size (µm) () Scrtch density (#/cm - ) Brittle Mixed Plstic ogue Concentrtion (cm - ) (b) Scrtch Length (µm) Scrtch Length Scrtch Width ogue Prticle Size (µm) (c) Scrtch or sleek width (µm) Scrtch length (µm) Scrtch Length Scrtch Width Sleek Width ogue Concentrtion (cm - ) (d) Scrtch or sleek width (µm) Figure 9: Scrtch number density observed fter ceri polishing of fused silic with rogue dimond prticle ddition s function of: () rogue prticle size t fixed rogue prticle concentrtion of 50 cm - ; nd (b) rogue prticle concentrtion t fixed rogue prticle size of 4 µm. Scrtch dimensions (length, width) observed fter ceri polishing of fused silic with rogue dimond prticle ddition s function of: (c) rogue prticle size t fixed rogue prticle concentrtion of 50 cm - ; nd (d) rogue prticle concentrtion t fixed rogue prticle size of 4 µm. The dt re from smples P-P10 described in Tble.

31 (b) (c) Figure 10: () Typicl scrtch observed on polished surfce upon ddition of 10 µm dimond prticles (P); (b) typicl scrtches observed on polished surfce upon the ddition of 45 µm dimond prticles (P10). The horizontl full scle on ech imge is 37 µm.

32 1.0 Cumultive Distribution P3: 4 µm P6: 6 µm P7: 10 µm P8: 15 µm P9: 0 µm Scrtch Lengths (µm) () 1.0 Cumultive Distribution T = 3.8 o C T = 7.7 o C T = 31.6 o C Scrtch Length (µm) (b) Figure 11: () Cumultive scrtch length distribution mesured for ceri polished smples with rogue prticles of different sizes nd constnt rogue dimond concentrtion of 50 cm -. The verge crck lengths determined from these distributions re reported in Figure 9c. (b) Effect of pitch temperture on the scrtch length distribution during pitch polishing with 0.5 µm Ceri nd 6 µm rogue dimonds t 50 cm - concentrtion.

33 () (b) Figure 1: Schemtic of proposed mechnism for explining the length of scrtch by rogue prticle on viscoelstic lp.

34 P Elstic sphericl indentor θ ( - ) 1/ h* Viscoelstic substrte () P Elstic sphericl indentor h h* Viscoelstic substrte (b) Figure 13: Schemtic illustrting the penetrtion of hrd sphericl prticle into viscoelstic substrte () without surfce displcement nd (b) with surfce displcement.

35 0 4 Penetrtion, h (µm) µm 14 6 µm 10 µm µm 18 0 µm 0 45 µm Time, t (µm) () 0 Penetrtion, h (µm) µm; 0.1 N 45 µm; 1 N 45 µm; 5 N Time, t (msec) (b) Figure 14: () Clculted depth of prticle penetrtion using Eqs s function of time for different size rogue dimond prticles; (b) Clculted depth of prticle penetrtion using Eqs s function of time for different lods.

36 6 8 8 Strin (ε ) Normlized contct zone ( /) Normlized Penetrtion (h /) ε / h / ε=3.88 h/=.0 /=0.97 α= () α 1 t /τ α (b) Figure 15: () Clculted equilibrium strin (ε ), normlized contct zone ( /), nd penetrtion (h /) s function of the stress prmeter (α); (b) Clculted normlized time for complete prticle penetrtion of rogue prticle into the lp t criticl strin of 3.88 s function of the stress prmeter (α). The line in (b) represents single exponentil fit to the clcultion for α>4.

37 Dt 1 N 5 N α= 3.64 Scrtch Length (µm) Finite scrtch lengths Infinite scrtch lengths ogue Prticle Size (µm) Figure 16: Averge scrtch length mesured s function of rogue prticle size (sme dt shown in Fig. 9c) compred with the simple viscoelstic model t two different lods of 1 N nd 5 N. Note the brs on the dt point represent the 80% of the distribution of scrtch lengths observed. Averge Scrtch Length (µm) Dimond Prticle Size (µm) Applied Pressure b (psi) Lp Mteril Viscosity c (Poise) Lp Temperture d ( o C) Figure 17: Averge scrtch length mesured s function of system vribles explored in this study (dimond prticle size (P3, P6-P9); pplied pressure (P11-13); lp mteril (P1,P15-P16); Lp (pitch) temperture (P11-P13).