3D TRANSIENT THERMAL MODELLING OF LASER MICRO-CHANNEL FABRICATION IN LIME-SODA GLASS. A. Issa, D. Brabazon and M. S. J. Hashmi

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1 3D TRANSIENT THERMAL MODELLING OF LASER MICRO-CHANNEL FABRICATION IN LIME-SODA GLASS A. Issa, D. Brabaz ad M. S. J. Hashmi Schl f Mechaical ad Maufacurig Egieerig, Dubli Ciy Uiversiy, Irelad, ahmed.issa@mail.dcu.ie; derm.brabaz@dcu.ie ABSTRACT Laser-fabricaed micrchaels i glass ffer a wide rage f biegieerig ad elecmmuicai applicais. A 1.5 kw CO laser wih 10.6 µm wavelegh was used i his sudy fabricae micrchaels he surface f sda-lime glass shees. A hermal mdel f he prcess was develped based rasie hea cduci due a pulsed hea ipu. The resulig equai prediced he emperaure disribui i he regis surrudig he laser fcus. Temperaure ime curves were draw frm hse equais, which were useful i esimaig he hermal hisry i he prcessed samples. The emperaure disribui was als used predic he chael gemery (based he vaprisai emperaure f glass). Ms f he laser pwer used was csumed i brigig he glass he vaprisai emperaure. The mdel was able predic he chael widh, deph ad surface rughess. These laser-fabricaed chael characerisics were measured ad cmpared he resuls baied frm he hermal mdel. The laser pwer, frequecy, pulse widh ad raslai speed were he crl parameers i bh sudies; hece a direc cmparis was esablished bewee he mdel ad he experimeal resuls. KEYWORDS: CO laser, glass, micrchaels, hermal mdellig 1. INTRODUCTION Glasses absrb laser radiai i a way ha depeds highly he icide wavelegh [1, ], ms raspare maerials are paque i he visible regi bu absrb srgly a r ear 10 µm, which makes CO laser very efficie fr machiig hese maerials [1, 3]. Laser-iduced plasma will als ehace he cuplig f laser radiai he maerial s surface raisig is emperaure he vaprisig emperaure a abu 3500C [4], which is sufficie ablae he maerial frm he irradiaed regi. This ca be accmplished despie he fac ha glasses may i sme cases reflec up 30% f he icide laser radiai [3]. Micr-chael fabricai, he surface r i he bulk f glass shees is widely used i varius applicais such as elecmmuicai, pical ad bi-medical egieerig [5, 6]. Sme sudies [7, 8] have ivesigaed irradiaig glass samples repeaedly alg he same pah ivesigae he effec f he amu f radiai depsii he micrchael fabricai. Hwever, such sudies use maily fixed peraig parameers. If hermal mdellig f he laser hea depsii is used, he i is pssible esimae he resulig effecs he maerials [1, 9]. I ca be useful esimae he emperaure rages ad hermal sresses ha he maerial is expeced experiece befrehad. This sudy cvered he mdellig ad he prduci f sigle micrchaels. Hwever, he cceps ad resuls preseed are exedible cver her D ad 3D micrchaels. The mdel ad priciples

2 preseed i his paper are als applicable meallic maerial prcessig ad hea reame usig pulsed laser irradiai.. THE THERMAL MODEL Hea cduci prblems i a medium ca be expressed i erms f parial differeial equais f emperaure wih respec space ad ime. The geeral frm f he hea cduci equai, prvided ha here is hea geerai i he medium ad ha all he hermal prperies are csas [10]: T T T T c p k (1) x y z where, (kg/m 3 ), c p (J/kg.C), k (W/m.C) are he desiy, hea capaciy ad hermal cduciviy f he maerial respecively. If he medium is mvig wih a csa velciy U parallel he x-axis, as shw i figure 1, he equai (1) becmes [10]: T T T T T U () x x y z where, (m /s) is he hermal diffusiviy f he maerial, equal k / c p. Figure 1: Hea pi surce i he surface f he wrkpiece. Slvig equai () gives a rasie hea r emperaure disribui i he medium i he frm T(x,y,z,). Hwever, he slui is uique all cases ad depeds a umber f assumpis, iiial cdiis ad budary cdiis. The assumpis made i his wrk fr he slui are: 1- The iiial emperaure is equal he ambie emperaure T(x,y,z,0) = T. - The medium is a slab f w parallel plaes ad hea eers frm e plae a z = 0. This slui is a hea cduci e, i requires ha here is hea lsses frm he medium a is w plaes, i.e. T / z There are phase chages i he medium. Alhugh he slui des explicily iclude he lae hea effecs, i is sill useful i esimaig he peerai f he melig isherms uder he cdiis f melig via cduci [1]. 4- The medium is a semi-ifiie slid, meaig ha he emperaure variais i he regi f ieres d affec he emperaures i regis csidered be far a way frm i, such as he

3 bm plae. This assumpi has bee verified by applyig he same cdiis differe hickesses ad geig he same resul. Based hese assumpis, equai () ca be slved fr a pulsed laser surce, wih a pulse repeii frequecy (RF) give i pulses per secd (Hz). The icide laser beam is mdelled as a ime-depede pi hea surce a (0,0,0). The slui f equai (), shw i equai (3), is based he impigeme f emperaure harmics a slab f maerial [9, 10]. 4 1 exp ) ( ),,, ( U i r x U i r k T z y x T (3) where, () is he ime depede pwer ipu, is he fudameal frequecy f he pwer ipu =.RF, ad r is he radial disace frm he pwer surce = z y x. The square r ake i equai (3) mus be he psiive real par. A pulsed laser pwer ipu as he e shw i figure is be used. This pwer surce has a perid = 1/RF ad is give i he ierval -½ < ½ by where, (W) is he average pwer ad τ (s) is he pulse widh. Figure : The pulsed pwer ipu give by equai (4). The i is pssible express his pwer sigal i erms f a Furier series f he frm 1 1 exp Re cs ) ( i a a (4) i which, d a / / cs = d / / cs = / / si = si si = si hus, () = / τ < ½ τ 0 ½ τ < < ½ / τ herwise

4 ( ) 1 1 si.re exp i (5) Subsiuig 5 i 3 gives T( x, y, z, ) T k U exp x r r 1 U si Re exp i x r 1 i Si k r 1 which whe akig he real pars f he expeial ad he square r gives T ( x, y, z, ) T k k r 1 U exp x r r 1 U si exp x r S U r Si cs 4 S where, Si (8 ) /( U ), is Sim s umber ha characerises a peridic slui wih perid ad was subsiued i equai (3), ad S [1 1 Si ]/. Oher mehds f baiig sluis similar equai (6) are give usig Furier series ad Laplace rasfrm [10]. Equai (6) was used calculae he emperaure disribui i he wrkpiece, T(x, y, z, ), based he pwer, RF, pulse widh ad sample maerial raslaial speed as he prcess parameers. 3. EXERIMENTAL WORK Tw millimere hick cmmercial sda-lime glass shees were used i his wrk. A 1.5 kw CO laser beam was fcused usig a 17 mm fcal legh les a sp diameer f apprximaely 90 m he surface f he samples ad delivered via a zzle wih a air je a e bar. Chaels f 15 mm i legh were prduced. The laser pwer (), pulse repeii frequecy (RF), pulse widh (τ) ad scaig speed (U) were chse as he prcess crl parameers. Afer prducig he chaels he samples were laer he same day waer washed ad air je dried. A gld caig was he applied i rder faciliae laser scaig f he samples. A hree dimesial prfile fr each chael was geeraed by scaig a 50 m legh seci f each chael a a reslui f 1.95 m i he laeral direcis (x ad y) ad 0.5 m i he heigh direci (z) [11]. Each chael was scaed a he same psii, 10 mm frm he sar f he chael. The chael parameers measured frm hese prfiles were chse be he widh (m), he deph (m) ad he surface rughess, Ra, (m). Three measuremes were made ad averaged fr each parameer. The surface rughess (Ra), ake alg he same direci as he chael axis, was measured alg he bm f he chael ad half way up eiher side f he chael. The Ra measureme ca be paricularly sigifica i fluid flw ad (6)

5 wave guide applicais. All measuremes were perfrmed usig a sfware cde buil specifically fr his sudy. 3.1 rcess csiderais The weigh perceage f sda-lime cmpes used i his wrk were ake as 73%SiO -15%Na O-7%CaO-4%MgO-1%Al O 3. The desiy was ake as = 500 kg/m 3, he hea capaciy was ake as C p = 870 J/kg. C ad he hermal cduciviy as k = 1.06 W/m. C, which give a hermal diffusiviy value f = m /s []. Based he laser iesiy rage used i his wrk ( MW/cm ), he plasma frmed is a laser-suppred cmbusi plasma (LSC). Durig he iiial sages f he pulse, LSC plasma sars frm, shieldig up 90 % he icide pwer frm he arge [4]. Hwever, as he plasma begis expad radially, he cupled eergy icreases 50% [4, 1]. The radiaive lsses i his plasma scheme are ypically 15 0% f he icide pwer. There is a sigifica amu f eergy csumed raise he glass is melig ad csequely is vaprisai emperaure. These amus f eergies are called he lae hea f melig ad vaprisai, respecively. Simple calculais ca shw he amu f eergy eeded raise he fcal vlume he vaprisai emperaure. The amu f hea required reach he vaprisai emperaure, T v, equals C p.(t v - T ) = 870.(347 - ) =,96,350 J/kg. The amu f hea required raise he emperaure f he vapur apprximaely 10 imes he vaprisai emperaure, T s, was als calculaed. This allwed a apprximai f he eergy required ablae he maerial i rder frm he chael, as per he prcedure fllwed by her wrkers [4]. This eergy was calculaed as C p.(t s - T v ) = 870.( ) = 6,833,410 J/kg. The scale legh f diffusi was baied frm, L D., where ad τ are he hermal diffusiviy ad he laser pulse widh. The average pulse widh used i his wrk was ms, s ha L D = 7. 3 µm was he average deph affeced by he hea wave diffused per a sigle pulse. The vlumeric mass ha will be affeced by his hea wave ca be calculaed frm, m.. r. LD, where r is he laser beam s radius. The average heaed mass, m, was equal kg. This mass was muliplied by he w lae hea f diffusi values calculaed abve, which gave he amu f eergies required brig his irradiaed vlume is vaprisai emperaure ad he beig ablaed. These were 1.87 mj fr heaig he vlume is vaprisai emperaure ad mj fr ablai. I his sudy he laser beam s pwer,, was varied bewee 18 ad 30 W, ad he pulse repeii frequecy, RF, was varied bewee 160 ad 400 Hz, his resuled i miimum ad maximum pulse eergies f 45 ad mj respecively. Table 1 liss he miimum ad maximum pulse eergies prduced i his sudy ad he miimum perceages f hese eeded fr breakdw. Table 1: Relaive breakdw eergies. Exp. eergy (mj) % Fr heaig % Fr ablaig % Tal The breakdw hreshld eergy, E h, was bserved a 45 mj, which crrespded a fluece, h E h /. r = J/cm. A chael ha was used ideify he breakdw hreshld i his wrk is shw i figure 3 (a). The surface cracks i his figure were prduced usig = 18 W, RF = 400 Hz ad U = mm/s, which crrespds he firs rw i able 1. The srucural chages i his image sugges ha abu 8% f he icide pwer was

6 ecessary iiiae ablai; he remaider f he pwer was shielded by he iduced plasma. A higher flueces, wider ad deeper srucural chages, as shw i figure 3 (b), were prduced. This chael was prduced usig = 30 W, RF = 160 Hz ad U = mm/s. These seigs crrespd he secd rw i able 1. The larger dimesis i he chael i figure 3 (b) sugges ha mre ha 6.91% f he eergy was cupled he sample. The larger pulse durai frm he prcessig parameers prduce he chael i figure 3 (b) wuld be expeced allw ime fr he hea diffuse ad furher eergy be cupled he arge [4, 1]. (a) (b) Figure 3: SEM image f chaels prduced a (a) miimum ad (b) maximum fluece seigs. Based he al perceages i able 1, plasma shieldig hery, radiaive lsses assciaed wih he LSC plasma scheme, ad simulai rial ad errr prcedures experimeal daa, a average 5% f he icide beam s pwer was calculaed as beig delivered he sample. This 5% f he icide pwer was used fr slvig he hermal mahemaical mdel. Based he pulse eergy rage shw i able 1, he mahemaical mdel wuld i sme cases, ver-esimae r uder-esimae he chael dimesis. This wuld affec he prediced chael shape; hwever, i has implicily reduced he cmplexiy f aalysis cmpared akig phase chages i accu i he mahemaical mdel [1]. 3. Mehd f calculais All he calculais ad graphical displays were perfrmed wih a umber sfware cdes buil fr his sudy. T slve equai (6), he laser pwer surce was assumed be a (0,0,0) fr all isaces f ime. Sice he wrkpiece is raslaed i he x direci a a csa velciy f U, he x values chage wih ime based a Eularia crdiae, accrdig x = a + *U, where, a, is he iiial x lcai ad,, is he ime elapsed sice he begiig f raslai [9] laar isherms Fr each z-plae, he ime ad he y isaces were eeded slve equai (6). Hece, a D mesh i ime ad space (, y) was csruced. The firs eleme is he pulse durai, = 1/RF, which als crrespds he x-axis values, as meied earlier. The secd eleme f he mesh was a sufficiely large value f y cver half f he chael widh, sice he slui is symmeric abu he y-axis, his als saved aalysis ime. Slvig fr a csa value f z ad seig x = 0 whe = 0 prduced he isherms i ha plae. The slui value a each mesh pi was idepede f he mesh size. Figure 4 shws he prediced isherms f hree pulses a plae z = 0 usig = 4 W, RF = 8 Hz, τ = ms, ad U = 5 mm/s. The mesh was geeraed fr = 0 = 0-1/8 = ( ms) ad y = m. Ierai sep sizes i

7 he x-axis were 0.37 m. The sep sizes i he y-axis were 1 m. The resulig isherm was refleced abu he y-axis give he full chael widh. The slui is peridic i ime, s ha slvig fr e pulse durai,, was sufficie calculae he hermal prfile ifrmai which culd he be repeaed fr he prceedig pulses. The emperaure eded ifiiy as y apprached 0, s fr his paricular simulai he emperaures were rucaed a 0,000 C. The daa cursrs he isherms i figure 4 shw deails f lcai ad emperaure (x,y,t) a w pis. These pis are f paricular imprace as hey are he isherm f vaprisai a a emperaure arud 3500 C. Figure 4: Isherms f hree pulses a z=0, (a) p view, (b) 3D emperaure prfile. 3.. Thermal hisry Equai (6) ca als be slved predic he hermal hisry f specific pis i he plae f ieres. This ca be useful i mirig hw he emperaures chage a hse pis ver a perid f ime which exceeds he pulse durai ad eables he sudy he heaig ad clig raes which ca be useful i esimaig he resulig micrsrucures due laser irradiai. Figure 5 shws he hermal hisries f he same sample as i figure 4, fr fur pis a y = 10, 150, 500 ad 1000 m. The iiial x crdiae was se s ha i crssed he laser pi surce a = 0. secds. The emperaures were calculaed fr a al ime f secds s a he raversig speed f 5000 µm/s he y pis were a perpedicular disace f 9000 m behid he laser pi surce. Temperarue ( C) Y = 10 μm Y = 150 μm Y = 500 μm Y = 1000 μm s s s 0.73 s Time (s) Figure 5: Thermal hisries f 4 pis he surface f glass shee.

8 The maximum emperaure a pi y = 10 m ccurred a he rucaed 6,000 C. The maximum emperaures were reached a 0.1, 0., 0.34 ad 0.73 secds fr he pis y = 10, 150, 500 ad 1000 m, respecively. This idicaes ha subsaial ime durai is required fr he hea be diffused as we mve far frm he hea surce. The emperaure falls belw 3500 C as he y value becmes mre ha m. This ca als be ed frm he isherms i figure 4. I ca als be ed ha he clig raes are differe fr he fur pis i figure 5, his may be used predic he resulig micrsrucure i hse regis Chael 3D gemery As explaied earlier i 3..1, he mdel calculai prcedure was repeaed fr all values f z uil he maximum levels f emperaure fall belw a desired value, usually ±T v s ha he chael gemery ca be prediced. The gemery f he chael was prediced by baiig he x, y ad z crdiaes a which he emperaures were a T v frm plaar isherms spaced apprximaely 1 m apar ad raged bewee z = 0 ad he deph f he chael. The chael widh, deph ad surface rughess were als calculaed frm hese prediced gemeries usig he same prcedure perfrmed he experimeal scas. 4. Resuls ad cmparis The prediced values fr chael widh, deph ad rughess are lised i able wih he crrespdig experimeal values. The resuls shw i able were seleced frm a desig f experimes ha cvered he rage f prcessig parameers examied i aher sudy [13]. These experimeal values were ake validae ad cmpare hem wih he prediced values frm he hermal mahemaical mdel.the effecs f, RF ad U were sudied he resulig widh ad deph f he chaels [14]. I was fud ha he had a direc prprial effec, while RF ad U had a iverse prprial effec he chael dimesis. Ch. N. Table : Lis f micrchael prcessig parameers icludig mdel ad experimeal values fr chael widh, deph ad rughess. (W) RF (Hz) τ (ms) U (mm/s) Widh Deph (m) (m) Ra (m) Mdel Experime % Differece Mdel Experime % Differece Mdel Experime % Differece Chael parameers The maximum errr i widh predici was % i he case f chael 1. The maximum deph predici errr was -30 % fr chael 1. Havig he highes pulse eergy, chael 1 predici errr agrees wih he hery, ulied earlier ha, a higher flueces, he delivered eergy is larger ha 5% f he icide laser beam. Furhermre his case, bh widh ad deph errrs are i agreeme idicaig ha he mdel is uder-esimaig he acual resuls. These predici errrs have affeced he accuracy f shape predici as explaied i he ex seci. The errrs i rughess predici are sigificaly high due he small scale f he parameer beig measured. Chael rughess values baied frm his sudy were i he

9 rage f 1 µm, ad i realiy his parameer depeded mre ha he crl parameers csidered abve. I geeral mre uifrm chael shape ad dimesial were fud fr he mid rages f he prcessig parameers. This is represeed i he fac he chael dimesis prediced fr chael w were clser hse measured ha fr eiher f he her w chaels. 4. Chael mrphlgy Figures 6, 8 ad 10 shw he predicaed versus he experimeal 3D gemery f chaels 1, ad 3 respecively. These prfiles were fud repea ver he legh f he chael i he mdel ad experimeal resuls. I each case herefre, he dimesis resulig frm a sigle laser pulse were pled. The viewig agle f he 3D view was mdified shw ms f he chael parameers fr bh he prediced ad experimeal chaels. Figures 7, 9 ad 11 shw he side view f he same chaels. The resuls represe he laser depsii prpagaig alg he psiive x-axis. All axes measuremes were ake i µm ad he legh scale hese figures is he same fr direc cmpariss. The peridiciy ad gd machig f chael dimesis i hese prfiles is evide frm examiai f figures Figure 6: Chael 1, 3D views (a) prediced ad (b) experimeal sca. (uis m). Figure 7: Chael 1, side views (a) prediced ad (b) experimeal sca. (uis m).

10 Figure 8: Chael, 3D views (a) prediced ad (b) experimeal sca. (uis m). Figure 9: Chael, side views (a) prediced ad (b) experimeal sca. (uis m). Figure 10: Chael 3, 3D views (a) prediced ad (b) experimeal sca. (uis m).

11 Figure 11: Chael 3, side views (a) prediced ad (b) experimeal sca. (uis m). Figure 1 (a) shws he micrscpic image f chael 1 ad figure 1 (b) shws a simulaed chael legh equal he legh i he micrscpic image fr a direc mrphlgical cmparis. Frm he RF ad U seig used prduce his chael, i was expeced ha each laser pulse wuld cver a disace equal U/RF = 8.333/160 5 µm. I ca be bserved frm figure 1 (a) ha he chael csised f a array f helical shapes ha were peridic i aure. These shapes were ccaved ppsie he laser ablai direci, which was frm he lef he righ f figure 1 (a). The separai bewee hese shapes was, average, arud 50 µm. The simulaed chael legh cais a pl f pulse shapes, ad i cfrms he experimeal resul frm he mrphlgical perspecive. The widh scale f he simulaed chael is half he legh scale. Figure 1: Mrphlgical cmparis f chael CONCLUSION Micrchaels were prduced usig a direc wriig sigle pass laser ablai echique raher ha muliple laser passes, as was applied i previus wrk [8]. Due he crllabiliy f he prfiles fabricaed, hese micrchaels ca be desiged a priry i rder ake advaage f specific chael dimesis i applicais such as MEMS ad cell grwh. Thermal mahemaical mdellig, wih ipu parameers f maerial physical prperies, laser average pwer, pulse repeii frequecy, pulse widh ad raslaial speed, is useful i visualisig he expeced chael shape ad dimesis befre chael fabricai. Mrever,

12 such resuls may be helpful i pickig he prcess crl parameers, by viewig heir effecs he chael gemery. Larger dimesial errrs bewee prediced ad experimeal resuls were ed a he exremiies f he parameer rages ivesigaed. Hwever, eve i hese cases he mdel was sill useful i deermiig he mrphlgy f he fabricaed chaels. Refereces [1] W. W. Duley, Laser prcessig ad aalysis f maerials, leum ress, New Yrk, (198). [] N. Basal ad R. Dremus, Hadbk f glass prperies, Academic ress Ic., Orlad, (1986). [3] J. O. Isard, Surface refleciviy f srgly absrbig media ad calculai f he ifrared emissiviy f glasses, Ifrared hysics, Vl. 0 (1980), [4] L. J. Radziemski ad D. A. Cremers, Laser-iduced plasmas ad applicais, Marcel Dekker Ic., New Yrk, (1989). [5] S. Judkazis, K. Yamasaki, A. Marcikevicius, V. Mizeikis, S. Masu, H. Misawa ad T. Lipper, Micrsrucurig f silica ad plymehylmehacrylae glasses by femsecd irradiai fr MEMS applicais, rc. Ma. Res. Sc. Symp., 00, B5.5.1-B [6] K. Miura, J. Qiu, H. Iuye, T. Misuyu ad K. Hira, hwrie pical waveguides i varius glasses wih ulrashr pulse laser, Appl. hys. Le., Vl. 71 (1997), [7] S. J. Qi ad W. J. Li, rcess characerizai f fabricaig 3D micr chael sysems by laser-micrmachiig, Sesrs ad Acuars A, (00), [8] S.-C. Wag, C.-Y. Lee ad H.-. Che, Thermplasic micrchael fabricai usig carb dixide laser ablai, Jural f Chrmagraphy A, 1111 (006), [9] J. M. Dwde, The mahemaics f hermal mdellig: a irduci he hery f laser maerial prcessig, Chapma ad Hall CRC, New Yrk, (001). [10] H. S. Carslaw ad J. C. Jaeger, Cduci f hea i slids, d edii, Clared ress, Oxfrd, (1959). [11] D. Cllis, Develpme f laser based surface prfilmeer usig he priciple f pical riagulai, MEg hesis, Dubli Ciy Uiversiy, Dubli, (005). [1] Y.-Ill Lee, K. Sg ad J. Sedd, Laser-iduced breakdw specrmery, Nva Sciece ublishers, Ic., New Yrk, (000). [13] A. Issa, D. Brabaz ad S. Hashmi, rcess mdellig f micr chaels prduci usig CO laser i silica glass usig RSM, rc. f he I. Cf. Advaces i Maerials rcessig ad Techlgies (AMT), Las Vegas, 006, NII6, 103, 1-5. [14] A. Issa, D. Brabaz ad S. Hashmi. Imprveme f lime sda glass laser micrfabricai prcessig parameers usig desig f experimes, i C. Bckig, D. Jacbs ad A. Reie (eds). rc. 7 h Naial Cferece Rapid Desig, rypig ad Maufacurig (RDM), Buckighamshire-UK, 006, 9-0.