Experimental. SC Solutions, Inc. The COMSOL. cal-mechanicall. wafers. We. for semiconductor. and species transport. model was fabricated,

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1 Expermental Valdaton of Model of Eletro-Chemal-Mehanal Planarzaton (ECMP) of Copper J. L. Ebert*, S. Ghosal, D. de Roover, and A. Emam-Naen SC Solutons, In. *Correspondng author: SC Solutons, In., 161 Oakmead Pkwy, Sunnyvale, CA Abstrat: Ths paper desrbes the development of a COMSOL model of Eletro-Chem al-mehanall Planarzaton (ECMP) that was valdated wth expermental data. ECMP s an emergng tehnology for proessng of semondutor wafers. We developed a D model of flow of phosphor ad soluton (the eletrolyte) between two parallel plates, the top plate representng the pad and the bottom plate representng the wafer. By usng ths relatvely smple geometry, we were able to fous on the physs and eletrohemstry n ECMP. The model nludes steady-state opper dssoluton and speess transport nsde the eletrolyte, on transportt nludng onveton, dffuson, and mgraton, and eletrod reatons represented by the Butler-Volmerr equaton. An expermental set-up for valdatng ths ECMP model was fabrated, and experments weree onduted to measuree the anode urrent was measured at varous spatal loatons for dfferent eletrode potentals. The results of the experment and the COMSOL model were found to be n very good agreement. Keywords: ECMP, Eletro-Chemal-Mehanal-- Planarzaton, eletropolshng. 1 Introduton The goal of ths work has been the development of an expermentally-valdatedd model of the Eletro- Chemal-Mehanal Planarzaton (ECMP) proesss usng COMSOL Multphyss. ECMP [1], [] s used for semondutor fabraton for planarzng (polshng) wafers, and s onsdered to be partularly suted to planarzng low-k nteronnets at tehnology nodes of 3 nm and below. The ECMP polshng tehnque uses eletrohemal ethng and gentle mehanal aton to remove opper atoms, and has a very low down-fore that mnmzes potental for damage that s assoated wth onventonal CMP. A shemat of a gener ECMP system s shown n Fgure 1. Whle there are smulaton results from smple eletral models (wthout eletrohemstr ry) reported n the lteraturee [3], we were not able to fnd any studes nvolvng detaled, physs-based models of the ECMP proesss smlar to the one desrbed n ths paper. The COMSOL model of eletrohemstry and spees transport predts the dependene of the removal rate on other proess parameters suh as eletrolyte onentraton and appled voltages. The D model omprses of phosphor ad soluton (the eletrolyte) flowng between two parallel plates representng the pad and the wafer as shown n Fgure. The pad movess wth a onstant veloty wth respet to the referene frame of the wafer. The flow veloty profle n the gap s lnear at steady-state. The wafer surfaee s the workng eletrode and s held at a onstant potental V a, and s oated wth a flm of opper thatt would be removed usng ECMP. The opper flm s suffently thk that we an gnore potental drops through the flm. Use of a relatvely smple geometry, allowed us to fous on the transport and eletrohemstry proesses nvolved n ECMP. The model nludes steady-state opper dssoluton and spees transport nsde the eletrolyte, on transport nludng onveton, dffuson, and mgraton, and eletrod reatons represented by the Butler-Volmer equaton. It omputes the steady-state opper dssoluton urrent densty as a funton of the voltage appled V e = (V a V ).. Fgure 1: Shemat of ECMP system. An expermental set-up for valdatng the ECMP model was fabrated, and experments were onduted to measure the anode urrent was measured at varous spatal loatons for dfferent eletrode potentals. The expermental apparatus onssted of a two-zone one-half of a ylnder, and a ounter-eletrode n the form of approxmately workng eletrode that onssts of a whole ylnder. The workng eletrode rotates near the statonary two-zone ounter-eletrodes. was ether eletrolyte or a pad materal. A The spae between eletrodes probee was embedded nto the workng eletrode to Exerpt from the Proeedngs of the 01 COMSOL Conferene n Boston

2 measure the loal urrent densty. Ths probe onssted of a opper wre nstalled perpendular to the urved surfae of the ylnder. Usng a rut, we mantaned the probe at ground whle measurng the small eletral urrents through the wre. The workng eletrode was also at ground whle the ounter-eletrode voltages were vared as desred. As the workng eletrode and probe rotated, we reordedd the probe urrent as a funton of angle. The results of the experment and the COMSOL model are n very good agreement. We onludedd that the valdated COMSOL model was ready for use n model-based ontrol of the ECMP proess. ECMP Model Development.1 Theory of Eletrolyt Removal of Copper In ths seton, we desrbe the physs and hemstry underlyng the COMSOL FEM model that was developed to smulate the eletrohemal removal of opper from a surfae. The system under onsderaton onssts of two parallel plates of length L separated by a dstane H as shown n Fgure. One plate s a wafer surfae oated wth a flm of opper (Cu) that we want to remove. Ths wafer surfae s the workng eletrode and s held at a onstant potental V a. The Cu flm s suffently thk that we an gnore potental drops through the flm. The other plate (the ounter-eletrode) ) s at potental V. The flow between the plates onssts of a soluton of phosphor ad (H 3 PO 4 ) and water. The rotatonal moton of the polshng pad s represented by moton of the pad surfae n the x dreton, whh results n a lnear veloty profle n the vertal dreton, u(y). Fgure : Shemat of the geometry used for COMSOL model development. We assume the ad dssoates n the soluton aordng to the followng reaton to form the hydronum on, H 3 O +. HPO 3 HOHPO 4 H. 4 3 O (1) The value equlbrum onstant K a s , and the forward reaton rate, K f s , both at 5 C [1]. The bakward reaton rate, K b, s hene (K f /K a ),.e., The forward and bakward rate onstants are used to estmate the onentratons of H PO 4 and H 3 O + as shown later (Eq. 6). In usng onentraton n plae of atvty wth rate onstants, we assume a standard onentraton of std = 1 mol/l and normalze onentratons usng std. Effetvely, ths means we need to use unts of mol/l for all onentraton ratos nvolved wth hemal reatons. For phosphor ad wth densty of 1700 kg/m 3 and moleular weght, M H3PO4 = 98 g/mol, we have a onentraton of approxmately [H 3 PO 4 ] = 17 mol/l. We an estmate the eletral ondutvty, k, of ths soluton usng the followng relatonshp: F k RT z DC () In realty, k dereases at hgh on onentratons whenn the moblty s more omplex [6]. For our model, however, we wll gnore these effets and assume D s onstant and use k from Eq.. The spees flux s the sum of the eletromgraton, dffusve and onvetve fluxes [6], [7]: N zuf F D v. (3) fluxx mgraton dffuson onveton Here, N s the flux densty of spees, mol/m s, z s the number of proton harges on on, e.g., z Cu+ =, u s the moblty of spees (u = D /RT), F s the Faraday's onstant,, 96,500 C/mol of harge, D s the dffuson oeffent for speess, (m /s), onentraton of spees, (mol/m ), and v s the s the veloty vetor (n m/s). The urrent densty n the eletrolyte s gven by F z (4) The spees onservaton equaton s N R. (5) t Here, R s the volumetr produton of speess. For our model, R s non-zero only for the hydronum on, and s governed by the forward and bakward reaton rate onstants (k f and k b, respetvely). R k [ H PO ][[ HO ] k b[ H PO ][ HO ]. (6) f 3 4 The net harge n the eletrolytee s zero, outsde the tny (un-modeled) double layers near eletrodes. z 0. (7) If wee rewrte the urrent densty expresson ( Eq. 4) by substtutng for flux densty (Eq. 3) then we obtan: F z u F zdc FV z (8) Exerpt from the Proeedngs of the 01 COMSOL Conferene n Boston

3 The last term of Eq. 8 s zero n the eletrolyte due to harge neutralty sne the flow feld does not arry urrent [7]. The frst term s regular eletrall ondutonn where eletral ondutvty s gven by: F z u (9). Both postve and negatve harges nrease the ondutvty sne the harge s squared,.e., z. Addtonally, urrent s generated as a result of potental gradents (harge mgraton) or from onentraton gradents (spees dffuson), and the urrent densty an be expressed as: F zd. (10) Imposng the harge neutralty ondton, z 0, also mples that z 0. Thus, t s noted that dfferenes n dffusvty (D ) s key to whether the spees onentratons term affets urrent flow. If all the dffusvtes were dental, the seond term n Eq. 10 would be zero. A voltage drop aross the eletrodes drves the followng hemal reaton at the anode, resultng n the formaton of a postvely harged opper-waterr omplex, Cu(H O) + 6 [4], [5]: Cu( s) 6 HO[ CuC ( HO) ] e. (11) 6 A double-layer, whh may be as thn as a few nanometers, wll form at the surfae of eah eletrodee wth a sgnfant voltage drop aross t. Consequently, enormous eletr felds exst arosss ths very thn double-layer. For our modelng purposes, we an gnore hanges over the length sales of the double layer and smply treat t as a boundary ondton. The onentratons of the four spees of nterest are denoted as follows: 1 [ HO ]; [ Cu( HO ) 6 ]; [ HO ]; [ H PO ] We use the Nernst equaton to ompute the zero- urrent equlbrum potental aross the double-layer: 0 RT E E log. 6 (1) nf 1 Here, T = 98 K, RT/F = 6 mv, and n= s the number of eletrons n the reaton and E 0 s the standard eletrode potental. Ths potental s relatvee to a Standard Hydrogen Eletrode (SHE) so thatt E 0 =0.34V for ths Cu + reaton. Ths equaton showss that f we nrease the opper or derease the water at the surfae the equlbrum potental wll drop. If we drve the eletrode wth a potental hgher than E then we wll drve urrent out of the eletrode, nto the eletrolyte, and out through the athode. The relatonshp that governs ths urrent flow s the Butler-Volmer equaton: 0 exp af s exp RT F s. (13) RT Here, η s = V a E s defned as the surfae overpotental. As we drve opper to the athode, the samee reaton (n reverse) wll take plae and the smlar equatons wll be used to ompute the potental drop aross the double-layer are approxmately equal, wth the Typally the onstants α a and α onstrant that α a + α = n. For the opper reaton near room temperature, the exhange urrent densty, 0 = 10 A/m, α a = 1.5, and α = 0..5 [6]. So Eq. 13 gves us a surfae urrent for a gven overpotental η s. When η s = 0 the urrent goes to zero. We an use ths dretly as a flux boundary ondton beause to onvertt from a urrent densty to spees densty we dvde by zf, where z s the harge of the on - here z =. Thus, the flux of nto the eletrolyte at the surfae s: N yˆ o F a F exp ex s xp s. zf RT RT (14) We note that Eq. 11 s atually a ombnaton of two reatons onee that generates Cu + at the surfae, and another that forms a omplex wth the opper atom and sx waterr moleules that s arred nto the eletrolyte [5]. Consequently, from flux balane, the flux Nof H O nto the eletrolyte at the surfae s gven by yˆ 16 ŷ. S of the NSome reports n the lterature assume that the overpotental, η s, has a large postve value on one eletrode (e.g., the anode) and has a large negatve at the other eletrodee (e.g., the athode). In suh ases, one may gnore one of the two terms n Eq. 13, and obtan the Tafel equaton. However, f one runs the overpotental to near zero, ths approxmaton may result n sgnfant errors. Also, f one uses a segmented eletrode that an be drven wth a voltage dstrbuton then ths anode/athode termnology an bee trky. It may be more useful to onsder α a and α as propertes at surfaes that depend on the spef loal hemstry. If the hemstry hanges along a gven surfae the onstants α s may hange as well. The urrent flow n the eletrolyte s due to the potental gradent n the eletrolyte (mgraton) and also due to onentraton gradents (dffuson) as desrbed by Eq. 10. To determne the potental Φ wthn the eletrolyte, we apply the urrent onservaton equaton: 0, and obtan: F zd 0. (15) Exerpt from the Proeedngs of the 01 COMSOL Conferene n Boston

4 The boundary values for the potentals are the equlbrum potentals E omputed at eah loaton on the surfae from the Nernst equaton, Eq. 1. The shemat n Fgure 3 shows a typal potental drop aross the eletrolyte. We assume thatt the anode (bottom) s at a voltage of V a and the athode (top) s at a voltage of V. From the loall surfae onentratons we ompute the equlbrum potentals E a and E at the anode and athode. Sne these onentratons wlll vary along the surfaes, so wll the equlbrum potentals. Then at eah surfae loaton we ompute the overpotental η s = V a E and use the Butler-Volmer equaton (Eq. 13 or 14) to ompute the surfae spees flux (or urrent). The ohm ontrbuton to the potental drop aross the ell ( ) may be small, dependng on the eletrolyte ondutvty and over-voltage values. Also, due to the ross-flow, t s unlkely that the profle of the voltage drop wll be a lnear as shown, but would derease n the dreton of urrent flow. Fgure 3: Potental dstrbuton aross the ell. The spees onentratons,... 1,4 have to be frst determned n order to ompute the eletrall ondutvty of the eletrolyte (Eq. ). The onentratons of water ( 1 ) and opper omplex ( ) are omputed usng spees onservatonn N 0 where we assume the absene of homogeneous reatons (R) and a steady-statee proess. The onentratons of the two harged spees, 3 = [H 3 O + ] and 4 = [H PO - 4 ] are omputed usng harge onservaton (Eq. 7) and the H 3 PO4 equlbrum dssoaton onstant,.e., we assume there s ample phosphor ad and t dssoates fast ompared to our fluxes. We further assume that the onentraton of phosphor ad s onstant and s denoted by 0. Then 3. 4 = 0, and the harge neutralty ondtonn yelds z z + z z 4 4 = 0. Substtutng z 1 =0, z =, z 3 =1, z 4 =1 gves =0. Solvng thesee two equatons, we obtan: 3 0,. Implementaton n COMSOL and Smulaton Results We used COMSOL Multphyss PDE (General Form) nterfae to mplement the model, together wth the Eletr Current nterfae. Fgure 4 shows the FEM geometry wth the eletrolyte flowng between the two plates separated by H =.9 mm. The eletrolyte flow enters from the left boundary and exts through the rght boundary. The eletrolyte flow veloty s spefed to nrease lnearly from the ounter-eletrode to the anode, the latter movng to thee rght wth a veloty U 0 (= 6 mm/s). The spees fluxes (Eq. 3) for water, opper- waterr omplex, Cu(H O) + 6, and the hydronum on, H 3 O +, were spefed under the Conservatvee Flux feld n the General Form PDE nterfae, and the produton of H 3 O + was spefed under Soure Term. Conentratons of the three spees at the entrane boundary were spefed usng Constrant nterfae, as was the flux balane between opper and + Cu(H O) 6 at thee anode. The onentratons of + Cu(H O) 6 and H 3 O + were spefed as zero at the ounter eletrode. The Flux/Soure nterfaee was + used to spefy thee flux of Cu(H O) 6 at the anode usngg the Butler-Volmer equaton. The Flux/Soure nterfae was also used to spefy the onvetve flux of thee three speess at the ext. The eletral ondutvty of the medumm (Eq. 9) was spefed n the Eletr Currents nterfae under Current Conservaton. The ontrbuton to the urrent densty n both x and y dretons by the dffuson of harged spees was spefed under External Current Densty nterfae. The voltage at the athode (ounter-eletrode), V, was spefed usngg Eletral Potental nterfae. The segment of the ounter-eletrode to the rght was groundedd (V = 0), and effetvely served as a seond anode wth the boundary ondton spefed usng the Ground nterfae. As desrbed later, ths segmented eletrode onfguraton was used n the experment to studyy the urrent dstrbuton n the regon at the boundary of the two segments. The dffusvtes of + the four spees H O, Cu(H O) 6, H 3 O +- -, and H PO 4 ( 1 4 ) used n the model are m /s, m /s,, m /s, and m /s, respetvely [8]. Fgure 5 shows that H 3 3O + s present n equlbrum onentratons n most of the eletrolyte exept near the eletrodes. At the anodes, water depleton results n H 3 O + depleton and at the athode, the on gves up the postve harge to the eletrode. Ths behavor s also seen n the (16) Exerpt from the Proeedngs of the 01 COMSOL Conferene n Boston

5 onentraton profle of H 3 O + n the y-dreton n the graphs of Fgure 6. The spees boundary layer for + Cu(H O) 6 s shown on the left graph, whle the onentraton of H PO4, omputed usng harge balane of Eq. 16, s shown on the rght of Fgure 6. Fgure 7 (left) shows the opper removal rate that was omputed from the gradent of the opper omplex flux,, at the anode, or alternatvely from Eq. 14. y The removal rate dereases n the dreton of the flow as less water s avalable to reate the opper omplex, and fnally fallng to zero at the end of the anode. The graph on the rght sde of Fgure 7 showss that the urrent densty at the ounter eletrodee (athode) drops qukly to a unform value over the length of the eletrode. 3 Expermental Valdaton 3.1 Expermental Apparatus and Proedure An experment was done to valdate the detaledd eletrohemal model. The apparatus was as shown n Fgure 8(a) onsstng of a ylndral opper eletrode (anode) and two adjaent partal ylndrall eletrodes (Eletrode 1 and ). The entral rotatng eletrode, the anode, was made from a opper ylnder wth dameter approxmately 3 mm. A small hole was drlled nto the ylnder wall (1. mm) and an nsulated wre (approx mmm n dameter) was plaed flush wth the hole. The nsulated wre ated as a probe that measured the urrent dstrbuton as the anode sweeps past the athode. The anode and probe are both held at ground, but the urrent through the probe s measured usng the nvertng amplfed rut shown n Fgure 8(b). We note that ths expermental onfguraton s welll approxmated by the D beause H s muh smaller than the radus of the ylndral ounter eletrodee used n the experment. For all of these valdaton experments Eletrodee was mantaned at ground (V = 0), and hene ated essentally as an addtonal anode. The voltage on Eletrode 1 was vared from zero to 3 V usng a Hewlett Pakard E3615A DC power supply. The urrent was measured through Eletrode 1 usng a shuntt resster. For most the results shown here, the probee amplfer resstor was R =.0 k, resultng n an amplfer gan of 000. Fgure 9 shows a photograph of the assembled apparatus. The rotaton was ontrolled wth a servo motor and servo motor ontroller (loated at the top of the assembly), and the speed ould be adjusted manually. For thee results shown here, the anode surfae speed was approxmately 6.3 mm/s. A poston sensor was onstruted by removng the housng from a 10 kw potentometer. Ths allowed the potentometer sweep arm to rotate freely and by applyng a onstant voltage aross the potentometer the sweep voltage ould be measured to determne angular poston. To onnet the probe to the probe amplfer, a rotatng eletral ontat made of graphte was onstruted usng a opper ylnder thatt was eletrally nsulated from the rotatng shaft. At the bottom of the assembly are the rotatng anode and the statonary ounter eletrodes. The poston of the ounter eletrodes relatve to the rotatng anode ould be adjusted usng the three eletrode algnment rods. Onee the assembly had been algned, the whole set- knob up ould be rased and lowered wth the releasee so that the bottom end ould be nserted nto a ontaner of eletrolyte. The eletrolyte used was 85% phosphor ad (H 3 PO 4 ) and the ontaner held approxmately 100 ml of ad. It was determned that one had to replae the eletrolyte farly regularly sne the ethed opper would reman n the eletrolyte so results would drft wth tme. After approxmately an hour of polshng (dependng on the rate) the eletrolyte would start to take on a green tnt, and the urrents would start to dmnsh. U o Anode (ground)..9 mm V 1 Insulaton V (ground) 1 mm 7.0 mmm 7.0 mm 7.0 mm Fgure 4: D COMSOL model for ECMP. The eletrolytee flow enters from the left. Polshng ours at the opper anode (top wall ) whh s movng at veloty U 0 wth respet to the bottom wall. There s 1 mm gap of nsulaton between the segmented ounter-eletrod des at voltages V1 and V. Exerpt from the Proeedngs of the 01 COMSOL Conferene n Boston

6 Fgure 5: Dstrbuton of the hydronum on, H 3 O +, onentraton (moles/m 3 ) throughout the eletrolyte. + Fgure 6: Left: Molar onentraton of Cu(H O) 6 n the vertal (y) dreton at x = m (shown as the vertal lne n Fgure 5). Rght: H PO 4 and H 3 O + molar onentratons. Fgure 7: Left: Copper polsh rates n A/mn at the anode. Rght: Current densty at the ounter eletrode. 3. Expermental Results vertal sale of the plot s n the unts determned Fgure 10 shows the measured urrent vs. voltage expermentally, butt the model results were saled by graph. The urrent startss to rse as the voltage from a onstant fator to math the values at the peak the anode to athode nreases above 0.5 V. After the urrent. Addtonally, we used a salng fator for the voltage exeeds approxmately 1.0 V, we start to seee nflow onentraton of H PO 4 sne there was some a noser sgnal. Ths s due to the formaton of unertanty n the atual onentraton. Nevertheless, bubbles of hydrogen (H ) at the athode. At 1.4 V, the haratersts are learly the same. As the probe the urrent nrease s large and the gas evoluton at sweeps from left to rght (nreasng poston) we see the athode s farly vgorous. At voltages above the urrent suddenly rse wthn approxmately 5-6 approxmately 1.4 V further voltage nrease does not mm range. After the peak, the urrent dereases nrease urrent very muh, and the nose due to gas gradually wth nreasng poston due to thkenng evoluton s sgnfantly large. of the Cu on dffuson boundary layer. The urrent dropss off suddenly as the probe exts the Eletrode 1 Fgure 11 shows the probe urrent for the ase area. As an be expeted, the shape of the graph s where the voltage between the eletrodes was very smlar to the opper flux from the anode shown approxmately 0.8 V. The dots are data and the red n Fgure 7. lne s the results from the COMSOL model. The Exerpt from the Proeedngs of the 01 COMSOL Conferene n Boston

7 (a) (b) Fgure 8: Left: Shemat of expermental apparatus (top vew). Rght: Crut for measurng probe urrent whle mantanng probe at V= =0. Fgure 9: Apparatus for ondutng the ECMP experments. Exerpt from the Proeedngs of the 01 COMSOL Conferene n Boston

8 Fgure 10: to athode. Eletrode 1 urrent versus voltage from anode 5 Referenes [1] Mroeletron Applatons of Chemal Mehanal Planarzaton, Ed. Y. L, Wleyand Intersene, (008). [] G. D. Padh, J. Yahalom, S. Gandkota, Dxt, Planarzaton of Copper Thn Flms by Eletropolshng n Phosphor Ad for ULSI Applatons, J. Eletrohem. So., Vol. 150, No.1, pp. G10-G14, (003). [3] D. Truque, X. Xe, and D. Bonng, Wafer Level Modellng of Eletrohemal- Res. Mehanal polshng (ECMP), Mater. So. Symp., Vol. 991, (007). [4] R. Vdall and A. C. West, Copper Eletropolshng n Conentrated Phosphor Ad. I. Expermental Fndngs, J. of Eletrohem. So., Vol. 14, No. 8, pp , (1995). [5] R. Vdall and A. C. West, Copper Eletropolshng n Conentrated Phosphor Ad II: Theoretal Interpretaton, J. Eletrohem. So., Vol. 14, No. 8, pp , (1995). [6] G. Prente, Eletrohemal Engneerng Prnples, (1991). [7] J. Newman and K. E. Thomas-Alyea, Eletrohemal Systems, 3 rd ed., (004). [8] CRC Handbook of Chemstry and Physs, 74 th ed., (1994). Fgure 11: Comparson of anode urrent data wth COMSOL model predtons. 4 Conlusons We have developed a steady-state COMSOL model of the ECMP proess that nludes opper dssoluton and spees transport nsde the eletrolyte, on transport nludng onveton, dffuson, and mgraton, and eletrod reatons represented by the Butler-Volmer equaton. The removal rate and unformty are predtedd as a funtonn of eletrolytee onentraton and appled voltage. An expermental apparatus was bult, and a seres of suessful experments were arred out. Our expermental results show exellent agreement wth the COMSOL model predtons. A redued-order verson of the valdated physal model may now be used as a basss for developng multvarable feedbak ontrol of the ECMP proess. 6 Aknowledgements Ths work was funded by the NSF SBIR Program, Award # IIP We gratefully aknowledge the help of Professor Jan B. Talbot of the Unversty of Calforna, San Dego (UCSD) Department of Nano-engneerng durng the ourse of ths researh. Exerpt from the Proeedngs of the 01 COMSOL Conferene n Boston