Contact resistance in flat thin films

Transcription

1 Contct reitnce in flt thin film The MIT Fculty h mde thi rticle oenly vilble. Plee hre how thi cce benefit you. Your tory mtter. Cittion A Publihed Publiher Red, M. B. et l. Contct Reitnce in Flt Thin Film. Electricl Contct, 29 Proceeding of the 55th IEEE Holm Conference on IEEE. htt://dx.doi.org/.9/holm Intitute of Electricl nd Electronic Engineer Verion Finl ublihed verion Acceed Thu My 3 5:23:53 EDT 28 Citble Link Term of Ue Detiled Term htt://hdl.hndle.net/72./6268 Article i mde vilble in ccordnce with the ubliher' olicy nd my be ubject to US coyright lw. Plee refer to the ubliher' ite for term of ue.

2 Contct Reitnce in Flt Thin Film M.B. Red, J.H. Lng 2, A.H. Slocum Dertment of Mechnicl Engineering 2 Dertment of Electricl Engineering nd Comuter Science Mchuett Intitute of Technology Cmbridge, USA melir@mit.edu. R. Mrten FormFctor Inc. Livermore, USA Abtrct MEMS-fbricted electricl contct re commonly ued in MEMS rely. Thee electricl contct cn be imle two flt urfce coming into contct []. Modeling their contct force/reitnce reltionhi cn be difficult becue much of the theory on contct reitnce w develoed for mcro-cle contct [2], nd contct roertie for MEMS-cle contct do not lwy gree with thoe redicted by thi theory [3]. One contribution to thi digreement i tht when the dimenion of the contct thickne re on the order of the -ot dimenion, the reding reitnce i ffected [4]. In order to determine the reltionhi between contct force nd reitnce for wide rnge of rmeter, we hve develoed two-couon tet ytem which llow the roertie of thee contct to be emiriclly determined. The deign of the two-couon ytem llow for the rid fbriction of multile contct mteril nd geometrie. The two-couon ytem w ued to tet the contct reitnce roertie of uttered nd electrolted Au film in thicknee of. μm,.3 μm, nd.5 μm. Contct force w meured uing cutom flexurl force guge nd the 4-oint contct reitnce w meured uing n integrted Kelvin Structure [5]. The reult re comred to trditionl Holm theory to determine the effect of film thickne on reding reitnce. Keyword- thin film; contct reitnce I. INTRODUCTION Trditionl contct theory ume tht when two urfce meet t ingle contct ot, the electricl current flow line red in ll direction uon exiting the contct ot, hown in Fig.. Holm theory hold tht the reding reitnce between thee two urfce i [2] ρ ρ R = + () 4 4 where ρ i electricl reitivity nd i the contct ot rdiu. However, in thin film, where the film thickne L i on the order of the contct ot rdiu, the geometry of the contct limit the current line from reding in ll direction. Inted, the current line mut curve firly ridly, hown in Fig. b. b Figure. ) The current flow line between two bulk mrteril meeting t contct ot umed in trditionl contct theory. b) The current flow line between two thin film meeting t contct ot. Severl method hve been ued to determine the effect of the rtio between contct rdiu nd film thickne L, /L, on contct reitnce. One method ue mthemticl model to redict the deendence of normlized contct reitnce ( defined the rtio between ctul contct reitnce nd tht redicted by Eq. ()) on the rtio /L [4]. Thi method theorize tht thin film geometry cue the reding reitnce to be contrined to much mller region thn the region where the reding reitnce tke lce in non-thin film. Thi method find tht the thin film ffected normlized contct reitnce i given by [4] R n 4 coth( λn L / b) in( λn / b) 2( / L) = = ln π 2 n= ( J ( λn ) λn ) π ( b ) N / Contct ot rdiu Film thickne, L where R N i the normlized reding reitnce nd b i the outer film rdiu for cylindricl contct. Thee geometrie re defined in Fig. 2. In Eq. (2) the rgument for the Beel function of the firt kind of order, λ n, i (2) /9/$ IEEE 3

3 Aerity rdiu Outer film rdiu b When force i lied to two thin film in contct, the Holm rdiu H i given by the clic formul [2] H F = (5) πh Figure 2. The contct ot rdiu, the film outer rdiu b, nd the film thickne L, for thin film meeting t ingle erity. where β i Film thickne, L β λn = β 3β 3β (3) β= π( 4n ). (4) Thee clcultion were bed on umtion which were only vlid where /L.5 [4]. The effect of thi on normlized contct reitnce re hown in Fig. 3. where F i force nd H i hrdne. Film thickne i not fctor in thi eqution; therefore, film hving identicl comoition but different film thicknee will hve identicl vlue of H for given lied force F. Auming tht with trditionl Holm theory, thi vlue H cn be ubtituted for the contriction rdiu when determining contct reitnce, then the /L vlue for ny given lied force will decree film thickne incree. According to Fig. 3, when /L decree, normlized contct reitnce will incree. Therefore, in thi model, normlized contct reitnce incree film thickne incree. Other work ugget tht Holm theory ctully underetimte contct reitnce for thin film. In [6], it i ointed out tht in the derivtion of Eq. (), Holm ume the contriction deth i equl to the contriction rdiu. However, thi i not licble in film where the Holm rdiu i on the order of the film thickne. In [6], n FEM model w develoed to look t the contct geometry hown in Fig. 4. Normlized Sreding Reitnce /L Figure 3. Normlized contct reitnce function of the rtio /L redicted by [4]. For very low vlue of /L there i no effect on contct reitnce. A /L incree, the normlized contct reitnce decree. At /L=.5, the mximum vlid vlue of thee eqution, the normlized contct reitnce i roximtely.52. A i tted by [4], the rtio between film thickne nd outer film rdiu, L/b, h n inignificnt effect on contct reitnce over the rnge. L/b.. Contct rdiu, Figure 4. Geometry of contct modeled in [6]. Film thickne, L The imultion in [6] found tht contct reitnce decreed film thickne increed over the rnge of L= -5. The /L vlue invetigted went high 3. Additionlly, the contct reitnce redicted for film thickne of μm t /L= 5 w roughly 2 time tht of Holm. The mthemticl model in [4] ugget tht contct reitnce incree with increing film thickne, where the FEM in [6] ugget tht contct reitnce decree film thickne incree. Additionlly, [4] redict contct reitnce below tht redicted by Eq. (), where [6] redict contct reitnce bove tht of Eq. (). However, thee two model looked t very different rnge. The model in [4] w limited to /L<.5 where the model in [6] looked t much higher /L vlue. However, the dt hown in [6] only looked t film thicknee where L> μm. It i not immeditely obviou how either of thee model would erform outide of the rnge reented in [4] nd [6]. Therefore, meurement were erformed on film thicknee of L=. μm,.3 μm,.5 μm nd /L= -7. The reult were evluted on their own well comred to thoe redicted by [4] nd [6] in their reective rnge. 3

4 II. SAMPLE PREPARATION A two-couon ytem w ued to meure the contct reitnce between two film of multile thicknee of uttered nd electrolted Au. The ytem conit of bottom ilicon couon hving ) metl trce nd 2) three hericl contct well to ilicon couon hving ) metl trce, 2) flexible membrne with tiff center cylinder, nd 3) three KOH etched it. The couon re embled by lcing the KOH etched it of the to couon over the hericl contct of the bottom couon. Thi tye of embly crete eudo kinemtic couling, llowing for reetble oitioning [7]. Thi ytem i decribed in detil in [5]. The embly leve g between the to nd bottom metl trce. When force i lied to the tiff cylinder in the center of the membrne, the membrne trin which bring the two metl trce into contct [5]. The trce re ech mm wide. The dimeter of the tiff cylinder in the center of the membrne i 4 mm mking the overll rent contct re 4mm 2. The metl trce crete Kelvin tructure llowing for the ioltion of the contct reitnce. Thi embly nd Kelvin tructure re hown in Fig 5. Dimeter of tiff center cylinder Current loo ide Actul re of contct, where r= H Arent re of contct (l*w) Figure 6. Arent re of contct, ctul re of contct, inidividul contct ot, nd the dimeter of the tiff center cylinder of the exerimentl etu. Drwing i not-to-cle nd current flow line re rimite nd do not how how current recombine from the individul contct ot. contct 4mm 2. However, the Holm rdiu correonding to the ctul re of contct i on the order of - μm. It i hyotheized tht even though the mcro-geometry i rectngulr, the contct ot ct loclly much like thoe modeled in [4] nd [6]. Thi i becue H << w nd H << l. Becue of thi inequlity of cle, it i unlikely tht the current flow line immeditely round the contct ot will be ffected by the mcro geometry. However, it i cknowledged tht thi i n umtion nd tht there might be mll effect to contct reitnce cued by the mcro geometry which thi er doe not ccount for. l Individul contct ot w Voltge loo ide Non-contcting ortion of trce Alo conidered w the true fltne of the contct. In deigning of thi fixture, chieving fltne w to riority. The ctul fltne cro the contct cn vry by much 2 nm. Thi men tht there i oibility of the contct rocking immeditely fter touchdown. No hyicl evidence of thi rocking w een under norml condition; however, when current greter thn one Amere w ut through the contct, the contct did tend to fil long one edge, uggeting tht the reure my hve been higher on tht edge. F Figure 5. ) An imge of the embled couon from bove. b) An exloded imge of the couon, hown in trnrency, dilying the integrted Kelvin tructure. c) The membrne deflecting howing how the two metl trce come into contct (not-to-cle). The contct re in thi ce i rectngulr, unlike the circulr contct dicued in [4] nd [6]. However, it i reonble to believe the individul contct ot re round. A not-to-cle drwing of few individul contct ot in reltion to the ret of the trce i hown in Fig. 6. For the exerimentl et u, the contct length l= 4mm nd the contct width w= mm mking the rent re of The uttered couon were rered by uttering.3 μm Ti dheion lyer followed by. μm,.3 μm, or.5 μm of uttered Au. An oxide lyer inulted the Ti from the ilicon ubtrte. Both the to nd bottom couon hd identicl film. The electrolted couon were rered by uttering.3 μm Ti dheion lyer followed by. μm Au eed lyer. On to of thi eed lyer,. μm,.3 μm, or.5 μm of dditionl Au w lted. Agin, n oxide lyer iolted the trce from the ilicon ubtrte nd both the to nd bottom couon hd identicl film. Due to the difficulty in meuring the hrdne of film with thicknee le thn μm, the hrdne of the uttered film w roximted 3.5 GP nd the electrolted film GP [8, 9]. The urfce roughne of the uttered film 32

5 w found to be bout 6 nm while the urfce roughne of the electrolted film w found to be bout 4 nm. The reitivity of the uttered mle w meured ρ= 4.27x -8 Ωm. Thi vlue w conitent cro ll three thicknee of the uttered film mle. Thi i ignificntly higher thn the bulk reitivity of Au. Suttered film re known to hve higher thn bulk contct reitivity []. Reitivity cn be ffected by vriou mechnim uch temerture, electron urfce cttering, imuritie, intrgrnulr defect, nd cttering t grin boundrie []. It h lo been hown tht in thin uttered Au film with n dheion lyer of Ti, the Au nd Ti cn form n lloy of ignificntly higher reitivity []. The reitivity of the electrolted mle w lo meured. Tking into ccount the reitivity of the eed lyer rllel reitnce, the reitivity of the bulk w found to be 2.8x -8 Ωm, conitent with literture vlue for Au reitivity. III. TESTING AND RESULTS A. Teting Procedure During the exeriment, force guge comreed the to membrne bringing the two metl trce into contct, hown in Fig. 5. The overll dilcement of the membrne, the force, nd the contct reitnce were recorded throughout the tet. When the membrne toed moving, contct w mde. Thi lo correonded to the firt time finite contct reitnce w een ince no oxide or film imeded current flow. Thi i the oint where the contct ee zero force. After thi oint, force w further increed to mn. The current w ourced t 5 ma nd 4-wire reitnce w meured uing Keithely 242 ource meure unit. B. Suttered Film Reult The contct reitnce function of contct force w meured for the three thicknee of uttered Au film. The reult long with the vlue clculted by trditionl Holm theory uing Eq. () nd Eq. (5) re hown in Fig. 7. The reitivity ued to clculte the Holm rediction w the meured reitivity of the uttered film, 4.27x -8 Ωm. The reult how contct reitnce decreing film thickne incree. The. μm nd.3 μm film both howed ignificntly higher contct reitnce thn tht redeicted by Eq. (). The.5 μm film howed lightly lower contct reitnce thn the Holm theory. When contct force w increed ignificntly, contct reitnce did dro below mω, indicting tht there i no ignificnt bulk reitnce in the tet etu. The force guge i ccurte within μn nd the reitnce meurement i ccurte to roximtley 2μΩ Thee reult hve imilr trend to the FEM reented in [6]. In both ce, the contct reitnce decree with increing film thickne. However, the reult of [6] howed ignficntly higher overll contct reitnce thn een in thee exerimentl reult. Reitnce(mΩ) Holm Theory. μm Suttered Au.3 μm Suttered Au.5 μm Suttered Au Force (mn) Figure 7. Contct reitnce of uttered thin Au film nd the contct reitnce redicted by Holm Theory. Thee me reult re hown lotted normlized contct reitnce R N v. /L re hown in Fig. 7. The normlized contct reitnce i the meured reitnce divided by the reitnce redicted by Holm theory. The vlue i clculted from Eq. (5) uing the roximted hrdne of 3.5 GP. Normlized Contct Reitnce /L. μm Suttered Au.3 μm Suttered Au.5 μm Suttered Au Figure 8. Normlized contct reince of uttered Au film. At vlue of /L>, there i cler trend of increed normlized contct reitnce /L i increed. Thi trend er omewht liner. However, t vlue of /L<, thi trend doe not exit. In thi region, the normlized contct reitnce dro below. It mke ene tht the reltionhi between normlized contct reitnce nd /L would be different in thi rnge. At vlue of /L<, the Holm rdiu i le thn the film thickne. However, t vlue of /L>, the Holm rdiu i greter thn the film thickne. One intereting note i tht [4] how decreing normlized contct reitnce with increing /L in the region of /L<.5, jut the exerimentl dt how decreing normlized contct reitnce with increing /L in the region 33

6 of /L<. Unfortuntely, the force guge ued w rther coure; o, it i difficult to look t the exerimentl reult where /L<.5 nd, therefore, difficult to directly comre thee reult. C. Electrolted Seed Lyer Correction Fctor Determining the contct reitnce for the lted Au w lightly more difficult becue of the dded effect of the eed lyer. Trditionl contct reitnce theory model thi dded reitnce hown in Fig. 9. However, thi model ume ll of the current line trvel into the eed lyer. In thi tet etu, hown in Fig. 9b, only ortion of the current flow line trvel into the eed lyer. In trditionl modeling, the dditionl reitnce R of the trnition from the electrolted Au into the uttered eed lyer would be [2] R = ( 8 / π )( ρ / ρ )( L / ) (8) where ρ i the reitivity in the lted region, ρ i the reitivity in the uttered region, L i thickne of the electrolted region, nd i the Holm rdiu. However, the frction of current tht ctully trvel in the bulk R % i defined R c R% = R. () Therefore, the contct reitnce for the lted film R c i R c m = R R () where R m i the reitnce meured in the Kelvin tructure. All of the reult for the electrolted film hve been corrected to remove the dditionl reitnce dded by the trnition from from the lted region to the uttered region. D. Electrolted Film Reult Three thicknee of lted Au film were teted. The reult long with the vlue clculted by trditionl Holm theory uing Eq. () nd Eq. (5) re hown in Fig.. The reitivity ued to clculte the Holm rediction w the meured vlue of 2.8 x -8 Ωm. A with the uttered film, contct reitnce increed for thinner electrolted film. All three film thicknee hd contct reitnce higher thn thoe redicted by Holm theory. Once gin, thi incree in contct reitnce with decree in film thickne correond to the trend een in [6]; however, the mgnitude of contct reitnce re till lower thn thoe een in [6]. c 2 Holm Theory. μm Plted Au.3 μm Plted Au.5 μm Plted Au Reitnce(mΩ) Figure 9. ) Current flow line in trditionl film theory. b) Current flow line in thin electrolted film on uttered eed lyer. R b % /( ρ ( l / wl )) ρ / L = = (9) ρ ( l / wl ) + ρ ( l / wl ) ρ / L + ρ / L Force (mn) Figure. Contct reitnce of lted thin Au film nd the contct reitnce redicted by Holm Theory. The me reult lotted normlized contct reitnce R N v. /L re hown in Fig.. The vlue re clculted from Eq. (5). The hrdne ued to clculte w the roximted vlue of GP. where l nd w re the length nd width of the bulk contct trce. Therefore, n roximtion of the dditionl reitnce dded by the trnition from the lted region to the uttered region R c i 34

7 Normlized Contct Reitnce μm Plted Au.3 μm Plted Au.5 μm Plted Au Normlized Contct Reitnce μm Suttered Au.3 μm Suttered Au.5 μm Suttered Au. μm Plted Au.3 μm Plted Au.5 μm Plted Au /L Figure. Normlized contct reince of electrolted Au film nd the normlized contct reitnce redicted by (2). Thi lot how tht normlized contct reitnce tend to incree with /L for /L>. While the normlized contct reitnce doe not dro below t low vlue of /L, it doe in the uttered film, it doe exhibit downwrd trend in the regoin /L< imiliry to how normlized contct reitnce decree with /L in the region /L<.5 in [4]. However, there i not enough exerimentl dt in the rnge of /L<.5 to mke direct comrion to the theory reented in [4]. Finlly, the reltionhi between normlized contct reitnce nd /L for both the uttered film nd the electrolted film were lotted together, which i hown in Fig. 2. In both ce, the trend in normlized contct reitnce hift round /L=. Thi my be becue t thi oint, there i miniml reding nd contricting of the current flow line. IV. SUMMARY A two couon ytem w ued to meure the effect of the rtio between contct re nd film thickne on contct reitnce. The contct reitnce between uttered Au film well between electrolted Au film were meured. The reulting contct reitnce were higher thn thoe redicted by Holm theory. Their normlized contct reitnce were comred to the rtio between the Holm rdiu nd the film thickne, /L. In high rnge of force, contct reitnce increed with decreing film thickne. The normlized contct reitnce roved to be deendnt on /L. For high vlue of /L, contct reitnce incree with /L, imilrly to the trend een in [6]. For low vlue of /L the contct reitnce decreed with /L, imilr to the trend een in [4]; however, there i inufficient dt to mke fr reching concluion bout thi ortion of the dt. It i cler /L Figure 2. Normlized contct reince of both electrolted film function of /L. the uttered nd tht thi reltionhi h two ditinct region. In the firt region where /L<, normlized contct reitnce decree with increing /L. Thi i where the Holm rdiu i le thn the film thickne. In the econd region where /L>, normlized contct reitnce incree with increing /L. Thi i where the Holm rdiu i greter thn the film thickne. The exct mechnim for thi trnition i not comletely undertood. Future work will include looking t the region where /L<.5 with finer force guge to ee how cloely thee reult mtch thoe een in [4] well looking cloely t the region ner /L= to invetigte the trnition from the re where Holm rdiu i le thn film thickne to the re where Holm rdiu i greter thn film thickne. REFERENCES [] A. Weber, J. Lng, nd A Slocum, {} Si etched lnr electricl contct for ower MEMS-rely, Proceeding of the 53rd IEEE Holm Conference on Electricl Contct, 27, [2] R. Holm, Electricl Contct: Theory nd Aliction, New York:Sringer-Verlg 967. [3] R. Timit, Electricl conduction through mll contct ot, IEEE Trnction on Comonent nd Pckging Technologie, Vol. 26, No. 4, 26, [4] R. Timit, Contriction reitnce of thin-film contct, Electricl Contct, Proceding of the 54 th IEEE Holm Conference on, , Oct [5] M. Red, A. Weber, O. Yglioglu, R. Mrten, J. Lng nd A. Slocum, A two-couon ytem for the reetble meurement of flt on flt microcle contct reitnce, Interntionl Conference on Electricl Contct, Proceeding of, Jun. 28 [6] G. Norberg, S. Dejnovic, H. Heelbom, Contct reitnce of thin metl film contct, Comonent nd Pckging Technologie, IEEE Trnction on, Vol. 29, No. 2, 26, [7] A. Slocum, Degin of three-groove kinemtic couling, Preciion Engineering, Vol. 4, No. 2, 992,

8 [8] D. Jng nd D. Kim, Tribologicl behvior of ultr-thin oft metllic deoit on hrd ubtrte, Wer, Vol. 96, No. -2, 996, [9] Y. Okink nd M. Hohino, Some recent toic in gold lting for electronic liction, Gold Bulletin, Vol. 3, No., 998, 3-3. [] S. Riedel, J. Roeber, nd T. Gener, Electricl roertie of coer film roduced by MOCVD, Microelectronic Engineering, Vol. 33, No. -4, 997, [] M. Gro, D. Alteter, T. Stieglitz, M Schuettler nd J. Meyer, Micromchining of flexible neurl imlnt with low-ohmic wire trce uing electrolting, Senor nd Actutor, Vol. 96, No. 2-3, 22,. 5-. [2] P. Slde, Electricl Contct, Princile nd Aliction, New York: Mrcel Dekker