Mechanical Properties of Evaporated Gold Films. Hard Substrate Effect Correction

Transcription

1 Mater. Res. Soc. Symp. Proc. Vol Materals Research Socety 1086-U08-41 Mechancal Propertes o vaporated Gold Flms. Hard Substrate ect Correcton Ke Du 1, Xaolu Pang 1,, Ch Chen 1, and lex. Volnsky 1 1 Department o Mechancal ngneerng, Unversty o South Florda, 40 Fowler ve. NB118, Tampa, FL, 3360 Department o Materal Physcs and Chemstry, Unversty o Scence and Technology, Bejng, Bejng, , Chna, People's Republc o bstract Nanondentaton tests usng the Berkovch ndenter tp were perormed on 50 and 00 nm thck polycrystallne gold lms deposted on hard substrates. Gold lm hardness ncreased wth the ndentaton depth due to the nluence o the substrate. procedure based on the Josln-Olver method was ntroduced to correct or the substrate eect. The method utlzes the act that the measured elastc modulus dd not change sgncantly wth the ndentaton depth or the two lms tested, whch allowed reducng the contact area varaton used n the hardness calculaton. Introducton The ablty to measure mechancal propertes o thn lms s mportant or varous applcatons. Typcally thn lms have hgher hardness compared wth ther bulk counterparts. There are many methods used or measurng thn lms mechancal propertes, whch utlze derent sample geometres, ncludng reestandng lms [1], mcrobrdge [], and mcrobeam cantlever beam [3] to name a ew. However, nanondentaton s the most commonly used method or measurng mechancal propertes. When ndentng bulk polycrystallne samples ther hardness and modulus do not change sgncantly wth ndentaton depth, however, or thn lms, the elastc modulus typcally changes a lot at very shallow ndentatons (<10% o the lm thckness) and tends to latten at deeper ndentatons. Hardness exhbts large scatter at very shallow depths, and then changes steadly wth the ndentaton depth. For the very shallow ndentatons, the hardness varaton can be explaned by the ndentaton sze eect or stran gradent plastcty theory [4]. Hardness change at deeper ndentatons can be explaned by the substrate eect [5], although hardness, a measure o the materals ductle propertes, should not change sgncantly wth ndentaton depth. Some researchers argue that the ncrease n hardness may be caused by the ndentatons perormed on the gran boundares rather than the grans [6]. However, the same may also happen n bulk materals, where expermental data normally does not show such changes. Generally speakng, the hardness and elastc modulus o thn lms are aected by the substrate. In order to correct the hardness, lots o models have been ntroduced. One o the most commonly used s the Olver and Pharr method [7]. Olver and Pharr used the elastc unloadng slope o the load-dsplacement curve along wth the calbrated tp area uncton to assess the elastc and plastc mechancal propertes:

2 1 (1 v ) (1 v ) (1), = r rop = π β S c (), H = OP P c (3), where r s the reduced modulus, β s an ndenter shape constant, S s the stness, and are the Young s modul o the ndenter and the lm, ν and ν are the Posson s ratos o the ndenter and the lm materals, respectvely. The Olver-Pharr method was orgnally appled or the bulk materals and n the case o elastc msmatch between the lm and the substrate can lead to errors. One o the man problems o the Olver-Pharr method s that the ple-up and snk-n phenomena can not be accounted or. Sot ductle lms (mostly metals) on hard substrates can exhbt sgncant ple-up. Fgure 1a shows plastc pleup around the Berkovch tp ndent nto 00 nm gold lm on mca. The ple-up dameter ncreases as a uncton o the maxmum ndentaton load n Fgure 1b. Heght, μm d Ple-up dameter, μm a) Lateral dstance, μm b) Maxmum ndentaton load, μn Fgure 1. a) Ple-up around ndentaton o 00 nm gold lm on mca wth Berkovch tp; b) Plastc ple-up dameter as a uncton o the maxmum ndentaton load. For the hard lms on sot substrates, the snk-n can be observed. nother problem wth the Olver-Pharr method s assocated wth the assumpton that the lm s smooth. However, the surace roughness may sgncantly aect the mechancal propertes measurements. Many researchers have suggested that the ndentaton depth should be less than 10% o the lm thckness. Ths approach can gve satsactory results or thck lms, however, or very thn lms (nanoscale), the surace roughness, machne

3 complance and ndentaton sze eect can nluence the results. Consderng all these problems, Josln and Olver [8] adopted another method that can mnmze the surace roughness, ple-up and snk-n eects when calculatng lm hardness. In the Josln-Olver method, the contact area s elmnated. s a result, equatons () and (3) can be rearranged as: H 4β π P S JO = r (4). In ths method, reduced modulus, r, was assumed to be constant and not changng wth the ndentaton depth. For sot lms on hard substrates, the reduced modulus can ncrease wth the ndentaton depth. Both the reduced modulus and the hardness measurements are nluenced by the substrate. Josln and Olver [8] suggested that the rato o the ndentaton load and the square o the unloadng stness, P/S, s a materal characterstc. For bulk materals, the value o P/S does not change much wth the ndentaton depth [9]. Former studes have shown that the Josln-Olver method s only good or homogeneous materals wth smlar modulus [9], thus many researchers utlzed FM to model the substrate eect and correct the measured reduced modulus. Kng et. al. [10] used a lat punch model to smulate nanondentaton, and the reduced modulus can be wrtten as: 1 r 1 ν = 1 ν 1 e α t 1 ν s s e C C α t (5), where c s the contact area, t s the ndentaton depth, s and ν s are the substrate elastc modulus and Posson s rato, respectvely, and α s a numercally determned scalng parameter. One o the man problems o ths model s that the Berkovch tp s a three-sded pyramd, and that the lm elastc modulus s assumed to be known. Thn lm Young s modulus may range wth gran sze and lm thckness [11], thus t s dcult to know the modulus pror to lm testng. n mproved method usng a concal tp has been suggested [5], and the reduced modulus can be wrtten as: 1 r 1ν = 1ν 1 e α ( th) α ( th) 1ν s s where h s the lm thckness. gan, the lm Young s modulus s not known beore testng, and when the ndentaton depth, t s equal to the lm thckness, h, the second term dsappears and the whole equaton goes back to the Olver-Pharr method. Recently Han et. al. [9] used a numercal method to calculate the corrected contact area. In ths method, the contact area s estmated by takng the measured contnuous stness rom ndentaton experments and usng the reduced calculated stness to assgn the corrected contact area. e C C (6),

4 We propose another procedure, whch s a varaton o the Josln-Olver method, and utlzes the act that the elastc modulus does not change sgncantly wth the ndentaton depth or the two gold lms tested, and has the 1/ 0.5 dependence, whle the hardness has the 1/ dependence. xpermental Detals In order to nvestgate the valdty o the proposed method, two gold samples were tested. One gold sample was evaporated on the mca substrate to the thckness o 00 nm. nother sample was evaporated on the (100) slcon waer, wth a 0 nm Cr nterlayer, to the thckness o 50 nm. The Hystron Trbondenter was used to test the lms mechancal propertes. Pror to each set o tests, the tp was calbrated by ndentng quartz n order to obtan the tp projected area as a uncton o the ndentaton depth or the Olver-Pharr method. For thn lms the surace roughness wll strongly nluence the results, so the n-stu magng capablty o the Hystron Trbondenter was used pror to ndentaton (Fgure 1a) to nd smooth areas. The surace roughness or the 00 nm gold samples s below 10 nm, and the roughness o the 50 nm samples s below 3 nm. One o the advantages o the gold samples s that they do not have surace oxdes, whch may aect the ndentaton results. Results and Dscusson Fgure a shows the P/S values or 50 and 00 nm gold lms. The P/S rato ncreases wth ndentaton depth, whch proves that the substrate nluences the measurements. For most homogeneous materals, other researchers have reported that P/S should be a constant [5]. Reduced modulus on the other hand does not change sgncantly wth the ndentaton depth (Fgure b). P/S (N -1 *m - ) Indentaton Sze ect 50 nm 00 nm Reduced modulus, GPa Indentaton Sze ect 50 nm 00 nm a) Indentaton depth/flm thckness b) Indentaton depth/flm thckness Fgure. a) P/S and b) reduced modulus results or 00 nm gold on mca and 50 nm gold on (100) slcon waer.

5 The hardness was rst calculated usng the Olver-Pharr method, whch shows a steady ncrease wth the ndentaton depth (Fgure 3). The ntal part o the expermental data, below the rato o the ndentaton depth to the lm thckness o 0.3, has been explaned by the ndentaton sze and the gran sze eects, whch can not be corrected or usng the proposed procedure. The Josln-Olver method can be used to obtan the true hardness or bulk materals, whle or the thn lm/substrate combnaton, ths method underestmates the substrate nluence. Other researchers have shown that the elastc msmatch between the lm and the substrate materals s one o the man reasons that causes ncorrect hardness values [9]. We propose to reduce the elastc modulus msmatch eect on the measured thn lm hardness. Frst the Josln-Olver method s used, and the data s lnear tted. For both gold samples, the shallow ndentatons (<0% o the lm thckness) were excluded. The corrected hardness s: H hc = a b (7), t s where a and b are the lnear t parameters or the Josln-Olver data (Fgure 3), and S are the reduced modul o the lm and the substrate, respectvely, h c s the contact depth and t s the lm thckness. The 00 nm gold lm reduced modulus s 75 GPa (Fgure b), whle the mca substrate modulus s 169 GPa. The 50 nm gold reduced modulus s 180 GPa (Fgure b), and the Cr underlayer modulus o s about 00 GPa. The proposed method results along wth the Olver-Pharr and the Josln-Olver hardness are shown n Fgure 3 or the two gold lms on mca and (100) S substrate wth a 0 nm Cr nterlayer. When the ndentaton depth reaches the lm thckness, the corrected hardness values approach the substrate materal hardness. The proposed procedure needs to be valdated urther on other thn lm systems. Hardness, GPa 1 10 S Hardness Hardness, GPa 4 8 J-O O-P Corrected a) Indentaton depth/flm thckness b) Indentaton depth/flm thckness Fgure 3. Hardness results or a) 50 nm gold lm on mca and b) 00 nm gold lm on (100) S waer wth 0 nm Cr nterlayer. 6 J-O O-P Corrected Mca Hardness

6 Conclusons procedure based on the Josln-Olver method has been proposed, and could reduce the substrate eect on hardness or ductle thn lms on hard substrates the measured lm elastc modulus does not vary much wth the contact depth. For the deeper ndents when the ndentaton depth to the lm thckness rato s one, the corrected hardness values approach the substrate hardness. cknowledgements The authors would lke to acknowledge support or ths project rom NSF (CMMI and CMMI ). We would lke to thank Davd Gracas group rom John Hopkns Unversty or provdng gold sample on slcon, Potr Cygank rom Jagellonan Unversty or provdng gold sample on mca, and Patrck Waters rom USF or help wth ndentaton experments. Reerences 1. D.T. Read and J.W. Dally, J. Mater. Res. 8 (1993) T.-Y. Zhang, X. Wang, B. Huang, Mater. Sc. and ng. 409 (005) S.P. Baker and W.D. Nx, J. Mater. Res. 9 (1994) 3131, lmastaa, D.S. Stone, cta Mater. 50 (00) R. Saha, W.D. Nx, cta Mater. 50 (00) M. Zhao, X. Chen, Y. Xang, J.J. Vlassak, D. Lee, N. Ogasawara, N. Chba, Y.X. Gan, cta Mater. 55 (007) G.M. Pharr, W.C. Olver, and F. Brotzen, J. Mater. Res. 1 (1986) D.L. Josln, W.C. Olver, J. Mater. Res. 5 (1990) S.M. Han, R. Saha, W.D. Nx, cta Mater. 54 (006) R.B. Kng, Int. J. Sold. Struct. 3 (1987) D.. Kramer,.. Volnsky, N.R. Moody and W.W. Gerberch, J. Mater. Res. 16 (001) 3150.