Solid state de-wetting observed for vapor deposited copper films on ...

280 C. Schrank et al. / Thin <strong>Solid</strong> Films 459 (2004) 276–281Fig. 6. Second Minkowski-functionals calculated <strong>for</strong> (a) ensembles of holes in 300 nm thick Cu-coatings after approx. 2 min heat treatment (——) in comparison with a random point ensemble (long dashed line) and a point ensemble of vertices in a polycrystal (------); (b) ensembles ofdroplets resulting from a 300 nm thick Cu-coating after 60 min heat treatment (——) in comparison with a random point ensemble (long dashedline) and a point ensemble calculated from the geometric centers of grains in a polycrystal (short dashed line).ularly spaced (i.e. the more correlated) the points are,the lower the width of the curve will be.Both, Fig. 6a <strong>for</strong> the hole positions and Fig. 6b <strong>for</strong>the droplet positions show a significant correlation ofthe object positions when compared to the functionalobtained <strong>for</strong> a random point distribution. In the case ofthe holes, the origin of this correlation is yet unclearand may be related to residual stress in the film. Holeswhich were located at the vertices of a simulatedpolycrystal (see below) are obviously also randomlydistributed (Fig. 6a, wi<strong>de</strong> dashed line). The correlationof the droplet position can be explained by the mechanism<strong>de</strong>picted in Fig. 8: in Fig. 8a a polycrystallinearray obtained from a 48-<strong>state</strong> Potts-mo<strong>de</strong>l of regulargrain growth w16x after 35 000 Monte Carlo Steps isshown. The white points encircled by a black regionindicate the geometric center of each grain and aschematic circular droplet, respectively. Fig. 8b showsthe ensemble of droplets of Fig. 3c. If one assumes thatthe whole amount of material of each grain is concentratedin a droplet then the correlation of droplets shouldbe reflected by the correlation of the geometric centersof the grains in the mo<strong>de</strong>l. In fact the dashed line inFig. 6b was obtained from the point distribution in Fig.8a and shows a reasonable similarity to the 2nd Minkowskifunctional obtained from the droplet array inFig. 7. SEM image of droplets resulting from a 300 nm thick Cucoatingafter 60 min heat treatment. The encircled region indicates afeature, which is a remanent of a Rayleigh-instability, which <strong>for</strong>medduring the separation of two previously connected droplets.Fig. 8. Visualization of a mo<strong>de</strong>l, which explains the correlation ofdroplet positions in the final phase of <strong>de</strong>-<strong>wetting</strong> (a) mo<strong>de</strong>l of a polycrystallinefilm. Each white dot indicates the geometric center of agrain. The black circles around the geometric centers shall symbolizethe droplets resulting from the spheroidization of the single grain. (b)Topographic AFM-image of an actual droplet array (see Fig. 3c).

C. Schrank et al. / Thin <strong>Solid</strong> Films 459 (2004) 276–281281Fig. 8b. There<strong>for</strong>e at least the correlation of the dropletsin the late phase of <strong>de</strong>-<strong>wetting</strong> is un<strong>de</strong>rstandable by themechanism of recrystallization and film rupture alongthe grain boundaries.4. Conclusion and outlookIn the present paper, it was shown that N -plasma2pre-treatment is a powerful tool to improve the mechanicaladhesion of Cu on C. Thermal treatment, on theother hand, leads to <strong>de</strong>-<strong>wetting</strong> of the Cu-film from theC-substrate and, there<strong>for</strong>e to a significant reduction ofadhesion values. The mechanism of the <strong>de</strong>-<strong>wetting</strong>process was found to be strongly correlated to therecrystallization of the Cu-film. This leads to the nucleationof holes at selected vertices of the recrystallizedcoating. Via film rupture along the grain boundaries, anarrangement of insulated droplets is <strong>for</strong>med in the latephase of thermal treatment if the film is sufficientlythin.It is, there<strong>for</strong>e of great technological importance toinhibit the first phase of <strong>de</strong>-<strong>wetting</strong>, i.e. the <strong>for</strong>mationof holes. The fact that not all vertices in the polycrystalare the nuclei of holes indicates that hole <strong>for</strong>mation isat least partially surface diffusion driven. Holes nucleateat positions where grains terminated by surface planeswith high diffusivity meet. One approach is, there<strong>for</strong>eto add materials to the Cu-coating, which reduce surfacediffusivity.However, hole nucleation is most probably not onlydue to surface diffusion as it is indicated by the nonrandomcorrelation of holes. This correlation is notobtained by constructing point ensembles of vertices,which are boun<strong>de</strong>d by grains of selected crystallographicdirections by a modified grain growth mo<strong>de</strong>l. A reason<strong>for</strong> this correlation might be residual stress in thecoating, which surely is also a driving <strong>for</strong>ce <strong>for</strong> <strong>de</strong><strong>wetting</strong>,as Srolovitz <strong>state</strong>s in w14x. There<strong>for</strong>e a <strong>de</strong>terminationof residual stresses in the Cu-Coatings will bea topic of further work, along with an adjustment of<strong>de</strong>position parameters to minimize intrinsic stresses.AcknowledgmentsThis Work is supported by the Austrian ‘Fonds zurFor<strong>de</strong>rung ¨ <strong>de</strong>r Wissenschaftlichen Forschung’ (FWF)un<strong>de</strong>r Grant Nr.: P-14534.Referencesw1x S.J. Sun, M.D. Zhang, J. Mater. Sci. 26 (1991) 5762.w2x Y.L. Petitcorps, J.M. Poueylaud, L. Albingre, B. Ber<strong>de</strong>u, P.O.Lobstein, J.F. Silvain, Key Eng. Mater. 127-131 (1997) 327.w3x Z. Zhu, X. Kuang, G. Carotenuto, L. Nicolais, J. Mater. Sci32 (1997) 1061.w4x Y.Z. Wan, Y.L. Wang, H.L. Luo, X.H. Dong, G.X. Cheng,Mater. Sci. Eng. A288 (2000) 26.w5x G. Korb, J. Korab, G. Groboth, Composites 29A (1998) 1563.w6x Leaflet: HTW Hochtemperaturwerkstoffe GmbH (data-sheetavailable on www.htw-germany.com).w7x R. Dubgen, ¨ G. Popp, Glasartiger Kohlenstoff SIGRADUR (R)– ein Werkstoff fur ¨ Chemie und Technik In<strong>for</strong>mation leafletof HTW Hochtemperaturwerkstoffe, Germany.w8x E. Neubauer, G. Korb, C. Eisenmenger-Sittner, H. Bangert, S.Chotikaprakhan, D Dietzel, A.M. Mansanares, B. Bein, Thin<strong>Solid</strong> Films, in press, doi:10.1016yS0040-6090(03)00318-3.w9x S. Herminghaus, K. Jacobs, K. Mecke, J. Bischof, A. Fery, M.Ibn-Elhaj, S. Schlagowski Sci. 282 (1998) 916.w10x J. Bischof, D. Scherer, S. Herminghaus, P. Lei<strong>de</strong>rer, Phys. Rev.Lett. 77 (8) (1996) 1536.w11x B. Du, F. Xi, Y. Wang, Z. Yang, O.K.C. Tsui, Langmuir 18(2002) 8510.w12x U. Thiele, M. Mertig, W. Pompe, Phys. Rev. Lett. 80 (13)(1998) 2869.w13x K. Jacobs, S. Herminghaus, K.R. Mecke, Langmuir 14 (1998)965.w14x D.J. Srolovitz, M.G. Goldiner, J. Mater. 47 (3) (1995) 31.w15x Lord Rayleigh, Proc. Lond. Math. Soc. 10 (1878) 4.w16x D.J. Srolovitz, J. Vac. Sci. Technol. A4 (6) (1986) 2925.