Real-Time Observation of Reactive Spreading of Gold on Silicon
Nicola Ferralis, Farid El Gabaly, Andreas K. Schmid, Roya Maboudian, Carlo Carraro
aa r X i v : . [ c ond - m a t . m e s - h a ll ] D ec Real-Time Observation of Reactive Spreading of Gold on Silicon
Nicola Ferralis, ∗ Farid El Gabaly, Andreas K. Schmid, Roya Maboudian, and Carlo Carraro Department of Chemical Engineering, University of California, Berkeley, California 94720, USA Sandia National Laboratories, Livermore, California 94550, USA National Center for Electron Microscopy, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA (Dated: December 3, 2009)The spreading of a bilayer gold film propagating outward from gold clusters, which are pinned toclean Si(111), is imaged in real time by low energy electron microscopy. By monitoring the evolutionof the boundary of the gold film at fixed temperature, a linear dependence of the spreading radiuson time is found. The measured spreading velocities in the temperature range of 800 < T <
930 Kvaried from below 100 pm/s to 50 nm/s. We show that the spreading rate is limited by the reactionto form Au silicide, and the spreading velocity is likely regulated by the reconstruction of the goldsilicide that occurs at the interface.
PACS numbers: 68.08.De, 68.35.Fx, 68.37.Nq, 68.43.Jk
Metal spreading dynamics play a defining role in thegrowth of semiconductor nanostructures, e.g., by de-termining pattern fidelity of structures grown by cat-alyzed vapor-liquid-solid or vapor-solid-solid mechanisms[1]. On a fundamental level, the problem is complicatedby its multiscale nature. The equilibrium of a partiallywetting microscopic drop on a solid surface often en-tails the existence of a thin adsorbed film, sometimes ofmonolayer or even sub-monolayer thickness. Similarly, aspreading drop or thick liquid film is preceded by a thinadvancing precursor film [2], whose kinetics have beenwidely debated. Patch-spreading experiments have beencarried out at different length- and time scales, rangingfrom essentially static and macroscopic measurements [3]to microscopic observations [4, 5, 6, 7, 8, 9] under dy-namic conditions [10], up to the temperature range whereevaporation is a factor [11].In this Letter, we employ low-energy electron mi-croscopy (LEEM) to image in real time the evolution ofa spreading precursor film in equilibrium with a clusterreservoir. As in Refs. [3, 10] the model system we useis Au/Si(111). In contrast to the previous studies, byfocusing on a smaller length scale we address a differentlimiting regime, as our experimental approach permits usto operate essentially under conditions of constant chem-ical potential. This condition is realized by supplying Auatoms from Au microparticles dispersed on the surface.These particles exist, at elevated temperature, as pinnedliquid droplets of Au/Si eutectic melt in bulk (3D) equi-librium with the Si substrate, as shown in Fig. 1 [12].With this experimental method, we are able to deter-mine the non diffusive spreading velocities of the atom-ically thin precursor film. We show that the linear timedependence in the formation of the interface between thegold silicide and the clean Si surface is a direct conse-quence of the limited reaction kinetics at the boundaryof the spreading precursor film. In atomistic terms, thedynamics of the spreading is regulated by the structuralreconstruction of gold silicide that that takes place at the interface.The experiments were carried out using the spin-polarized LEEM at Lawrence Berkeley National Labo-ratory [13], which operates under ultrahigh vacuum con-ditions (base pressure of 5 · − Torr) and on a separateUHV chamber (base pressure of 2 · − Torr), equippedwith conventional rear-view low-energy electron diffrac-tion and a cylindrical mirror analyzer for Auger electronspectroscopy [14]. Gold microspheres (Aldrich, radii be-tween 0.7-1.5 µ m) were dispersed using a N carrier gason hydrogen terminated Si(111) substrates, as describedelsewhere [12]. The areal density of Au clusters was in therange of 10 − µm . The Si chips were immediately intro-duced into ultra-high vacuum. The absence of native ox-ide was verified by the lack of either SiO or O peaks inthe Auger electron spectra. The heating was performedby electron bombardment of the Si substrate from theback. The temperature during the annealing experimentswas measured with a W-Re thermocouple spot-welded toa tantalum plate touching the sample. The thermocouplewas calibrated using the Si(111) (1 ×
1) to (7 ×
7) surfacephase transition at 1120 K [10, 15], resulting in a pre-cision in the temperature measurement of ±
10 K. Datawere recorded with a high resolution charge-coupled de-vice camera, with acquisition rates varying from 1 to 2frames per second. Data analysis was performed usingthe image manipulation program ImageJ [16].The 3D gold-silicon phase diagram is characterizedby a deep, Au-rich eutectic (composition Au Si atT E =636 K, Fig. 1). This is a well-understood conse-quence of the frustration in the covalent bonding of sil-icon brought about by the electron-rich gold. Thus, thesolubility of Au in Si is negligible, and the AuSi eutecticmelt does not wet the Si surface (the measured contactangle is ∼ ◦ ) [12]. In the dewetting equilibrium, anisolated liquid AuSi drop coexists with a thin adsorbedAu film, uniformly spread over the substrate. This filmconsists of a crystalline monolayer of gold silicide (i.e., areconstruction of the Si surface in which Au atoms form FIG. 1: 3D gold/silicon phase diagram. At temperaturesabove the eutectic T E =636 K, the composition of the eutecticmelt in the cluster is readjusted to follow the eutectic liquidus(bold line). Inset: Schematic diagram of an Au-Si cluster inthermodynamic equilibrium on the Si surface. Under equi-librium condition, the surface is covered by an intermetalliccrystalline monolayer of covalently bonded gold silicide with √ × √ three chemical bonds with √ × √ ∼ T E , the cluster melts, acquir-ing a composition of Au Si . Previous studies showthat the Si is “dug up” from under the cluster, and theeutectic drop remains pinned in the resulting cavity [12].The eutectic drop is in local thermodynamic equilibrium,so that at constant pressure the local chemical potentialis specified by the temperature only, along the coexis-tence curve depicted in bold in Fig. 1. Upon raising thetemperature above ∼
783 K, hydrogen desorbs and thesurface consists entirely of the clean 7 × × √ FIG. 2: The increment in the radius of the gold silicide layer ismeasured directly from the LEEM images. In each LEEM im-age, the position of the Au-Si eutectic microparticle is withinthe dark circle [19], while the surrounding bright disc cor-responds to the √ µ m. the gold silicide layer is extracted from the resulting pro-file, as shown in Fig. 2, and plots of radius vs time atconstant temperature are generated [19]. Several exam-ples are shown in Fig. 3. The slopes of the curves showthe spreading velocity of the √ < T <
930 K), the plots display alwaysa linear behavior, showing that the surface reconstruc-tion spreads at constant velocity (at a given T). We havemeasured spreading velocities ranging over nearly threeorders of magnitude, from below 100 pm/s to 50 nm/s,some examples are plotted in Fig. 3. Linear growth mayseem surprising at first glance, as it implies an increas-ing flux of atoms from the molten drop. However, in ourexperiments gold droplets can be regarded as practicallyinexhaustible reservoirs. Although power laws R ( t ) ∝ t α FIG. 3: Gold silicide spreading velocities are measured at dif-ferent temperatures. The persistence of linear time evolutionof the spreading of the silicide layer, incompatible with diffu-sive spreading, indicates that reaction-limited kinetics endureover a wide temperature range. ( α ≤ .
5) are often encountered in the spreading of pre-cursor films [9, 20], constant spreading velocities havealso been predicted in some models [21]. Below, we showthat the observed time dependence of the spreading isdue to the reaction-limited nature of the structural re-construction of gold silicide that takes place at the inter-face.For the general problem of reactive spreading at in-terfaces, one can imagine two limiting cases. In a dif-fusion limited case the area of a homogeneous precursorshould expand linearly with time, because of the con-stant flux of atoms supplied by the source. With circularspreading, this corresponds to square-root dependence ofthe spreading radius on time (as observed for examplein Ref. [9].) In a reaction limited case, the spreadingvelocity is limited by the rate at which the structuraltransition from the pristine substrate surface to the pre-cursor layer reconstruction occurs. This corresponds to alinear dependence of the spreading radius on time. Otherlimiting cases are conceivable, including the presence ofa length scale over which the reaction limited regimebecomes diffusion limited, as the distance between thesource and the boundary of the precursor layer increases.As discussed below, all our measurements, spanning awide range of temperatures and spreading velocities, arewithin the reaction-limited case, although earlier experi-ments probing Au/Si spreading on a much larger lengthscale appear to indicate diffusion limited conditions [3],suggesting that the crossover length scale is between theregime probed here and that discussed in Ref. [3].In order to understand which mechanisms can be re-sponsible for the non diffusive behavior, let us considerthe diffusion equation for steady state conditions that governs the concentration C Au of Au atoms at the sur-face (Fig. 4), ∇ C Au = 0 . (1)Assuming the Au chemical potential on the terrace inproximity to the Au-Si eutectic microparticle is in equi-librium with bulk Au, the equilibrium concentration ofAu atoms close to the microparticle, C r eq , can be con-sidered constant in time, i.e., C ( r ) = C r eq , where C ( r )is the concentration of Au atoms at position r . In thetemperature range used in these experiments, the concen-tration and mobility of Au adatoms over the Si-(7 × J diff = − D dC Au d r = D C r eq − C ( r )ln( r /r ) 1 r (2)where D is the diffusivity of Au atoms over the silicideand C ( r ) the concentration at r (see Fig. 4). To pre-serve the steady state condition, Au arriving at the in-terface must be consumed in the two main mechanismsresponsible for the advance of the interface: (i) the for-mation of the AuSi silicide over the Si surface, and (ii)the rearrangement of Si atoms to reconstruct the surfaceunderneath from Si-(7 ×
7) to Si-( √ × √ J reac = m [ C ( r ) − C r eq ] (3)where C ( r ) − C r eq corresponds to the deviation from theAu concentration at which both sides of the interfacewould be in equilibrium [22]. m is a constant determinedby how fast Au adatoms are incorporated into the inter-face. Under steady state conditions, both fluxes shouldbe equal, J diff = J reac , a condition that leads to a valueof C ( r ). Using this value in Eq. 2 we can define aninterfacial spreading flux, J interface = m ( C r eq − C r eq )1 + mr ln( r /r ) /D (4)The factor mr ln( r /r ) /D determines a length scalewhich specifies when the interface motion crosses overfrom interface reaction limited ( D ≫ mr ln( r /r )) todiffusion limited ( D ≪ mr ln( r /r )). Note that in thereaction limited case, the concentration gradient acrossthe spreading region is small, C ( r ) ∼ C r eq (see Fig. 4).If the interface velocity were diffusion-limited, i.e., dom-inated by the diffusion of Au over the silicide, the mea-sured velocity would be non-linear over the measured dis-tance. Furthermore, the variation in the distance the in-terface moves, r , (up to 3 µ m in our experiments, see Au( 3 x 3)-Si(111) Si(7x7)
Aumicroparticle(reservoir)
Spreading distance eq C C r i CC (this experiment) r C eq l i (general case experiment) l r FIG. 4: Schematics of the evolution of the concentration C ofthe Au atoms spreading.
Fig. 3) would result in a non-constant velocity measure-ment independent of the value of D ( C r eq − C r eq ).Our observation is that the interface advances at con-stant velocity for a given temperature, over the men-tioned distance. This indicates that the interface velocityis reaction limited: the diffusivity of Au over the silicideis so fast that it does not affect the final velocity. Theinterface flux J interface corresponds to the reaction fluxat the interface, J reac , which is ultimately controlled bythe reaction rate at the interface, (Eq. 3). This rate isdetermined by the slowest atomistic processes necessaryto move the interface. Since the attachment or detach-ment of Si from Si steps to reconstruct the surface isthe process with higher barrier it is possibly the limitingprocess.The length scale at which the crossover to diffusionlimited kinetics is expected depends on the value of thediffusivity D of Au on the silicide [3] and on the Auatom concentration C , which cannot be determined fromthese experiments. The Au atom concentration might bejust barely more than the interface reaction can consume(close to crossover), or the availability of gold adatomscould exceed the reaction rate by a huge factor (far fromcrossover), either case would look identical in these ex-periments. Understanding the mechanism controlling thespreading of Au on Si surfaces is of practical importancein applications where Au clusters are used as catalystsfor growth of complex nanostructures, such as epitaxialgrowth of branched nanotrees by catalyst re-flow [23, 24].On a fundamental level, we have shown that the rele-vance of atomic kinetics in the adlayer structure is dic-tated by a non-diffusive process. These reaction processesfix the velocity of an otherwise fast diffusing Au for theprecursor film mobility of a partially wetting metal-on-semiconductor system.We thank N.C. Bartelt for fruitful discussions. Thiswork was supported by the National Science Foundationunder Grant EEC-0425914 through the Center of Inte-grated Nanomechanical Systems, by DARPA N/MEMSScience and Technology Fundamentals Center on Inter-facial Engineering for MEMS, and by the National Cen-ter for Electron Microscopy, at the Lawrence BerkeleyNational Laboratory, which is supported by the U.S.Department of Energy under Contract No. DE-AC02- 05CH11231. ∗ Electronic address: [email protected][1] C. Carraro, R. Maboudian, and L. Magagnin, Surf. Sci.Reports , 499 (2007).[2] P.G. de Gennes, Rev. Mod. Phys. , 827 (1985).[3] Yu.L. Gavrilyuk and V.G. Lifshits, Phys. Chem. Mech.Surfaces , 1091 (1984).[4] G.W. Jones and J.A. Venables, Ultramicroscopy 18, 439(1985).[5] M. Hanbucken, T. Doust, O. Osasona, G. Le Lay, and J.G. Venables, Surf. Sci. 168, 133 (1986).[6] T. Ichinokawa, I. Hamaguchi, M. Hibino, Surf. Sci. 209,L144 (1989).[7] D. Reuter, G. Gerth, and J. Kirschner, J. Appl. Phys.82, 5374 (1997).[8] D. Reuter, G. Gerth, and J. Kirschner, Phys. Rev. B 57,2520 - 2529 (1998).[9] D. Reuter, G. Gerth, and J. Kirschner in Surface Diffu-sion
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