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Thermal fragmentation of nano-size clusters on surfaces

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2010 EPL 90 16001

(http://iopscience.iop.org/0295-5075/90/1/16001)

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April 2010

EPL, 90 (2010) 16001 www.epljournal.org

doi: 10.1209/0295-5075/90/16001

Thermal fragmentation of nano-size clusters on surfaces

P. V. Kashtanov1(a), R. Hippler

2, B. M. Smirnov

1 and S. R. Bhattacharyya3

1 Joint Institute for High Temperatures, Russian Academy of Sciences - Izhorskaya 13, Building 2,Moscow 125412, Russia2 Institut fur Physik, Ernst-Moritz-Arndt-Universitat Greifswald - Felix-Hausdorff-Str. 6, 17489 Greifswald,Germany, EU3 Surface Physics Division, Saha Institute of Nuclear Physics - 1/AF Bidhan Nagar, Kolkata 700 064, India

received 21 December 2009; accepted in final form 23 March 2010published online 21 April 2010

PACS 64.70.Nd – Structural transitions in nanoscale materialsPACS 81.07.Bc – Nanocrystalline materialsPACS 82.60.Qr – Thermodynamics of nanoparticles

Abstract – Nano-size silver clusters deposited on a silicon surface with a native-oxide layerundergo rapid thermal annealing, and after fast cooling a partial fragmentation into smallerclusters is observed. The observations are explained by a simple model where the behavior of aliquid droplet on a surface is characterized by the surface tension for a free droplet and the surfacetension at the interface with the silicon surface. A method is suggested for the determinationof the ratio of these parameters. Within the framework of this model cluster fragmentation intoseveral smaller droplets is caused by thermal fluctuations due to droplet oscillations. The modelcould prove useful for controlling the size of nano-particles on a surface.

Copyright c© EPLA, 2010

A cluster is a system of bound atoms or moleculesand as such is an intermediate physical object betweenindividual atoms or molecules and condensed bulk matter.Typical cluster sizes vary from a few atoms up to nano-sizeclusters (particles) with more than 106 atoms or molecules.Clusters due to their limited size, e.g., have specificelectronic, optical, magnetic, and catalytic properties thatare of both fundamental and applied interest [1–8].In this communication we present a novel theoretical

approach for the recently observed fragmentation of nano-size silver clusters deposited on a surface that weresubjected to rapid thermal annealing (RTA) [9]. Thisthermal fragmentation could be useful in controlling theparticle size in the fabrication of nano-size materials.In that experiment, nano-sized silver clusters were

produced inside a gas aggregation nano-cluster source[10,11]. The silver atoms were sputtered from a silvertarget in a direct current magnetron sputtering device [12].Small clusters form by attachment of free atoms andfurther grow by coagulation processes inside the liquidnitrogen (LN2) cooled aggregation tube of variablelength [13]. The clusters flow together with the buffer gas(Ar) through a variable orifice with a typical diameter of0.3 cm.

(a)E-mail: kashtanovpv@gmail.com

Nano-size clusters with a diameter of 5.6 nm wereselected by a mass filter and deposited onto silicon waferswith a native-oxide (SiO2) layer. Deposited clusters wereexamined by a scanning electron microscope (SEM) withenergy-dispersive X-ray analysis (SEM/EDX) [9]. Thedeposited clusters were further treated by rapid thermalannealing (RTA) at temperatures of 473K, 673K, 873K,and 1073K for 3min each in a nitrogen environment.Figure 1(a) shows the morphology of as-deposited clus-ters on a Si substrate [9]. The morphology of the as-deposited clusters shows irregular islands or aggregatesof varying size. The average size, i.e. mean diameters ofthe aggregates, is found to be approximately 32 nm whichis much bigger than the 5.6 nm size of the incident mass-selected nano-clusters. This means that solid nano-clustersdeposited on a surface merge to form bigger agglomerateswhile maintaining much of their individual structure. Theas-deposited aggregates thus have a porous structure.SEM images of the deposited clusters after sequential

rapid thermal annealing (RTA) at temperatures of 473K,673K, 873K, and 1073K for 3min in a N2 environmentwere taken, see [9]. Here we evaluate the transition from873K to 1073K. During annealing at 673K, and the moreso at 873K, see fig. 1, the silver nano-clusters presumablyreached a molten liquid state and, in order to minimize thefree surface energy, they transform into a compact liquid

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P. V. Kashtanov et al.

Fig. 1: Morphology (top panel) and histogram (bottom panel)of deposited nano-size silver clusters (mean size 5.6 nm). SEMoperating voltage 10 kV, magnification 60000 [9].

droplet and become round. This shows that Ag nano-clusters have a much lower melting temperature comparedto the Ag bulk phase (1233K). After annealing at 1073K,the morphology is dominated by smaller clusters withsizes around 25 nm and a drastically increased numberof clusters (fig. 2). This is further illustrated in fig. 3which compares the size distributions at 873K and 1073K.The 873K sample shows a normal size distribution (solidline) with a maximum around 65 nm. By contrast, the1073K sample displays a bimodal distribution (dashedline) with a large maximum at small sizes around 25 nmand a smaller second maximum around 55 nm which iscomparable in number to the 873K size distribution. Theobservation suggests the fragmentation of (on average) onelarge cluster with mean size of 65 nm into one smallercluster of mean size around 55 nm plus 2–3 small clustersof mean size 25 nm.In analyzing the fragmentation of a liquid cluster

(droplet) located on a surface, we note that the majorinteractions include i) interaction between atoms insidethe droplet and ii) interaction of these atoms with thesurface. These interactions determine both the surfaceenergy on a free droplet surface and the surface energyon the interface and, hence, govern the behavior of the

Fig. 2: Morphology of deposited nano-size silver clusters (meansize 5.6 nm) after rapid thermal annealing in a N2 environmentfor 3min at 873K (top panel) and 1073K (bottom panel). SEMoperating voltage 10 kV, magnification 60000 [9].

Fig. 3: Histogram of mass-selected silver nano-size clusters of5.6 nm sizes after rapid thermal annealing (RTA) to 873K and1073K in a N2 environment for 3min in each case. The solidline represents a Gaussian distribution with an average size of65 nm, while the dashed line represents a bimodal Gaussiandistribution with average sizes of 25 nm and 55 nm.

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Thermal fragmentation of nano-size clusters on surfaces

liquid droplet on the surface including its fragmentationunder corresponding conditions.In order to understand the observed phenomenon we

consider the behavior of an incompressible liquid dropleton a surface. Assuming the droplet size to be small, weignore the weight force on this behavior. As the maininteractions are those among the atoms inside the dropletand of the atoms with the surface, the total droplet energyU thus is composed of the surface energy of a free dropletdetermined by its surface tension σ1 and the surface energydue its interaction with the underlying surface with asurface tension σ2,

U =−ε0 V +S1σ1+S2(σ1−σ2), (1)

where ε0 is the binding energy per unit volume, V isthe droplet volume, S1 is the area of the free dropletsurface, S2 is the area of the interface surface, σ1 is theliquid surface tension, σ2 is the surface tension of interfacethat corresponds to attraction of droplet molecules to thesurface. We assume the droplet liquid to be non-wetting,i.e. σ1 >σ2.The parameters for the liquid droplet under consider-

ation are shown in fig. 4. Taking the droplet radius andvolume in vacuum as R0 and V0 = 4πR

30/3, respectively,

the droplet volume V on a surface is

V =π

3R3(1− cosα)2(2+ cosα) = πR

3

3x2(3−x), (2)

where x= 1− cosα. Since the droplet consists of anincompressible liquid, i.e., V = V0, its radius R for a givenangle α is given as

R=22/3R0

x2/3(3−x)1/3 . (3)

From this we have for the total droplet energy U inaccordance with eq. (1):

U =−ε0 V +4πR20σ1Φ(x, z), Φ(x, z) =4−x+ z(x− 2)x1/3(6− 2x)2/3

(4)and z = σ2/σ1. One can find the optimal value x fromthe condition ∂ lnΦ(x, z)∂x= 0 that leads to the Youngformula [14,15]

xmin = 2− z. (5)

Correspondingly, under optimal conditions we have for theparameters of this droplet

R

R0=

22/3

(2− z)2/3(1+ z)2/3 , h=R(2− z),

S1

4πR20=

21/3

(2− z)1/3(1+ z)2/3 ,

S2

4πR20=

21/3z

(2− z)1/3(1+ z)2/3 ,

Φ(xmin, z) =2+ z− z2

22/3(2− z)1/3(1+ z)2/3 , (6)

Fig. 4: Parameters of a liquid droplet on a plane surface.

where h is the droplet height, S1, S2 are the areas ofthe free droplet surface and the interface surface, andthe function Φ(xmin, z) characterizes the surface dropletenergy in accordance with formula (4).On this stage one can formulate the method to measure

the droplet parameters. Of course, it is impossible tomeasure simultaneously different parameters of an individ-ual droplet. But, one can find the distribution of depositedclusters over transversal cluster sizes on the basis of theSEM (scanning electron microscope) measurements, andthe distribution over cluster heights from AFM (atomicforce microscope) measurements. Comparison of the distri-butions over the interface diameters and droplet heightsgives the value z = σ2/σ1 along with another information.Now within the framework of the above model we

analyze the possibility of cluster fragmentation as aresult of its oscillation. Therefore we now investigatethe oscillations of a droplet located on a plane surfaceaccounting for the forces due to surface tension. As theliquid is incompressible, the droplet volume is conservedduring the oscillations. If we assume that all off the dropletpartakes in the oscillation, one can find the oscillationfrequency ω as

ω≈√U ′′

m, (7)

where m is the droplet mass, U ′′ = ∂2U/∂α2 is the secondderivative of the droplet energy (4) with respect to theangle α, and we assume the mass difference for a static andoscillating droplet to be ∆m�m∆α2. Note that the totaldroplet mass is conserved in the course of its oscillations,and we denote by ∆m its part that is located over thedroplet boundary.Taking the droplet separation in parts during its oscil-

lations to be connected with this extra part that slidesover the stable droplet surface, one can estimate a size ofdroplets that can be separated from the stable droplet.Indeed, droplet oscillations are determined by thermalfluctuations, and the energy of this fluctuation is of theorder of T (the droplet temperature expressed in energyunits). We have on the basis of eq. (4) for a typical

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P. V. Kashtanov et al.

Fig. 5: Φ(xmin, z) and Φ′′(xmin, z) vs. z.

amplitude of oscillations

4πR20σ1Φ′′(xmin, z)∆α2 ≈ n2/3T.

Introducing the specific surface energy A according to therelation An2/3 = 4πR20σ1, where n is the total number ofdroplet atoms, we obtain for a typical amplitude of dropletoscillations

Φ′′(xmin, z)∆α2 ≈ Tn2/3

An2/3=T

A.

Taking the mass ∆m of the separated part as

∆m≡m∆nn�m∆α2

and assuming Φ′′(xmin, z)≈ 0.28, because it correspondsto the mean value of α which varies over the range from90◦ to 180◦ (see fig. 5), we obtain the number of atoms ina separated droplet as

∆n≈ 3.6 TAn. (8)

One can compare this result with the experimental datawhere silver clusters with a mean size R0 ≈ 32.5 nm (n≈7.5 · 106) are in contact with an oxidized silicon surface.Taking the temperature T = 0.1 eV and the specific surfaceenergy A= 2.0 eV [16], we obtain ∆n≈ 1.35 · 106 and R0 ≈18.3 nm which is within a factor of ≈1.5 of the smalldroplets size, see fig. 3.In conclusion, a simple model of a liquid nano-size

droplet on a surface describing its fragmentation intoseveral smaller droplets leads to reasonable agreementwith the experimental observations. This model includesone aspect of the cluster behavior and assumes thecluster analogy with a macroscopic droplet. In reality, the

surface of a liquid cluster differs from that for a largedroplet [17, 18]. Therefore, a macroscopic liquid dropletlocated on a surface under thermodynamic equilibriummay be divided into small fragments at temperaturescompared with the critical one, while in the cluster case itis possible at lower temperatures.

∗ ∗ ∗

We like to thank Prof. T. K. Chini, Dr. D. Datta,and Dr. A. Majumdar for helpful discussions. The workwas supported by the Deutsche ForschungsgemeinschaftDFG through SFB/TRR 24 and by RFBR, Russia(09-02-00108a).

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