convective self-assembly of stoeber sphere arrays for

Colloids and Surfaces

A: Physicochemical and Engineering Aspects 182 (2001) 275–283

Convective self-assembly of stoeber sphere arrays forsyntactic interlayer dielectrics

Martin Bunzendahl, Pallas Lee-Van Schaick, John F.T. Conroy,Charles E. Daitch, Pamela M. Norris *

Department of Mechanical and Aerospace Engineering, Uni6ersity of Virginia, 122 Engineer’s Way, Charlottes6ille,VA 22904, USA

Received 28 June 1999; accepted 12 September 2000

Abstract

A simple protocol for the production of close-packed, Stoeber sphere arrays for use in syntactic low dielectricinterlayer materials is described. Particle arrays are formed using convective self-assembly and deposited directly fromthe production solution. The influence of withdrawal rate and particle size upon film characteristics is given. Finally,evidence of drying-induced film defects is given. © 2001 Elsevier Science B.V. All rights reserved.

Keywords: Dielectric constant; Syntactic foam; Particle array; Convective self-assembly

www.elsevier.nl/locate/colsurfa

1. Introduction

Nanocomposite organic/inorganic syntacticthin films are currently being investigated as lowdielectric constant interlayer materials. Re-searchers hope to produce organic/inorganic com-posites that retain the dielectric and thermalproperties of inorganic particles and the mechani-cal robustness of a host organic component [1,2].Previously examined inorganic particles includehollow glass microspheres [3] and silica aerogelnanospheres [2]. To date, these thin film syntacticfoams have been formed by simple blending of theinorganic and organic components followed by

either spin coating [2] or Champagne lamination[3].

Researchers have found, however, that syntac-tic thin films formed from blends are unsatisfac-tory in both thickness and particle volumefraction. The minimum thickness of such films isinadequate to meet the demands of the microelec-tronics industry because the films must be signifi-cantly thicker that the particle size to makedefects or surface roughness due to the particlesnegligible. The current particle volume fractionsare also unsatisfactorily low. A large number ofparticles (high particle volume fraction) increasesboth the viscosity of the blend and the probabilitythat the particles will not completely disperse inthe organic phase. Both high viscosity and incom-plete dispersion make simple thin film formation

* Corresponding author. Fax: +1-804-9246295.E-mail address: [email protected] (P.M. Norris).

0927-7757/01/$ - see front matter © 2001 Elsevier Science B.V. All rights reserved.

PII: S0927 -7757 (00 )00783 -4

M. Bunzendahl et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 182 (2001) 275–283276

techniques such as spin coating problematic re-sulting in a large number of defects in the com-posite film.

Since high particle volume fractions are neces-sary to obtain a composite with a low dielectricconstant, we have begun to examine methods thatlead to increased control over the location andvolume fraction of the inorganic component inthe syntactic foam. Specifically, we are examiningclose-packed arrays of inorganic particles wherethe interstitial volume can be filled with an or-ganic component during or after array formation.The volume fraction of the inorganic componentin such arrays approaches the theoretical maxi-mum for a monolayer and close-packed monolay-ers provide precision placement of the particles inthe base of the composite film.

While it is possible to produce a variety ofinorganic silica particles with a range of densities,porosities, and sizes, this work was performedwith relatively high density and high dielectricconstant Stoeber spheres, which are well-knownand well-characterized particles [4,5]. Stoeberspheres are a good candidate for low dielectricconstant microelectronic composites because theymatch the size scale of ILD films. Their chemistryand microstructure closely resemble that of xe-rogel, which is a sol–gel-derived porous mediacommonly suggested as a low dielectric constantmaterial [6,7]. Although both xerogels’ and Stoe-ber spheres’ pore sizes are significantly smallerand densities higher than aerogel, researchershave shown that xerogels have competitive dielec-tric constants [1,6–8]. Deshpande et al. reportdielectric constants of 1.138–1.520 at optical testfrequencies for chemically modified xerogels with50–84% porosity. Unmodified xerogels typicallyhave a dielectric constant of 1.8 at 75% porosity[6,7].

2. Background

The formation of particle arrays is a topic ofincreasing importance in the fields of electronics,drug discovery, and optics. Both ordered anddisordered two-dimensional (2-D) films have beenproposed as tunnel resonance resistors [9], 2-D

protein crystals [10], and model systems for re-search [11–13]. Several methods of producingclose-packed particle arrays have been described.These include Langmuir–Blodgett trough deposi-tion [13], self-assembly [9,12,14], chemical immo-bilization, electrodeposition [11], and mostrecently, convective self-assembly [15–19].

Convective self-assembly is a process wherebycolloidal particles spontaneously self-assemble inarrays during the translation of a three phaseinterface across a solid surface while evaporationof the liquid phase is occurring. The three phaseinterface should have a positive contact angle andcan be translated either by evaporation of theliquid phase [15–17,19] or by combined evapora-tion of the liquid and withdrawal of the solidphase (i.e. dipcoating). It is believed that colloidalparticles are convectively drawn to the three phaseinterface by the local evaporation in the meniscus.Once particles that are wet by the solution phaseapproach the region where the meniscus depth iscomparable with particle diameter, they aredrawn together into a close-packed array by capil-lary forces between the individual particles[20,21]. Convective self-assembly has been exam-ined both theoretically and experimentally[10,15–17,19].

Despite these recent investigations, it remainsdifficult to predict the experimental conditionsnecessary for the deposition of low defect arraysof arbitrary particles from arbitrary solvents. Fur-ther empirical research on different particle andsolvent systems is thus necessary.

This report describes the influence of with-drawal rate and sphere diameter upon the convec-tive self-assembly of Stoeber sphere arraysdeposited directly from an ethanolic productionsolution. The report will introduce the theory ofevaporation deposition and mathematical model-ing of array nucleation and growth, as well aspresent our own experimental results.

3. Theory

The formation of close packed arrays by con-vective self-assembly has been described as twodiscrete steps. The first step, transport of particles

M. Bunzendahl et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 182 (2001) 275–283 277

to the three phase interface, is thought to bedriven by local evaporation at a positive menis-cus. Dimitrov and Nagayama [17] described theadvective flux of particles to the meniscus, jP, interms of a mass balance with an evaporative fluxof the solution liquid, je, giving

jp=b8

(1−8)ljehf

(1)

where 8 is the particle volume fraction, l thelength of the meniscus, hf the wetting film thick-ness at the leading edge, and b is an empirical‘coefficient of proportionality’ related to the ratioof liquid solvent flux to particle flux. In mostexperimental situations, b is expected to approachthe maximum theoretical value of 1. Factors thatmay decrease b include strong particle–surfaceand particle–particle repulsion. During film for-mation, the flux of particles to the meniscus isbalanced by the volume rate of increase of thefilm due to particle deposition, as in

jphf=d6ap (2)

where d is the particle diameter, 6a is the velocityof the three phase interface across the substrate,and p is the packing density. Assuming an idealpacking density of 0.605 for the monolayer array,the ideal withdrawal velocity, 6ai is given by

6ai=b8

(1−8)lje

0.605d(3)

From Eqs. (1) and (3) it can be seen that thefilm formation process depends on the nature ofthe suspension (8, d), the evaporation conditions( je, l), and the experimentally determined coeffi-cient b.

The second step in thin film formation is thepacking of the particle array. The theory behindparticle interactions in thin films and at threephase interfaces has been examined for severalsituations [18,20–23]. The net force acting uponparticles in a thin film can be approximated by atwo term force balance, given by

F (k)=UII ·7

L k

dlug+UII ·&

S k

ds(−np) (4)

where UII is the unit surface tensor of the sub-strate plane, n is the outer unit normal vector of

the particle’s exposed surface, and u is the unitnormal vector to the circular contact line which istangential to the meniscus surface. This forcebalance shows that the perturbation of the liquidsurface by the close approach of a pair of wettedparticles is the driving force behind attraction in athin liquid film. If the liquid/particle contact lineswere plane — parallel with the substrate, bothintegrals in Eq. (4) would be zero. If the liquid/particle contact angle were positive, the first inter-facial tension term would be repulsive and thesecond hydrostatic term attractive. It has beenconcluded that for submicrometer particles, theinterfacial tension force of Eq. (4) is far greaterthan the hydrostatic pressure force [18].

4. Materials and methods

Stoeber spheres were prepared in ethanolic so-lution as described in references [4,5]. Briefly,anhydrous ethanol, 30% ammonium hydroxide,and tetraethylorthosilicate (TEOS) were mixed inmolar ratios of 70:3:2 and 40:1:1 to yield 200 and70-nm particles, respectively, with discrete dropsof TEOS being added after mixing the other twocomponents. The stirred solution was allowed toreact for periods in excess of 4 h.

Volumes of reactants were chosen to provide anearly identical solid volume fraction. Typically, atotal volume of approximately 200 ml was pro-duced. This provided several fractions that couldbe used in successive depositions that examinedthe influence of other experimental variables suchas withdrawal speed.

Deposition substrates were fragments of siliconwafers cut to approximately 3 cm wide and 4 cmlong. After cutting, the wafers were soaked in‘piranha’ solution (60 vol.% fuming sulfuric acid,40 vol.% 30% hydrogen peroxide) for approxi-mately 5 min. The wafer was then rinsed withdeionized water and placed in neat acetone untilneeded. Upon removal from acetone, the waferdried and was ready for use without further pro-cessing. Neither cleaning nor deposition were car-ried out in a cleanroom environment.

An in-house built dip-coater was used to drawthe wafer directly out of the Stoeber sphere pro-


duction solution, hence translating the three phaseinterface across the wafer surface. An adjustablespeed stepper motor geared to a step size of onemicron was placed above the solution on an opti-cal table. The wafer was vertically suspended fromthe motor by a string and clip. Withdrawal speedwas adjusted by controlling the number of stepsper second. This provided sufficiently smoothwithdrawal, however it may be beneficial in thefuture to move to a continuous motor. Humiditywas not controlled or monitored during thecourse of these experiments.

The production, cleaning, and deposition pro-cedures were repeated with various particle sizes,wafer speeds, and solutions. Particle sizes wereadjusted to determine the optimal size for anethanol/silica meniscus. Wafer speed was adjustedto characterize its effect on deposition thicknessand consistency on deposition from the sameproduction solution. Lastly, the experiment wasrepeated with different production solutions ofnominally the same particle size in order to char-acterize the repeatability of the results.

Only the first, 3–5 mm of each particle arraywas selected for characterization. This was donebecause particle deposition was not uniformacross the entire length of the wafer, presumablybecause the rate of evaporation was dependentupon the constantly changing particle solution.The particle arrays were characterized using SEMand light microscopy. After the withdrawal pro-cess, the wafers were scribed and fractured inorder to fit in the SEM. It is believed that fractur-ing the wafer did not affect the particle arrayexcept at the fracture line. The wafers were thencoated with a 10 nm layer of gold for SEMcharacterization. SEM characterization was per-formed on a JEOL JSM-35.

5. Results and discussion

The influence of withdrawal rate upon arraymicrostructure for 200 and 70-nm particles isshown in exemplary SEM micrographs (Figs. 1–4). The corresponding particle sizes, wafer speeds,and images are given in Table 1.

The average surface coverage Gave, as given inTable 1, is an approximate measure of the com-pleteness of the film and is modified from thetraditional definitions of surface coverage used inmolecular systems. Specifically, only defects that

Fig. 1. (a–c) Particle (200 nm) arrays formed at a withdrawalrate of 8 mm s−1. Scale bars represent 10, 1, and 1 mm,respectively.


Fig. 2. (a)–(c) Particle (200 nm) arrays formed at a withdrawalrate of 2 mm s−1. Scale bars represent 10, 1, and 1 mm,respectively.

the wafer. This definition was chosen to compen-sate for both multilayer deposition and the voidsbetween particle clusters that appear regardless ofwithdrawal rate between clusters of particles asshown in Figs. 1–3. Using this definition, the

Fig. 3. (a–c) Particle (70 nm) arrays formed at a withdrawalrate of 6 mm s−1. Scale bars represent 10, 1, and 1 mm,respectively.

are larger than the average particle diameter andexpose the substrate are considered in the mea-surement of surface coverage. In Langmuirianterms, the only available sites are those largerthan the average particle diameter and located on


Fig. 4. Particle arrays (70 nm) formed at a withdrawal rate of6 mm s−1. The scale bar represents 100 nm. Despite the highresolution, there is no evidence of multilayer deposition.

liquid to the mensicus does not provide a suffi-cient supply of particles to cover the entire sub-strate. Furthermore, when the withdrawal rate isdecreased to 2 mm s−1, as in Fig. 2(a–c), thesetypes of defects are no longer present.

One unexpected characteristic of these films wasthe large extent of multilayer deposition. At leastpartially complete multiple layers of particles arepresent in films from every withdrawal rate exam-ined. For example, even the submonolayer film inFig. 1(c), formed at withdrawal rates of 8 mm s−1,clearly displays some particle deposition beyond asingle monolayer. In these lowest coverage films,the onset of multilayer deposition appears to berelated to particle polydispersity, monolayer re-gions do exist in areas where the particles areclosest to monodisperse, as in the right-hand sideof Fig. 1(c). However, as one moves to highersurface coverage films formed at slower with-drawal rates, such as Fig. 1(a–c), particle deposi-tion appears to be almost entirely multilayer. Thisis true even in the regions with the lowest particlepolydispersity.

Previous empirical investigations of convectiveself-assembly do not report such combined multi-layer and submonolayer deposition [10,15,17].These investigations were performed with latexspheres deposited from aqueous solution ontoeither glass [15,17], mica [15,17], or mercury sub-strates [10,17]. The polarizabilities of these parti-cles and substrates were never so closely matchedas they are in the system examined here. Further-more, other researchers have noted that surfac-tants sometimes cause preadsorption of particles

surface coverage of Fig. 2(c) is 100%, althoughvoids between particle clusters clearly exist.

5.1. Two hundred-nanometer particles

The influence of withdrawal rate upon filmstructure for 200-nm particles is shown in Table 1and exemplary micrographs in Figs. 1 and 2. Onegeneral trend that is apparent from these results isthe increase in surface coverage with decrease inwithdrawal speed. For example, the film formedat the highest withdrawal rate of 8 mm s−1 shownin Fig. 1(a–c) has the lowest surface coverage ofany withdrawal rate examined. There are defectson the size of several tens to hundreds of particlediameters. This is presumably related to the highwithdrawal rate for this film, the advective flux of

Table 1Average surface coverage Gave (as defined in the text) as a function of particle diameter and withdrawal rate, along with thecorresponding figure numbers

Withdrawal rate (mm s−1) GaveAverage particle diameter (nm) Corresponding figures

200 Fig. 1(a–c)8 45200 667

4200 83973.5200

2200 99 Fig. 2(a–c)9470 20

1170 99670 99 Fig. 3(a–c), 4


to the substrate before and during withdrawal,and increase the defect density [16]. Thus, largerparticle/substrate attraction may account for themultilayer deposition.

Another striking feature of these films is theomnipresence of anisotropically — oriented voidsbetween clusters of particles. The clusters appearto contain between 5 and 30 particles and areapproximately the same size for all depositionconditions examined. The voids between theseclusters range in thickness from one-quarter toover a full particle diameter and are likewisepresent in every film, regardless of depositionconditions. Unlike multilayer deposition, both an-isotropic [15] and isotropic [17] voids betweenclusters have been reported, but only in somelatex films. The presence of these voids in all ofthe films produced here may indicate that thevoids are unique to this experimental system.

It is strongly suspected that these voids betweenparticle clusters arise due to shrinkage of thespheres during drying, as others have previouslysuggested. [17] In this experimental system, theparticles are Stoeber spheres. Undried Stoeberspheres have densities that are 75–90% that ofbulk fused silica [4,5], which indicates a relativelyhigh porosity. During drying, solvent evaporationfrom inside pores will result in a capillary pressurethat acts to draw the pore walls together. If thepressures are sufficiently high, the capillary pres-sure can collapse pores and result in a decrease inporosity and the net shrinkage of the sphere.

Such a decrease in volume of the Stoeberspheres is directly analogous to the volume de-crease of a hydrogel during drying.

Since the decrease in volume occurs only upondrying, there is no possibility for the solution toprovide more particles to the array. The numberof particles per unit area is fixed and the attractiveforces between neighboring particles oppose oneanother. When the net forces in one direction aresufficient to draw a particle, the particle movesaway from its other neighbors and the voidsbetween clusters are formed. The forces present insuch a process should be independent of with-drawal rate. Furthermore, they should exist de-spite the larger defects seen in the highestwithdrawal rate films, which would account for

their presence in all of the Stoeber sphere filmsexamined.

The highest quality films produced are shown inFig. 2(a–c) which were formed at a withdrawalrate of 2 mm s−1. The surface coverage on thesefilms was greater than a monolayer and appearedto be uniform over areas of several square cen-timeters. The only defects present in these filmsare shown in Fig. 2(a) and appear as white speck-les at low magnification. At higher magnification,it can be clearly seen that these defects arise dueto dust on the surface of the wafer. As statedbefore, the films were not produced in a clean-room environment and contamination is notsurprising.

5.2. Se6enty-nanometer particles

The influence of withdrawal rate upon filmstructure for 70-nm particles is shown in Table 1and the exemplary micrographs in Figs. 3 and 4.The speckling on these micrographs is believed tobe an artifact of the coating and imaging processand does not represent features of interest. Thewithdrawal rates of 20, 11, and 6 mm s−1 for the70-nm particles were scaled to approximately ex-amine the same deposition conditions as the 200-nm particles, as described in Eq. (3). This,however, was not the case.

The most striking difference between 70 and200-nm particle deposition is the relatively minorchanges in film microstructure seen with largechanges in withdrawal rate. The differences be-tween films over the range of examined with-drawal rates appears to be minimal, the films arenearly indistinguishable.

This lack of variability in the 70-nm particlefilms belies the theoretical predictions of Eq. (3).Since the solid volume fraction and evaporativeflux should be nearly identical for both the 70 and200-nm particle suspensions and the withdrawalvelocities were chosen to approximately scale withthe different sphere diameters, the deposition be-havior of both particle diameters should be nearlyidentical if the empirical coefficient of proportion-ality b is identical. Furthermore, if the empiricalcoefficient of proportionality does indeed repre-sent the real physical properties of the solution,


there should still be variability in the film mi-crostructure since the influence of the coefficientshould be the same in all three films. In otherwords, the coefficient of proportionality is con-stant across all three films and independent ofwithdrawal rate. Thus, a change in the coefficientof proportionality should only shift the observedvariability to faster or slower withdrawal rates,not remove it altogether.

The apparent lack of variability in the threefilms may still be interpreted in light of Eq. (3) ifthe coefficient of proportionality is dramaticallylarger in the 70-nm particle system and if oneassumes that the multilayer deposition seen withthe 200-nm particles is no longer a physical possi-bility with 70-nm particles. In this case, the fastestwithdrawal rates examined might still be lowerthan the ideal withdrawal velocity, 6ai, for the70-nm particle system and dense particle arraysformed under all of the deposition conditionsexamined.

This hypothesis is supported, in part, by thenearly monolayer deposition shown in Fig. 3, andat increased resolution in Fig. 4. Although theresolution of the 70-nm particles is not compara-ble to the resolution obtained with 200-nm parti-cles, there is no reason to suspect extensivemultilayer deposition in any of the films. Indeed,SEM micrographs of defects caused by manualhandling (not shown) show only single layerdeposition.

The dramatic elevation of the coefficient ofproportionality in the 70-nm particle systemwould have to be due almost entirely to a diame-ter-related decrease in repulsion between the Stoe-ber sphere particles with each other and the silicasurface. The composition and polarizabilities ofthe solvent, solutes, and particles in both solu-tions are very close. The largest difference be-tween the two solutions is the particle size. Sincethe solid volume fraction of both solutions isapproximately constant, the 70-nm particles maybe subject to a much smaller DLVO repulsionwith the wafer surface and with each other.

All films formed at 70 nm also display theinter-cluster voids characteristic of the 200-nmparticle films. The relative size in number of parti-cles in each cluster and the thickness of the voids

relative to particle size appear approximatelyequal for both 200 and 70-nm particles. This is inagreement with the theory that the voids occurdue to shrinkage during drying if one assumesthat the porosity and hence volume shrinkage ofboth 70 and 200-nm particles is identical. If this isthe case, the percent decrease in diameter will bethe same for given percent volume shrinkage,independent of initial particle radius.

6. Conclusions

The first steps toward the production of lowdielectric constant syntactic interlayer dielectricshave been taken. High density arrays of porousinorganic particles have been formed using evapo-rative deposition during dip-coating. Best resultsfor the deposition of Stoeber spheres onto anuntreated silicon wafer were obtained with a with-drawal rate from the production solution of lessthan 2 mm s−1. The films displayed nearly com-plete coverage over areas of several square cen-timeters, and can be useful for low dielectricconstant syntactic foams.

Evaporative deposition during dip-coating hasalso been shown to be a useful technique for thedeposition of high density arrays of Stoeberspheres. A range of different films has beenformed using two particle varieties and a range ofwithdrawal rates. The deposition behavior of theStoeber spheres bears certain similarities to thebehavior of latex particles, but some unusual dif-ferences have also been identified. These differ-ences include extensive multilayer deposition of200-nm particles and an apparent independence offilm microstructure from withdrawal rate for 70-nm particles. Further research into the influenceof polydispersity and particle–particle and parti-cle–surface interactions is necessary for a betterunderstanding of this system.

Acknowledgements

The authors would like to thank ChristinaElzey and Erich Rayment for their assistance withthe scanning electron microscopy and CatherineIliesa for her editorial comments.


References

[1] P. Brueesch, F. Stucki, T. Baumann, P. Kluge-Weiss, B.Bruehl, L. Niemeyer, R. Struempler, B. Ziegler, M.Mielke, Appl. Phys. A 57 (1993) 329.

[2] M. Ree, W.H. Goh, Y. Kim, Polym. Bull. 35 (1995)2150222.

[3] R.M. Japp, K.I. Papathomas, Mater. Res. Soc. Symp.Proc. 372 (1994) 221.

[4] W. Stoeber, A. Fink, E. Bohn, J. Coll. Int. Sci. 26 (1968)62.

[5] A. van Blaaderen, A. Vrij, Langmuir 8 (1992) 2921.[6] D.M. Smith, J. Anderson, C.C. Cho, B.E. Gnade, Mater.

Sci. Res. Symp. Proc. 371 (1995) 261.[7] E.M. Zielinski, IEDM’97 (1997) 936.[8] R. Deshpande, D.M. Smith, C.J. Brinker, US Patent

5,565,142 (1996).[9] A. Taleb, C. Petit, M.P. Pileni, J. Phys. Chem. B 102

(1998) 2214.[10] H. Yoshimura, M. Matsumoto, S. Endo, K. Nagayama,

Ultramicroscopy 16 (1990) 411.[11] M. Giersig, P. Mulvaney, Langmuir 9 (1993) 3408.

[12] V.L. Colvin, A.N. Goldstein, A.P. Alivisatos, J. Am.Chem. Soc. 114 (1994) 5221.

[13] B.O. Dabbousi, C.B. Murray, M.F. Rubner, M.G.Bawendi, Chem. Mater. 6 (1994) 216.

[14] L. Motte, F. Billoudet, M.P. Pileni, J. Phys. Chem. 99(1995) 16425.

[15] C.D. Dushkin, H. Yoshimura, K. Nagayama, Chem.Phys. Lett. 204 (1993) 455.

[16] N.D. Denkov, O.D. Velev, P.A. Kralchevsky, I.B.Ivanov, H. Yoshimura, K. Nagayama, Langmuir 8 (1992)3183.

[17] A.S. Dimitrov, C.D. Dushkin, H. Yoshimura, K. Na-gayama, Langmuir 10 (1994) 432.

[18] P.A. Kralchevsky, K. Nagayama, Langmuir 10 (1994) 23.[19] E. Adachi, A.S. Dimitrov, K. Nagayama, Langmuir 11

(1995) 1057.[20] K. Hinsch, J. Coll. Int. Sci. 92 (1983) 243.[21] D.Y.C. Chan, J.D. Henry, L.R. White, J. Coll. Int. Sci.

79 (1981) 410.[22] P.A. Kralchevsky, V.N. Paunov, I.B. Ivanov, K. Na-

gayama, J. Coll. Int. Sci. 151 (1992) 79.[23] V.N. Paunov, P.A. Kralchevsky, N.D. Denkov, K. Na-

gayama, J. Coll. Int. Sci. 157 (1993) 100.

.

convective self-assembly of stoeber sphere arrays for

Documents