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“Author(s):

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Los AlamosNAT IO NAL LABORATORY

Precision Cleaning of Semiconductor

Surfaces Using Carbon Dioxide-Based

Fluids

J.B. Ru bin CS T-12 LANL

L.D. Sivils CS T-12 LANL

A.A. Busna ina

Microcontamina tion Research

Clark son University

Pots dam, NY

13699-5725

Laboratory

SEMI CON WEST 199 Symposium on

Comtami nation Free Manufacturing

Semiconductor Processing

July 12-14, 1999

San Franc i so, CA

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Precision Cleaning of SemiconductorSurfaces Using Carbon Dioxide-Based Fluids

J.B. Rubin and L. D. SivilsPhysical Organic Chemistry Group (CST-12)

Chemical Science & Technology DivisionLos Alamos National LaboratoryLos Alamos, New Mexico 87544

A.A. BusnainaMicrocontamination Research Laboratory

Clarkson UniversityPotsdam, NY 13699-5725

Biography

Jim Rubin is a TechnicalStaff Member with the SupercriticalFluids Facility (SFF), within thePhysical Organic Chemistry Groupat Los Alamos. He received hisPh.D. in Materials Engineering fromthe New Mexico Institute of Miningand Technology in 1992.

Dale Sivils is a TechnicalStaff Member with the SupercriticalFluids Facility (SFF), within thePhysical Organic Chemistry Groupat Los Alamos. He received hisPh.D. in Chemistry from theUniversity of Missouri-Rolls in1995.

Ahmed A. Busnaina, Ph.D.,is a Professor and Director of theMicrocontamination ResearchLaboratory, at Clarkson University.He specializes in wafer cleaningtechnology, chemical and particulatecontamination in LPCVD and

sputtering processes, particleadhesion and removal, submicronparticle transport, deposition andremoval in clean environments. Heauthored more than 200 papers injournals, proceedings andconferences.

Abstract:The Los Alarnos National

Laboratory, on behalf of the Hewlett-Packard Company, is conductingtests of a closed-loop C02-based

supercritical fluid process, known asSupercritical C02 Resist Remover

(SCORR). We have shown that thistreatment process is effective inremoving hard-baked, ion-implantedphotoresists, and appears to be fillycompatible with metallizationsystems. We are now performingexperiments on production wafers toassess not only photoresist removal,but also residual surface

F3EXXHVEDBIX 132000

(N-i!

contamination due to particulate andtrace metals.

Dense-phase (liquid orsupercritical) C02, since it is non-

polar, acts like an organic solventand therefore has an inherently highvolubility for organic compoundssuch as oils and greases. Also, denseC02 has a low-viscosity and a low

dielectric constant. Finally, C02 in

the liquid and supercritical fluidstates can solubilize metalcompleting agents and surfactants.This combination of properties hasinteresting implications for theremoval not only of organic films,but also trace metals and inorganicparticulate. In this paper we discussthe possibility of using C02 as a

precision-cleaning solvent, withparticular emphasis onsemiconductor surfaces.

Data:Aqueous-based solutions

currently used for wafer cleaninggenerate large waste streams, and theinherently high surface tension ofthese solutions limits their use incleaning substrates containing very-fine-scale structures. Surfactants canbe used to reduce surface tension,but this necessitates a subsequentrinsing and drying step, requiringadditional amounts of ultrapurewater, Also, the withdrawal ofwafers through the liquid/gasboundary following the cleaninvariably leads to re-deposition ofparticulate.

2

One of the processes beingevaluated for advanced ICmanufacturing is dry (vapor-phase)cleaning, to replace traditionalaqueous-based immersioncleaning. [1] As, an extension ofcurrent work on photoresiststripping, performed at Los Alamoson behalf of the Hewlett-PackardCompany, we are investigating thepossibility of using carbon dioxide(C02), either as a liquid or a

supercritical fluid, as a precisioncleaning solvent.

The temperature at which thevapor pressure above a pure liquidreaches one atmosphere is known asthe normal boiling point. The normalboiling point of liquid water, at oneatmosphere, is 100”C. In an opencontainer, Figure 1, the temperatureof liquid water cannot be raisedabove 100”C since this would causethe vapor pressure of the water torise above one atmosphere,

SealedContainer

B~:>.:.J,..,.“. ,!. . .....”..~ $.. , ..’,?.+-+’. . ........ ..: : Wate/- ~;~;.,. .>-.} - --- -.2;::?:,.. ..,. .-Figure 1. Formation of asupercritical jluid by heating of aliquid in a sealed container.

exceeding the ambient pressure. Ifwe place a quantity of water in asealed container, however, then wemay heat the liquid water to highertemperatures, since the vaporpressure of the water can increasebeyond one atmosphere. As weuniformly heat the sealed container,the density of the liquid waterdecreases through thermalexpansion. Simultaneously, thedensity of the water vapor increases.We can continue this heating processuntil, eventually, the density of theliquid becomes so reduced, and thedensity of the vapor phase is soincreased, that the two densitiesbecome equal. The temperature atwhich the liquid and vapor densitiesbecome equal is called the criticaltemperature. Since the temperatureinside the sealed container iseverywhere equal, and the density is

Table 1. Critical temperature, TO

and pressure, PO for some common

jluids.

Fluid I Tc I Pc(“c) (@)

Neon. Ne -229 400Nitrogen, N2 -147 492

Argon, Ar -122 706

SF6 III I

propane, C3H8 97 617

ammonia, NH3 I 133 I 1654

water, H20 374 3209

everywhere equal, thermodynamicsdictates that the pressure inside thecontainer be everywhere equal. Thispressure is called the criticalpressure. A fluid which has beenbrought to conditions above itscritical temperature and pressure isknown as a supercritical fluid. Thisphysical description of the criticaltemperature and pressure suggeststhat all simple liquids (and gases)can be made into a supercritical fluidby generating the appropriateconditions of temperature andpressure. This is indeed correct, andTable 1 gives the critical temperatureand pressure of some common fluids.

Supercritical fluids are usedas solvents in many commercialapplications, including the extractionof caffeine from coffee and essentialoils and spices from plants for use inperfumes and foods. Theattractiveness of supercritical fluidsas solvents stems from their uniquecombination of liquid-like and gas-like properties. Table 2 gives acomparison of the diffisivity,viscosity and density of a typicalorganic fluid in the liquid, gas, andsupercritical fluid state.

To a first approximation, thesolvent power of a fluid is related toits density. The high, liquid-likedensities achievable in supercriticalfluids therefore allows for substantialsolubilities. Figure 2 shows thepressure-temperature-density surfacefor pure C02. The critical point for

pure C02, TC=31°C andPc = 1072 psi (=73 atmospheres), is

Table2. Comparison ofphysico-chemical properties ofa~pical organicJuidin the liquid,gas, and supercriticaljluid state.

Diflsivity Viscosity Density

(Cnlzls) (cl?] or &hn3](rnN#m2)

Liquid 10-5 1 1000

Supercritical 10-3 10-2 300fluidGas 10-1 10-2 1

shown in Figure 2 by the large solidcircle. It can be seen that relativelysmall changes in temperature orpressure, near the critical point,result in large changes in density. Itis this tunability of density, andtherefore tunability of solvent power,which is one of the most attractiveattributes of supercritical fluids.Also, the gas-like properties of lowviscosity and high diffusivityprovides for effective penetrationinto very fine scale structures such ashigh aspect ratio vias and throughholes. Finally, the absence of surfacetension provides for excellentnettability.

There has been considerableprogress in developing supercriticalfluids, and supercritical C02

(SCC02) in particular, for theprecision-cleaning of inorganicsurfaces, [2,3,4] includingmetals, [5,6,7,8] glass, [9,10] opticalelements,[l 1] and one report on itsapplicability to Si wafers.[12]

One advantage of C02 forprecision cleaning is that the processleaves no residues, since itevaporates completely when

depressurized. As a result,subsequent aqueous rinsing anddrying steps are not required. Thereis a commercial system available forSCC02 cleaning of micro-electromechanical devicefabrication,[13] and is becoming apopular processingtechnique. [14,15,16,17].

Another advantage to usingC02 for surface cleaning is its

inertness with respect to inorganicmaterials. Aluminum films exposedto dry C02 gas showed low rates of

adsorption and little or no chemicalreaction.[18] Pure, dry supercriticalC02 has been shown to have no

Figure 2. Pressure-temperature-density surjace ofpure C02.

corrosive action on stainlesssteel,[l 9] iron,[20] orcopper. [21,22,23] It is known fromgeochemical studies that there is avanishingly small volubility for Si02

in C02.[24,25] Also, Khemka and

Chow [26] found that an oxidationanneal of Si in pure C02 at 1000 and

1100”C produced an oxide thicknessof only 10 nm, independent ofannealing time. A thermodynamicanalysis of possible reactionsbetween C02 and Si3N4 [27] shows

that, at the temperatures andpressures of semiconductorprocessing, no reaction betweenthese compounds is expected.Finally, it has been shown thatsurface-adsorbed C02 does not

disassociate or chemically reactwith a highly active, hydroxylatedSi02 surface.[28]

In this paper, we examine thepotential of liquid and supercriticalfluid C02 for removing organic

films, trace metals and particulatefi-om Si wafers. We accomplish thisby comparing how immersion inliquid and supercritical C02 would

behave, relative to immersion in purewater.

1. Orgailic surfacefilmsSCC02 is an excellent

solvent for nonpolar, low molecular-

weight organic compounds, such asgreases, oils, lubricants andfingerprints. [29,30] It is this abilityto solubilize organic compoundswhich underlies the commercialapplications mentioned previously.Extensive compilations of thevolubility of organics in liquid C02

can be found in [31], whilecompilations for supercritical C02

can be found in [32].

2. Trace Metals

Current aqueous immersioncleaning removes metalliccontaminants by the formation ofsoluble metal complexes. Forexample, HC1/H202 and

H2S04/H202 solutions are effective

at removing Cu by forming solublechloride and sulfate complexes,respectively.[33] In a similarmanner, a reactive component,dissolved in a supercritical fluid, canbe used to remove trace metalcontaminants either by surfaceetching of Si and Si02, or by

selective chelation. The potentialadvantage of using SCC02 to

“scavenge” these metals is anenhanced removal rate resulting fi-omthe low viscosity and highdiffhsivity.

By definition, compoundswhich are gaseous at the conditionsof temperature and pressure ofSCC02 will be soluble. Therefore,

compounds such as SF6, BF3, and

C2F6, which are gaseous at SCC02conditions, will be soluble inSCC02. For the case of liquids and

solids, the situation is only slightlymore complex. While it is wellknown that dense C02 is capable of

solubilizing low molecular weightorganic compounds, it is also truethat C02 can solubilize inorganic

compounds 1~they act like organiccompounds, in terms of (a) lowmolecular weight (b) nonpolarity,and (c) existing as discrete molecularspecies. For example, TiC14 [34] and

SnC14 [35,36] have been shown to

be very soluble in supercritical C02.

As an example of a potentialapplication, Sugino et al. [37] used adry C12+ SiC14 mixture to remove

Fe contamination fi-om Si and Si02

surfaces. Both of these compoundsare soluble in dense C02. George et

al. [38] has shown that a CVDprecursor compound, called a~-diketonate and shown in Figure 3a,dissolved in a flowing N2 stream,

can scavenge Cu from Si surfaces.Ueno et al. [39] used this samecompound, dissolved in a flowingargon stream, to remove CU20 and

CUO from Si02 and Cu surfaces.

Also, Pearton et al. [40] used thiscompound, dissolved in N2, to

remove metallic ions from dry-etched AIGaAs at elevatedtemperature. ~-d~etonatecompounds have been shown to beeffective

.chelators

SCC02.[41,42,4344,45,46,47,48,4;

a) 1,1,1,5,5,5-hexafluoro-2,4-pentanedione.

s-‘\/c

w’i’H H

b) bis(trifluoroethyldithiocarbamate).

F F o

\

+“

o.

F /F—C

/

C—N

\F F

~-H

F H/\H

c) n-methylheptafluorobutyrichydroxarnicacid.

Figure 3. Structures of somechelating compounds used forchelation/extraction of metals insupercritical C02.

50] Finally, a compound closelyrelated to the ~-diketonates,trifluoroacetic anhydride (TFAA), isbeing evaluated for PECVD chambercleaning.[51] A similar approach canbe used with dense-phase C02 as the

carrier stream. The solubilities andbehavior of several metal/chelatesystems, in addition to ~-diketonates,have been investigated insupercritical C02, including crown

ethers,[52] dithiocarbamates(Figure 3b)[53,54,55,56,57,58,59,60]amines,[61] hydroxamic acids(Figure 3c),[62] andorganophosphates. [63,64,65]

3. Particlates

3.1. Mechanics of Particle Removal

To evaluate the ability ofliquid and supercritical C02, to

remove particulate, we estimate themagnitude of various adhesion forcesacting between a perfectly smooth,spherical Si02 particle and a

perfectly smooth, flat Si surfaceimmersed in liquid C02,

supercritical C02 and water. We

choose Si02 as representative of the

particles which are largely insolublein aqueous acidic and alkalinecleaning solutions.

There are a number ofadhesion forces that can act betweena particle and a surface, includingchemical bonding. In this discussion,however, we will neglect such

chemical bonding forces, as these arenot well enough understood to alloweven approximate calculation. Also,we neglect diffisive mixing, surfacediffision and other less-commonly-encountered adhesion mechanisms.

Figure 4 shows the types oflong-range attractive forces betweena particle and a surface. We willassume that the particle is non-magnetic. In addition to the forcesshown in Figure 4, we will alsoconsider the magnitude of thegravitational force holding theparticle onto the (horizontal)substrate and the capillary forceswhich exist in humid environments.

A. van der Waals ForceThere are several components

to the van der Waals force between aparticle and a surface. There is acomponent due to (i) interactionbetween permanent dipoles (van derWaals-Keesom force), (ii)interaction between permanentdipoles and induced dipoles (van derWaals-Debye force), and(iii) interaction between induced

Long-rangeAttractive interactions

II

van der Waak electrAatic ma~neticfops forces

I Iimage electricalforces double-layer

forces

Figure 4. Long-range attractiveforces acting between a particle anda surface.[66]

dipoles (van der Waals-Londonforce) .[67] The one of greatestimportance here is the van derWaals-London force. This is anattractive force that arises due toinstantaneous fluctuations ofmolecular dipoles, and occurs in allsubstances.

For the case of a sphericalparticle of material 1, a planarsubstrate of material 2, bothimmersed in a medium 3, the van derWaals-London force, Fv~W,is given

by [68,69]

FA,,, d

vdW = —12h2

(1)

where d is the particlediameter and h is the separationdistance between the particle and thesubstrate surface, usually taken to be4 A.[70]

The van der Waals-Londonforce will increase if there isadhesion-induced deformation of theparticle or substrate, producing anincrease in the contact area. Themodified van der Waals-Londonforce in this case is [71]

F[)

Al~2d 2a2=— l+—

‘dw 12h2 dh

(2)

where a k the contact radius betweenthe deformed particle and thesubstrate surface. However, becauseof the high intrinsic hardness of bothSi02 and Si, it is not expected that

either will suffer thisdeformation,[72] so that Eq. (1)applies.

A132 is called the Harnaker

constant and is given by

where Al 1, A22, A33 are the

Harnaker constants of the purematerials 1, 2 and 3. These purematerial Hamaker constants varyfrom nearly zero for polymers to3 eV for metals. The “binary”Harnaker constants, A12, A13 and

A23, are calculated using various

mixing rules, the most commonbeing a geometric mean: [73,74,75]

Combining Eqs. (3) and (4), we have

(5)

(6)

Various methods have beenproposed to estimate the purematerial Hamaker constants usingexperimentally accessible quantities.One such model,[76] applicable tonon-polar (having no permanentdipole moment) molecules and

which therefore exhibit only the vander Waals-London force, relates Aii

to the work of cohesion: r1 e2 (11)vo. —27c aOm, ‘()Aii=24zyi d; i (7)

where ~i is the surface tension and

()d; i is approximately equal to themolecular diameter of material i.

‘sing ~liquid CO, = 0.6 dyne/cm at

25”C,[77] and assumingdo= 0.20 nm,[78]

A,, =A liquid C02 = 0.011 (eV) (8)

This approach cannot be usedto calculate the Hamaker constant ofSCC02 since, by definition, a

supercritical fluid has no surfacetension. The general expression forthe Hamaker constant betweenmolecules of material i is

Aii = n’ q2 ~ii (9)

where q is the number of atoms perunit volume (Loschrnidt number),~fi is given by [79]

‘( 3 ) (lo).. =11 —a: IZVO ,411 is Planck’s constant

(h= 6.626 x 10-34 Fs), vo is the

ground-state frequency of theelectron

e“ the electron charge

(e= ll;O X 10-19 C), me is the

electron rest mass

(me= 9.11 x 10-31 kg), ~d ao is

the molecular polarizability. Fornon-polar molecules like C02, the

polarizability can be found from theClausius-Mossotii (C-M) fimction

C–M=s–l M 4—O—=— ZNOaO&+2 p 3

(12)

Where s is the dielectric constant, pis the density, M is the molecularweight and No is Avogadro’s

number. Michels and Kleerekoper[80] have shown, throughmeasurements ofs and p, that over awide range of temperatures andpressures, including both liquid andsupercritical C02, ao = (2.97-

3.05) x 10-30 m3

Assuming ao = 3.0 x 10-30 m3,

along with p~ccoz= 0.668 g/cm3 at

50”C and 2000 psi(136 atmospheres), we have

VO= 1.46 X 1015 s-l,

P,, =8.71 x10-76 J.m6, and

A3~= A~cco, = 0.045 (eV) (13)

For comparison, London [81] reports

u() = 2.86 x 1o-3O m3 and

h ‘2.18 x10-77 J.mG for

gaseous C02.

For Si02, Si and water, the

following Hamaker constants havebeen reported: A~io, =1.02 (eV),[82]

A~i = 1.6 (eV),[83] and

A ~,. = 0.27 (eV) .[84] Substituting

these values into Eq. (6), we haveA 132 = A~io2,1i~co,,si=1.05 (eV),

Al,, = A Si02 ISC C021Si = 0.84 (eV), and

A 132 =A . =0.37 (eV) ForSi02 /H20/SIcomparison, Menon et al. [85] givesA . = 0.07 (eV).glass/ H20/Sl Finally,

Eq. (1) gives

O+++

+ chargedparticle +

+++

‘t 1

--- ------ .

h F“Image

~ ,. =---c -------/_ J \1/ \

/— image —:\\ particle /\~ —,/

~. — .

Figure 6. Experimentally measuredvalues of the dielectric constant, g ojpure C02 as a function oj

temperature andpressure.

medium between the particle and thesurface, eo is the permittivity of

vacuum,

so = 8.854x 10-12 C2/~m2), and 1

is the separation distance betweenthe charge centers (approximatelyequal to 2r when the charge isuniformly distributed on the particlesurface). If the charge density on theSi02 particle is 10 electron charges

per square micron,[87]

Fire,, (dynes)= 2“28X10-8 ‘2&

I (15) Iwhere d is in microns.

Iinmersion of the particle/surfacesystem in a fluid affects themagnitude of ~~~~ through shielding

of electical charges, as manifestedthrough the dielectric constant. Thehigh static dielectric constant ofwater, e = 80, compared to e = 1.5for liquid C02 (15°C and 800 psi),

and E = 1.4 for SCC02, (50”C and

2000 psi) (see Figure 6) results inhigher image forces for immersion inC02 for a given particle charge.

2. Electrical double layerforceWhen two dissimilar materials

come into contact, a surface contactpotential is created due to thedifference in their respective workfimctions. The resulting surfacecharge buildup needed to preservecharge neutrality sets up a double-layer charge region, creating anelectrostatic attraction. ~tienvironments, this electrical doublelayer force dominants for smallerparticles, less than approximately5 microns in diameter.[88] Thiselectric double layer force, F~~l, is

given by

F =rcsOd@2 (16)dbl 2h

where @ is the contact potentialestablished on contact of the twomaterials and is equal to thenumerical difference in their workfimctions.[89] Assuming ~ = 0.5 V[90,91,92,93,94] and again usingh=4~,

I F,., (dynes) = 8.69x 104 d (17) Iwhere d is in microns.

Immersion in a fluid willaffect the magnitude of Ffi,*,Y.,

through charge neutralization. [95] Inpractice, the initial contact potentialwill decrease with time because thehigh electrical conductivity of doped

Si will result in the charge “leakingaway”.

C’.Capillary ForceIf a surface-adhered particle is

subjected an environment wherethere is a high vapor pressure ofcondensable fluid, the fluid maycondense in the gaps between theparticle and the substrate surface,Figure 7. The surface tension of thiscondensate draws the surfacestogether, resulting in capillaryattraction.[96] It is observed that theadhesion of particles to surfacesincreases with relative humidity,[97]indicating that capillary force, FC,P,

can make a significant contributionto overall adhesion. For high relativehumidities (> 50 ‘%o), for materialswhich are wetted by the fluid, andfor materials having similar wettingproperties, FC.Pis given by [98,99]

FC,P=2md~ (18)

or

IsubstmkI

Figure 7. Schematic illustration ojthe meniscus formed by acondensable jluid and resultingcapillaryforce.

I F,,, (dynes) = 6.28x 104 d y I

where d is in microns and y is indynes/cm.

If the particle/substratesystem is totally immersed in a fluidwhich wets both materials, includingliquid C02 and water, the capillary

force should be eliminated. [lOO]This is also true for SCC02 because

a supercritical fluid, by definition,cannot be made to condense.

D. Gravitational ForceA solid particle will

experience a downward gravitationalforce, F=,, tending to hold it down

onto a horizontal surface. (Weassume that the particle is at itsdistance of closest approach to thesubstrate so that the buoyancy forcecan be neglected.) Fgv is given by

Fmv=; d3pg .(20)

For Si02, p =2.60 g/cm3 and

g = 980.67 cm/s2, so that

I Fmv(dynes) = 1.34 x 10-9 d3 (21) I

where d is in microns.If the particle and the

substrate surface are immersed, thenthe actual particle density, p, shouldbe replaced by the apparent density,

(P -l%.,). However, the densitiesof liquid C02, supercritical C02 and

water are similar, Figure 2, so thatEq. (21) will not be gr~atly changed.

Thus far, we have considered“static” forces acting between theSi02 particle and the Si surface.

Typically, however, particulateremoval is accomplished byimmersion cleaning with a _j70wingsolvent. This fluid motion generatestwo additional, hydrodynamic forces:lift and drag. In the followingsections, the magnitudes of theseforces will again be examined forliquid C02, supercritical C02 and

liquid water as the immersion media,for both laminar and turbulent flowconditions.

E. Drag Force

O’Neill [101] gives an exactsolution to the linearized Stokes flowequation for the case of a uniformlinear shear flow, Figure 8, and forlow values of the Reynolds number

where VY=,is the fluid velocity at a

distance r normal to the substratesurface (r is the radius of theparticle). For laminar flow, thevelocity gradient is related to thefluid viscosity by

7?=(dxY)y=o ’23)where zo is the shear stress on the

substrate surface due to theflow. [102] Also, since the velocitygradient of the flow is linear, we canintegrate Eq. (23) from y = Oto y = r,where V= Oaty=O:

r ZO= q VY=, (24)

Substituting into Eq. (22), andcollecting terms,

Chitanvis et al. [103] ~havecarried out an analysis for the case ofturbulent flow with a viscoussublayer, deriving an expression forthe drag force as a fi.mction of thefluid (stream) velocity, V:

Fti, =1 O.27Cp (~~)V2 r’ ’26)

where ~ is Fanning’s friction factor,~= 0.04. Simpli@ng Eq. (26) gives

~g =0.16 p V’ d’F (27) 1

Comparing this drag force with thefrictional force, which varies linearlywith particle diameter, they fl.mthershow that the removal of the smallest

particles by rolling varies as V-%

while removal by sliding varies asv-’ .

F. Lift ForceThe (idealized) gradient in

flow velocity illustrated in Figure 8shows that the flow past a surface-adhered particle is a fimction of thedistance normal to the surface. Thelower flow velocity at the bottom ofthe particle relative to the velocity offlow at the top of the particle resultsin a lifting force, tending to dislodgethe particle in the direction of thesurface normal. This force is exactlyanalogous to the lift generated byairfoils. The magnitude of the liftforce, ~ifi, will depend on the nature

of the near-surface flow, andexpressions have been put forwardfor different flow conditions.

Saffman [104] gives theinertial lifting force in a linear shearflow as

Y () Y–2CIV 2F,ifi= 6.46 r2 q v —dy ‘y=r(28)

Combining Eqs. (28-30) gives [106]

In turbulent flow, where theturbulent flow component normal tothe substrate surface variesquadratically with distance fi-om thesurface, Cleaver and Yates [107]give the lift force as

(PNdT*l’32)Ffifi= 0.076p ~Again using Eqs. (29) and (30), wehave

Ffifi= 0.076 q-1 p% ZOd3 (33)

3.2. Surfactauts-Surfactants, in addition to

lowering the surface tension ofliquids, are used to assist in particleremoval by modifjing the surface

/where v = q This equation was

tY

P“ Iderived for the case of a small Dspherical particle in an unbounded, ,linear shear flow in the absence of !wall effects, but serves as an t

a8approximation to the problem of a gparticle in a shear flow along a rigid ewall.[1 05] As before, f v

(/)dV (29)dy ,=O=;substrate -

Velocity

and Figure 8. Schematic illustration of alinear shear jlow past a surface-adheredparticle.

charge/zeta potential of particle“andor substrate surfaces.[ 108] Thereare several compilations on thevolubility of commercial surfactantsin liquid and supercriticalCO2.[109,11O,111] These

compilations show that there anionic,cationic and nonionic surfactantswhich have significant solubilities.Also, considerable progress has beenmade in the design of surfactantsspecifically for use in supercriticalC02, where it is well-known that

highly fluorinated compoundsexhibit excellentsolubilities.[1 12,113] Figure 9 shows

,w~””F FFFFF

lH,lH,2H,2H-Perfluorooctanesulfonic acid,miscible at Ps 144 bar and

T = 50”C [114]

perfluorobutyric acid, miscible atP= 186 barand T=50°C [115]

Figure 9. Examples of surfactantswhich are completely miscible insupercritical C02, along with the

conditions where completemiscibility is observed.

two representative examples ofperfluorinated surfactants and theconditions of temperature andpressure where complete volubility insupercritical C02 is observed.

3. DiscussionThe ability of C02, particularly

in the supercritical state, to removeorganic contaminants would seemsuperior to the use of aqueoussystems, which normally containoxidizers along with acids oralkalies, since the former would bemuch less corrosive to fabricatedsurface structures.

The removal of trace metalsusing a sequence of acidic and/oralkaline aqueous rinses, i.e., SC-1and SC-2, “is capable of producinglow levels of trace metals. Pure C02

does not solubilize these metals dueto charge neutrality considerations,and would require the use ofchelators. However, there are manysuch compounds which have beenshown to be soluble and these wouldbe required in very small amounts.Although any additive is undesirablein terms of potential residues, a finalrinse using clean, dry C02 should

remove these.Inspection

that, in general,between a particlelinearly with the

of Table 3 showsadhesion forces

and a surface varyparticle diameter.

Removal forces, however, vary as ahigher power of d (hydrodynamicdrag acts on the cross-sectional areaof the particle and therefore scale as

&!, while hydrodynamic lift,vibrational and centrifugal forces acton the volume of the particle and

therefore scale as d3). Consequently,particle removal becomes moredifficult as the particle sizedecreases.[1 16]

The calculations of the Hamakerconstant for liquid and supercriticalC02 presented here are only

approximate, but it is apparent thatthe resulting values of the van derWaals-London forces are higher thanthe corresponding value forimmersion in water.

For the image force, it can beseen that the lower dielectricconstant of both liquid andsupercritical C02 results in larger

values of the image force, for a givenparticle charge.

Exact calculations for the liftand drag forces on a surface-adheredparticle are extremely complex, andallow only trends to be deduced.However, the lift force dependsinversely on fluid viscosity, whichfavors C02, Figure 10. For the drag

force a higher viscosity is preferred,which is not favorable for C02.

However, the boundary layerthickness, which is proportional to

v~P , would be much thinner. Also,the addition of soluble polymersmight be used to independentlyadjust the viscosity of liquid and/or

Figure 10. Empirically measuredviscosity, q, in centipoise (cP) ojpure C02, as a function oj

temperature andpressure.

supercritical C02.

It has been mentioned thatthe migration of surface-adheredparticles due to Brownian motionand their subsequent agglomerationmay be a mechanism by which thesmallest particles are removed. Thismotion is greatly enhanced in bothliquid and supercritical C02 because

of the low viscosity. The mean-square displacement, X, byBrownian motion is given by

(34)

where T is the absolute temperatureand t is time. The lower viscosity ofliquid and supercritical C02

(approximately a factor of 50compared to water), along with thevan der Waals attractive forceswhich exist between particles, wouldpromote this agglomeration.[l 17]

Table 3. E#ect on the various adhesionforces between a Si02 particle contacting

a flat, horizontal Si surface immersed in (a) liquid C02, and (b) supercritical

C02 (SCCO~, and (c) H20, based on the empirical relationships for these

forces. Allforces are given in dynes.

Si02/ Si02/

liq. C02 SCC02

/Si /SiFvdW 8.76x 10-3 d 7.01 X10-3 d

Si02/

water/Si

3.09x10-3 dI 1 I

Fdbl 8.69x 10A d 8.69 X 10+ d 8.69 X 10A d

‘image I 1.52x 10-8 d’ I 1.62x 10-8 d’‘cap — —

Fdrag 8.02 d’ TO 8.02 d2 ZO

p similar p similaro similar Fti,. . - similar FtiZ. .

‘lift I lower q -+ I lower q -I p similar I p similar

o higher ~ifi .“.higher ~ifi. .

lower q -+ lower q -+p similar p similar

I “ higher ~i~. . I - higher ~ifi. .Fgrav I similar Fmv I similar Fmv

2.85x 10-10d2

(6.28 X;4 d y)

(7aminarJow)

8.02 d’ TO

(turbulentjlow)

0.16 p V’ d’

(laminarflow)

1.615r/-’ p% # d3

(turbulentjlow)

0.076 q-l p% TOd3

1.34 X 10-9 d3

Based on the foregoinganalysis of adhesion forces forimmersion in C02 versus water, it is

probable that additional removalforces must be generated if dense-phase C02 is to achieve comparable

removal forces obtainable withwater-immersion. These forces canbe generated in a number of ways,including increased shear, flow,either through higher volumetric

flow rates or mechanical agitation ofthe wafer, or electrical forces.

We are currently pefiormingexperiments on pre-contaminatedwafers to quantitatively evaluate theability of dense-phase (liquid andsupercritical) C02 to remove

particulate, and the results of thisstudy will be the subject of a fiturereport.

References

1. R.A. Bowling, S.C. O’Brien, L.M.Loewenstein, M.H. Bennett and B.K.Bohannon, “MMST WaferCleaning”, Solid State Tech.January, 1994 pp. 61-65.2. D.P. Jackson, “Cleaning ProcessUsing Phase Shifting of Dense PhaseGases”, US Patent 5,013,366 (1991).3. D.P. Jackson, “Dense Phase GasPhotochemical Process for SubstrateTreatment”, US Patent 5,068,040(1991).4. K.L, Hoy and K.A. Nielsen,“Methods for Cleaning ApparatusUsing Compressed Fluids”, USPatent No. 5,306,350 (1994).5. L.J. Silva, “Supercritical Fluid forCleaning Metal Parts”, HazardousWaste Consultant, 13 (1995)pp. A25-A26.6. R. Purtell, L. Rothman, B.Eldridge and C. Chess, “PrecisionParts Cleaning Using SupercriticalFluids”, J. Vat. Sci. & Tech. Al 1(1993) pp. 1696-1701.7. W.K. Tolley, P.B. Altringer andD.C. Seidel, “Stripping Organicsfrom Metal and Mineral SurfacesUsing Supercritical Fluids”, Sep. Sci& Tech. 22 (1987) pp. 1087-1101.8. N. Dahmen, J. Schon,H. Schmieder, and K. Ebert,“Supercritical-Fluid Extraction ofGrinding and Metal-Cutting WasteContaminated with Oils”,Sut)ercritical Fluids – Extraction andPollution Prevention, ACSSymposium Series, vol. 670 (ACS,

Washington, D.C., 1997) pp. 270-279.9. N. Dahmen, J. Schon and H.Schmeider, “Extractive Separation ofOils from Glass-Processing andMetal-Processing Residues withSupercritical Carbon-Dioxide”,Chem. Ing. Tech. 67 (1995)pp. 1501-1504.10. J. Schon, N. Dahmen, H.Schmieder and K. Ebert, “Separationof Oil-Contaminated Glass Grinds bySupercritical-Fluid Extraction (SFE),Sep. Sci. & Tech. 32 (1997) pp. 883-897.11. J. McHarty, T.B. Sttiord, L.R.Benjamin, T.E. Vlhiting and S.C.Chao, “Progress in SupercriticalCleaning”, SAMPE J. 29 (1993)pp. 20-27.12. E. Bok, D. Kelch and K.S.Schumacher, “Supercritical Fluidsfor Single Wafer Cleaning”, SolidState Technology 35 (1992) pp. 117-120.13. High Pressure SupercnticalCarbon Dioxide Drying/CleaningSystem, GT EquipmentTechnologies, Inc., 472 Amherst St.Nashua, NH 03063.14. M.A. Douglas and R.M. Wallace,“Method for Unsticking Componentsof Micro-Mechanical Devices”, USPatent No. 5,482,564 (1996).15. E.M. Russick, C.L.J. Adkins andC.W. Dyck, “Supercritical CarbonDioxide Extraction of Solvent fi-omMicromachined Structures”,Su~ercritical Fluids – Extraction andPollution Prevention, ACS

Symposium Series, vol. 670 (ACS,Washington, D.C., 1997) pp. 255-269.16. J. Bi.ihler, F.-P. Steiner, R.Hauert and H. Baltes, “Linear Arrayof Complimentary Metal OxideSemiconductor Double-Pass MetalMicromirrors”, Opt. Eng. 36 (1997)pp. 1391-1398.17, T. Shirnizu, Y. Murakoshi, T.Sane, R. Maeda and S. Sugiyama,“Fabrication of Micro-Parts by HighAspect Ratio Structuring and MetalInjection Molding using theSupercritical Debinding Method”,Microsys. Tech. 5 (1998) pp. 90-92.18. J.L. Falconer, S.D. Bischke andG.J. Hanna, “Electron-EnhancedC02 Adsorption and Stabilization on

Aluminum Films”, Surf. Sci. 131(1983) pp. 455-462.19. E.M. Russick, G.A. Poulter,C.L.J. Adkins and N.R. Sorensen,“Corrosive Effects of SupercriticalCarbon Dioxide and Cosolvents onMetals”, J. Supercrit. Fluids, 9(1996) pp. 43-50.20. H. Behner, W. Spiess, G. Wedlerand D. Borgmann, “Interaction ofCarbon Dioxide with Fe(l 10),stepped Fe(l 10) and Fe(l 1l)”, Surf.Sci. 175 (1986) pp. 276-286.21. A.C. Collins and B.M.W.Trapnell, “C02 Chemisorption on

Evaporated Metal Films”, Trans.Faraday Sot. 53 (1957) pp. 1476-1482.22 F,H.P.M. Habraken, E.Ph. Kiefferand G.A. Bootsma, “A Study of theKinetics of the Interaction of 02 and

N20 with a Cu(l 11) Surface and of

the Reaction of CO with AdsorbedOxygen Using AES, LEED andEllipsomet@, Surf Sci. 83 (1979)pp. 45-59.23. J. Krause. D. Borgmann and G.Wedler, “PhotoelectronSpectroscopic Study of theAdsorption of Carbon Dioxide onCu(l 10) and Cu(l 11)/K – AsCompared with the SystemsFe(l 10)CO2 and Fe(l 10)/K+ C02”,

Surf. Sci. 347 (1996) pp. 1-10.24. D.L. Shettel, Jr., “Volubility ofquartz in H20-C02 Fluids at 5 kb

and 500”-900”C”, EOS 54 (1973)pp. 480-480.25. A.L. Boettcher, “The SystemSi02-H20-C02 : Melting, Volubility

Mechanisms of Carbon, and LiquidStructure to High-Pressures”, Amer.Miner. 69 (1984) pp. 823-833.26. V. Khernka and T.P. Chow,“Thermal Oxidation of (100) Siliconin 02 and C02 and Its Effect on the

Si02-Si Metal Oxide Semiconductor

Parameters”, J. Electrochem. Sot.144 (1997) pp. 1137-1143.27 A.I. Kulikov, “EnvironmentalProtection. Oxidation of SiliconNitride in Gaseous C02 + H20”,

Izvestiya Akademii Nauk,Neorganicheskie Materialy, 23(1987) pp. 688-690.28. A. Ueno and C.O. Bennett,“Irdiared Study of C02 Adsorption

on Si02”, J. Catalysis 54 (1978)

pp. 31-41.

29. E. Stahl and K.W. Quirin,“Dense Gas Extraction on aLaboratory Scale: A Survey ofRecent Results”, Fluid PhaseEquilibria 10 (1983) pp. 269-278.30. W.K. Tolley, P.B. Altringer andD.C. Seidel, “Stripping Organicsfrom Metal and Mineral SurfacesUsing Supercritical Fluids, Sep. Sci.Tech. 22 (1987) pp. 1087-1101.31. A.W. Francis, “Ternary Systemsof Liquid Carbon Dioxide”, J. Phys.Chem. 58 (1954) pp. 1099-1114.32. K.D. Bartle, A.A. Clifford andS.A. Jafar, “Solubilities of Solids andLiquids of Low Volatility inSupercritical Carbon Dioxide” J.Phys. Chem. Ref. Data ~ (1991)713-757.33. J.A. Amick, “Cleanliness and theCleaning of Silicon Wafers”, SolidState Tech., November, 1976,pp. 47-52.34. W.K. Tolley, R.M. Izatt and J.L.Oscarson, “Titanium Tetrachloride-Supercritical Carbon-DioxideInteraction : A Solvent-Extractionand Thermodynamic Study”, Met.Trans. B-Process Metallurgy 23(1992) pp. 65-72.35. W.K. Tolley, R.M. Izatt, J.L.Oscarson, R.L. Rowley and N.F.Giles, “Comparison of theThermodynamics of Mixing ofTitanium Tetrachloride and TinTetrachloride with SupercriticalCarbon-Dioxide”, Sep. Sci. Tech. 28(1993) pp. 615-623.36. N.F. Giles, J.L. Oscarson, R.L.Rowley, W.K. Tolley and R.M. Izatt,

“Thermodynamic Properties ofMixing for SnC14 Dissolved in

Supercritical C02 : A Combined

Experimental and Molecular-Dynamics Study, Fluid Phase Equil.73 (1992) pp. 267-284.37. R. Sugino, Y. Okui, M. Shigeno,S. Ohkubo, K. Takasaki and T. Ito,“Dry Cleaning for Fe Contaminantson Si and Si02 Surfaces with Silicon

Chlorides”, J. Electro. Sot. 144(1997) pp. 3984-3988.38. M.A. George, D.W. Hess, S.E.Beck, J.C. Ivankovits, D.A. Bohlingand A.P. Lane, “Reaction of1,1,l,5,5,5-Hexafluoro-2,4-Pentanedione (H(+)hfac) with CUO,CU20, and Cu Fihns”, J. Elect. Sot.

142 (1995) pp. 961-965.39. K. Ueno, V.M. Donnelly and Y.Tsuchiya, “Cleaning of CHF3

Plasma-Etched Si02/SiN/Cu Via

Structures Using a HydrogenPlasma, an Oxygen Plasma, andHexafluoroacetylacetone Vapors”, J.Vat. Sci. & Tech. B16 (1998)pp. 2986-2995.40. S.J. Pearton, F. Ren, A. Katz,U.K. Chakrabarti, E. Lane, W.S.Hobson, R.F. Kopfl C.R. Abernathy,C.S. Wu, D.A. Bohling and J.C.Ivankovits, “Surface Cleaning ofPlasma-Etched High ElectronMobility Transistors”, J. Vat. Sci.Tech. B 11 (1993) pp. 546-550.41. A.F. Lagalante, B.N. Hansen,T.J. Bruno, R.E. Sievers,“Solubilities of Copper(II) andChromium(III) Beta-Diketonates in

Supercritical Carbon-Dioxide”,Inorg, Chem. 34 (1995) pp. 5781-5785.42. J.M. Murphy and C. Erkey,“Copper(II) Removal from Aqueous-Solutions by Chelation inSupercritical Carbon-Dioxide usingFluorinated Beta-Diketones’’, Ind. &Eng. Chem. Res. 36 (1997) pp. 5371-5376.43. J.M. Murphy and C. Erkey,“Thermodynamics of Extraction ofCopper(II) from Aqueous-Solutionsby Chelation in SupercriticalCarbon-Dioxide”, Env. Sci. & Eng.31 (1997) pp. 1674-1679.44. B.W. Wenclawiak, T. Hees, C.E.Zoner and H.P. Kabus, “Rhodiumand Palladium Beta-DiketonateDetermination with OnlineSupercritical-Fluid Extraction High-Performance Liquid-Chromatography Via Solid-PhaseExtraction, Fres. J. Anal. Chem. 358(1997) pp. 471-474.45. J.A. Darr, M.A. Poliakoff, W.S.Li and A.J. Blake,“Hexafluoropentanedionatosilver(I)Complexes Stabilized byMultidentate N-Donor Ligands :Crystal-Structure of a Charge-Separated Salt Species Soluble inSupercritical Carbon-Dioxide”, J.Chem. Soc.-Dalton Trans. (1997)pp. 2869-2874.46. K.E. Laintz, S. Iso, Y. Meguroand Z. Yoshida, “A Brief Study ofthe Supercritical-FluidChromatographic Behavior ofLanthanide Beta-Diketonates”,

.

HRC-J. High Res. Chrom. 17 (1994)pp. 603-606.47. K.G. Furton, L. Chen and R.Jaffe, “Rapid-Determination ofUranium on Solid Matrices bySynergistic In-Situ ChelationSupercntical-Fluid Extraction andw Absorption-Spectroscopy”,Anal. Chim. Acts 304 (1995)pp. 203-208.48. Y.H. Lin, C.M. Wai, F.M.’ Jeanand R.D. Brauer, “Supercritical-Fluid Extraction of Thorium andUranium Ions from Solid and LiquidMaterials with Fluorinated Beta-Diketones and Tributyl-Phosphate”,Env. Sci. & Tech. 28 (1994)pp. 1190-1193.49. M.Z. Ozel, M.D. Bw%ord, A.A.Clifford, K.D. Bartle, A. Shadrin,N.G. Smart and N.D. Tinker,“Supercritical-Fluid Extraction ofCobalt with Fluorinated and Non-Fluorinated Beta-Diketones”, Anal.Chim. Acts, 346 (1997) pp. 73-80.50. N. Saito, Y. Ikushima and T.Goto, “Liquid Solid Extraction ofAcetylacetone Chelates withSupercritical Carbon-Dioxide”, Bull.Chem. Sot. Japan 63 (1990)pp. 1532-1534.51. L.C. Pruette, S.M. Karecki, R.Reifi J.G. Langan, S.A. Rogers, R.J.Ciotti and B.S. Felker, “Evaluationof Trifluoroacetic-Anhydride as anAlternative Plasma-EnhancedChemical-Vapor-DepositionChamber Clean Chemistry”, J. Vat.Sci. & Tech. A 16 (1998) pp. 1577-1581.

52. S.F. Wang, S. Elshani and C.M.Wai, “Selective Extraction ofMercury with Ionizable Crown-Ethers in Supercritical Carbon-Dioxide”, Anal. Chem. 67 (1995)pp. 919-923.53. J. Wang and W.D. Marshall,“Recovery of Metals from Aqueous-Media by Extraction withSupercritical Carbon-Dioxide”, Anal.Chem. 66 (1994) pp. 1658-1663.54. Y.H. Lin, N.G. Smart and C.M.Wai, “Supercritical-Fluid Extractionand Chromatography of Metal-Chelates and OrganometallicCompounds”, TRAC-Trends Anal.Chem. 14 (1995) pp. 123-133.55. W. Cross, Jr., A. Akgerman andC. Erkey, “Determination of Metal-Chelate Complex Solubilities inSupercritical Carbon Dioxide”, Ind.Eng. Chem. Res. 35 (1996) pp. 1765-1770.56. K.E. Laintz, G.M. Shieh andC.M. Wai, “SimultaneousDetermination of Arsenic andAntimony Species in Environmental-Samples usingbis(trifluoroethyl) dithiocarbamateChelation and Supercritical FluidChromatography”, J. Chromatogr.Sci. 30 (1992) pp. 120-123.57. M. Ashrafkhorassani, M.T,Combs and L.T. Taylor, “Volubilityof Metal-Chelates and TheirExtraction from an AqueousEnvironment via Supercritical C02”,

Talanta 44 (1997) pp. 755-763.58. M. Ashraf-Khorassani and L.T.Taylor, “Supercritical Fluid

Extraction of Mercury(II) Ion vja InSitu Chelation and Pre-FormedMercury Complexes from DifferentMatrices”, Anal. Chim. Acts 379(1999) pp. 1-9.59. C.M. Wai, S.F. Wang, Y. Liu, V.Lopez-Avila and W.F. Beckert,“Evaluation of Dithiocarbamates andBeta-Diketones as Chelating-Agentsin Supercritical-Fluid Extraction ofCd, Pb, and Hg from SolidSamples”, Talanta 43 (1996)pp. 2083-2091.60. Y. Cai, M. Abalos and J.M.Bayona, “Effects of CompletingAgents and Acid Modifiers on theSupercritical-Fluid Extraction ofNative Phenyl-Tin and Butyl-Tinfrom Sediment”, App. Organomet.Chem. 12 (1998) pp. 577-584.61. W.J. Schmitt and R.C. Reid,“The Volubility of ParaffinicHydrocarbons and their Derivativesin Supercritical Carbon-Dioxide”,Chem. Eng. Comm. 64 (1988)pp. 155-176.62. J.D. Glennon, S. Hutchinson, A.Walker, S.J. Harris and C.C.McSweeney, “New FluorinatedHydroxamic Acid Reagents for theExtraction of Metal-Ions withSupercritical C02”, J. Chromatogr.

A, 770 (1997) pp. 85-91.63. H.WU, Y.H. Lin, N.G. Smart andC.M. Wai, “Separation ofLanthanide Beta-Diketonates viaOrganophosphorus AdductFormation by Supercritical-FluidChromatography”, Anal. Chem. 68(1996) pp. 4072-4075.

64. Y.H. Lin, N.G. Smart and C.M.Wai, Supercritical-Fluid Extractionof Uranium and Thorium fromNitric-Acid Solutions withOrganophosphorus Reagents”, Envir.Sci. & Tech. 29 (1995) pp. 2706-2706.65. T. Sasaki, Y. Meguro and Z.Yoshida, “SpectiophotometricMeasurement of Uranium(VI)-Tributylphosphate Complex inSupercritical Carbon Dioxide”,Tantala 46 (1998) pp. 689-695.66. R.A. Bowling, “An Analysis ofParticle Adhesion on SemiconductorSurfaces”, J. Electr. Sot. 132 (1985)pp. 2208-2214.67. R.H. OttWill, “Attractive ForcesBetween Surfaces” in Aspects ofAdhesion 2, edited by D.J. Alner(University of London Press,London, 1966) pp. 9-17.68. H.C. Hamaker, “The London-vander Waals Attraction betweenSpherical Particles”, Physics 4(1937) pp. 1058-1072.69. M.B. Ranade, “Adhesion andRemoval of Fine Particles onSurfaces”, Aerosol Sci. & Tech. 7(1987) pp. 161-176.70. W.C Hinds, Aerosol Technolow.Properties, Behavior, andMeasurement of Airborne Particles(John Wiley & Sons, New York,1982) p. 128.71. K.L. Johnson, K. Kendall andA.D. Roberts, “Surface Energy andthe Contact of Elastic Solids” Proc.Royal Sot. A324 (1971) pp. 301-313.

72. H. KrUpp, “Particle Adhesion:Theory and Experiment”, Adv.Colloid Jnterface Sci. 1 (1967)pp. 111-239.73. J. Visser, “Adhesion of ColloidalParticles” in Surface and ColloidScience, VO1.8, edited by E.Matijevi6 (Wiley-Interscience, NewYork, 1976) pp. 3-84.74. J. Visser, “On HamakerConstants: A Comparison betweenHamaker Constants and Lifshitz-vander Waals Constants”, Adv. ColloidInterface Sci. 3 (1972) pp. 331-363.75. M. Void, “The Effect ofAdsorption on the van der WaalsInteraction of Spherical ColloidalParticles”, J. Colloid Sci. 16 (1961)pp. 1-12.76. Ia. I. Frenkel, Kinetic Theory ofLiquids (Dover Publications, NewYork, 1955).77. J.J. Jasper, “The Surface Tensionof Pure Liquid Compo~ds”, J. Phys.Chem. Ref. Data 1 (1972) pp. 841-1009.78. S. Glasstone, Textbook ofPhysical Chemistry 2“d ed. (D. vanNostrand, New Yor~, 1946) p. 275.79. J. Gregory, “The Calculation ofHamaker Constants”, Adv. ColloidInterf. Sci. 2 (1969) pp. 396-417.80. A. Michels and L. Kleerekoper,Measurements on the DielectricConstant of C02 at 25°, 50° and

100°C up to 1700 Atmospheres”,Physics 6 (1939) pp. 586-590.81. F. London, “The General Theoryof Molecular Forces”, Trans.Faraday Sot. 33 (1937) pp. 8-26.

82. F.M. Fowkes, “Intermolecularand Interatomic Forces at Interfaces”in Surfaces and Interfaces, edited byJ.J. Burke, vol.1 (SyracuseUniversity Press, New York, 1967)pp. 197-224.83. G. Bohme, H. Krupp and W.Schnabel, “Adhesion of Small GoldSpheres to Silicon” in MolecularProcesses on Solid Surfaces, editedby E, Drauglis, R.D. Gretz and R.I.Jaffee (McGraw-Hill, New York,1969) pp. 611-626.84. H. Krupp, W. Schnabel and G.Walter, “The Lifshitz-van der WaalsConstant”, J. Colloid Interface Sci.39 (1972) pp. 421-423.85. V.B, Menon, L.D. Michaels, R.P.Donovan and V.L. Debler,“Comparison of DecontaminationEfficiencies of Organic andInorganic Particles from SiliconWafers”, Proc. Inst. EnvironmentalSciences (King of Prussia, PA,1988).86. A. Khilnani, “CleaningSemiconductor Surfaces: Facts andFoibles”, Particles on Surfaces I,edited by K.L. Mittal (Plenum Press,New York, 1988) pp. 17-35.87. A.D. Ziman, Adhesion of Dustand Powder, english translation byM. Corn (plenum Press, New York,1969) pp.77.88. A. Khilnani, “CleaningSemiconductor Surfaces: Facts andFoibles”, Particles on Surfaces I,edited by K.L. Mittal (Plenum Press,New York, 1988) pp. 17-35. .

89. H. Krupp and G. Sperling,“Theory of Adhesion of SmallParticles”, J. Appl. Phys. 37 (1966)pp. 4176-4180.90. E.A. Irene and E.A. Lewis,“Thermionic Emission Model for theIhitial Regime of Silicon Oxidation”,Appl. Phys. Lett. 51 (1987) pp. 767-769.91. J.L. Chartier L. Pilorget and R.Le Bihan, “Work FunctionTopography of Silicon and SiliconOxide”, Revue Phys. Appl. 19(1984) pp. 927-931.92. K. Pater, “Silicon Work Functionin A1-Si02-Si System”, Surf. Sci.

200 (1988) pp. 187-191.93. C. Raisin, E. Vieujot-Testemale,A. Ben Bra.him, J.M. Palau and L.Lassabatere, “Work FunctionMeasurements During Growth ofUltra Thin Films of Si02 onCharacterized Silicon Surfaces”,Solid-State Elec.27 (1984)pp. 413-417.94. R.R. Razouk and B.E. Deal,“Hydrogen Anneal Effects on Metal-Semiconductor Work FunctionDifference”, J. Electro. Sot. 129(1982) pp. 806-810.95. A. Khilnani, “CleaningSemiconductor Surfaces: Facts andFoibles”, Particles on Surfaces I,edited by K.L. Mittal (Plenum Press,New York, 1988) pp. 17-35.96. A. Khilnani, “CleaningSemiconductor Surfaces: Facts andFoibles”, Particles on Surfaces I,edited by K.L. Mittal (Plenum Press,New York, 1988) pp. 17-35.

97. W.J. Whitfield, “A Study of theEffects of Relative Humidity onSmall Particle Adhesion toSurfaces”, in Surface Contamination:Genesis, Detection and Control,vol. 1, edited by K.L. Mittal (PlenumPress, New York, 1979) pp. 73-81.98. J.S. McFarlWe and D. Tabor,“Adhesion of Solids and the Effectof Surface Films”, Proc. Royal Sot.(London) A202 (1950) pp. 224-243.99. W,J. O’Brien and J.J. Hermann,“The Strengfh of Liquid BridgesBetween Dissimilar Materials”, J.Adhesion 5 (1973) pp. 91-103.100. A. Khilnani, “CleaningSemiconductor Surfaces: Facts andFoibles”, Particles on Surfaces I,edited by K.L. Mittal (Plenum Press,New York, 1988) pp. 17-35.101. M.E. O’Neill, “A Sphere inContact with a Plane Wall in a SlowLinear Shear Flow”, Chem. Eng. Sci.23 (1968) pp. 1293-1298.102. R.W. Fox and A.T. McDonald,Introduction to Fluid Mechanics(John Wiley & Sons, New York,1978).103. S.M. Chitanvis, C.W. Patterson,W.D. Span and K.E. Laintz,“Dynamics of Particle Removal bySupercritical Carbon Dioxide” inSupercritical Fluid Cleanhw:Fundamentals, Technology andApplications, edited by J. McHardyand S.P. Sawan (Noyes Publications,Westwood, NJ, ‘1998)pp. 70-86.104. P.G. Saffimm, “The Lift on aSmall Sphere in a Slow Shear Flow”,

J. Fluid Mech. 22 (1965) pp. 385-400.105. A.A. Busnaina, 1.1. Kashkoushand G.W. Gale, “An ExperimentalStudy of Megasonic Cleaning ofSilicon Wafers”, J. Electrochem.SOC. 142 (1995) pp. 2812-2817.106. M. Hubbe, “Theory ofDetachment of Colloidal Particlesfrom Flat Surfaces Exposed toFlow”, Colloids & Surf. 12 (1984)pp. 151-178.107. J. Cleaver and B. Yates,“Mechanism of Detachment ofColloidal Particles from a FlatSubstrate in a Turbulent Flow”, J.Colloid & Interface Sci. 44 (1973)pp. 464-474.108. M. Itano, T. Kezuka, M. Ishii,T. Unemoto, M. Kubo and T. Ohmi,“Minimization of ParticleContamination During WetProcessing of Si Wafers”, J. Electro.SOC. 142 (1995) pp. 971-978.109. J. Porschmann, L. Blasberg, K.Mackenzie and P. Harting,“Application of Surfactants to theSupercritical Fluid Extraction ofNitroaromatic Compounds fromSediments”, J. Chromatogr. A 816(1998) pp. 221-232.110. L. Blasberg, P. Harting and K.Quitzsch, “Solubilities of SelectedCommercially Available Surfactantsin Supercritical Carbon Dioxide andEthane : Determination, Correlation,Comparison”, Tenside Surf. Det. 35(1998) pp. 439-447.111. K. Jackson and J.L. Fulton,“Surfactants and Microemulsions in

Supercritical Fluids” in SuPercritical Surfaces”, J. Electro. Sot. 142Fluid Cleaning, edited by J. (1995) pp. 966-970.McHardy and S.P. Sawan (NoyesPublications, Westwood, NJ, 1998)pp. 87-120.112. J.B. McClain, D.E. Betts, D.A.Canelas, E.T. Samulski, J.M.Desimone, J:D. Londono, H.D.Cochran, G.D. Wignal, D.Chillurarnartino and R. Triolo,“Design of ‘Nonionic Surfactants forSupercritical Carbon-Dioxide”,Science 274 (1996) pp. 2049-2052.113. K.P. Johnston, K.L. Harrison,M.J, Clarke, S.M. Howdle, M.P.Heitz, F,V. Bright, C. Carlier, T.W.Randolph, “Water in Carbon-Dioxide Microemulsions: AnEnvironment for HydrophilesIncluding Proteins”, Science 271(1996) pp. 624-626.114. K.A. Consani and R.D. Smith,“Observations on the Volubility ofSurfactants and Related Molecules inCarbon Dioxide at 50”C”, J.Supercrit. Fluids 3 (1990) pp. 51-65.115. K,A. Consani and R.D. Smith,“Observations on the Volubility ofSurfactants and Related Molecules inCarbon Dioxide at 50°C”, J.Supercrit. Fluids 3 (1990) pp. 51-65.116. A. Khilnani, “CleaningSemiconductor Surfaces: Facts andFoibles”, Particles on Surfaces I,edited by K.L. Mittal (Plenum Press,New York, 1988) pp. 17-35.117. H. Morinaga, T. Futatsuki, T.Ohmi, E. Fuchita, M. Oda and C.Hayashi, “Behavior of UltrafineMetallic Particles on Silicon Wafer