Dynamic Particle Removal by Nanosecond Dry Laser Cleaning: Theory

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1 Dynmic Prticle Removl by Nnoecond Dry Ler Clening: Theory N. Arnold, G. Schrem,, T. Mühlberger, M. Bertch, M. Mobcher,, P. Leiderer nd D. Bäuerle Angewndte Phyik, Johnne - Keler - Univerität, A- Linz, Autri Univerität Kontnz, Fchbereich Phyik und Otikzentrum, Fch M676 D-7857 Kontnz, Germny E-mil: [email protected] A model for n dry ler clening tht tret the ubtrte nd rticle exnion on unified bi i uggeted. Formul for the time-deendent therml exnion of the ubtrte, vlid for temerturedeendent rmeter re derived. Vn der Wl dheion, the elticity of the ubtrte nd rticle, well rticle inerti i tken into ccount for n rbitrry temorl rofile of the ler ule. Time cle relted to the ize of the rticle nd the dheion/eltic contnt i reveled. Clening roceed in different regime if the durtion of the ler ule i much horter/longer thn thi chrcteritic time. Exreion for clening threhold re rovided nd comred with exeriment on the clening of Si urfce from hericl SiO rticle with rdii between nd 585 nm in vcuum with 8 nm KrF excimer ler nd 5 nm frequency doubled Nd-YAG ler. Lrge dicrencie between the exerimentl dt nd theoreticl reult for KrF ler ugget tht n dry ler clening cnnot be exlined on the bi of therml exnion mechnim lone. Keyword: Ler clening, modeling, dheion, ocilltion, SiO, Si, LPM.. Introduction Ler clening i under conidertion for uge in mny mnufcturing rocee,. In dry clening (DLC) therml exnion i believed to be reonible for rticle removl. Stem ler clening (SLC), though more efficient 5, i incomtible with ome liction 6. Uully, one comre clening nd dheion force. Nnoecond ler clening, due to hort time involved, require conidertion of dynmic effect. The model uggeted in the literture o fr require imrovement. Therml exnion of the ubtrte 7 w treted inccurtely nd ertely from tht of the rticle 8,9. When eltic deformtion of the rticle comreed by the exnding ubtrte w conidered, dheion nd eltic force were conidered ertely nd the influence of the rticle on the ubtrte deformtion w not treted roerly. Removl of borbing rticle nd elticity of the ubtrte w nlyzed on the bi of force blnce only, without tking rticle movement into ccount nd rticle temerture w etimted in very crude wy. Mot of the model do not conider temorl rofile of the ler ule, which ume infinite ccelertion/decelertion. Though energy criterion w mentioned, it region of licbility w not clerly tted. Redeoition nd diitive rocee were conidered in,, but only fter the ule. Numericl reult did not rovide comct formul for clening fluence. It i not cler, which rmeter cn imrove the clening efficiency nd decree the clening threhold. We develo n nlyticl model, which incororte the influence of exerimentl rmeter nd different fctor tht contribute to DLC. Sound effect nd field enhncement 5,6 re not conidered.. Adheion otentil nd evolution eqution Let u introduce n roximte dheion otentil tht tke into ccount Vn der Wl (VdW) ttrction nd eltic force. If rticle with rdiu r nd lne re roched by ditnce h (ee Fig. ) the energy of the ytem i the um of the VdW energy (work of dheion ϕ over the contct re πhr) nd eltic energy, which i tken from the Hertz contct roblem 7. Thi reult in the following roximte otentil nd force: / / 5 / / h r U = πrhϕ+ h r, F = πϕ r () 5θ θ Here θ chrcterize eltic roertie of the rticle () nd the ubtrte (). It i dominted by the roertie of the ofter mteril (where the eltic energy i minly tored).

2 σ σ = θ + () E E Potentil () reult in equilibrium vlue h nd U : / / h = ( πϕθ) r () / U ( ) 5/ / = πϕ θ r () 5 A detchment of the rticle occur when h=. The mximum (ull-out) force i reched there nd i given by F = πrϕ (5) Thi llow one to infer ϕ from force meurement. The otentil () cn be roximted by rbol of the me deth with chrcteritic ocilltion frequency nd eriod: U h h τ = π/ ω n (7) Here v i the ound velocity. Etimtion ume r~ µm nd mteril rmeter from Tble. Thi frequency i lwy lower thn the frequency of the firt ound mode. More relitic JKR 8 otentil reented in Fig. i quite imilr. For DMT 9 ce the greement i comrble. Eqution for the evolution of h. The roch h i the ditnce over which rticle nd ubtrte re cloer comred to oint contct. Let x be the coordinte of the rticle center nd l the urfce dilcement in the lbortory frme, both counted from the initil oition of the urfce. Then h = l + r x (8) All quntitie deend on time. By rewriting Newton eqution with the force () for h inted of x with the hel of (8), we obtin the eqution for the evolution of h (dot tnd for time derivtive): / h / r h && h& + γ = πϕ r + ( l&& r&& ) m θ + (9) The term m l && cn be interreted the force of inerti, but rticle exnion ct in imilr wy. r r x ε ENERGY U/ U h Fig. Schemtic of the rticle-ubtrte deformtion. Solid line - boundrie of ubtrte nd rticle. Dhed line -- imginry non-deformed boundrie. Dh-dotted line -- initil oition of the ubtrte nd not heted (but dilced) rticle. l - ubtrte dilcement, r -current rticle rdiu, r - rticle exnion, x - oition of the rticle center referred to initil (non-deformed) ubtrte. h - overll deformtion, h nd h it frction belonging to the ubtrte nd the rticle. -contct rdiu. ε-equilibrium ditnce between dhering urfce. Adheion otentil U(h) i hown chemticlly. / 6 / 6 9 ϕ v ϕ ~ ~.5 / / 7 7 ( ) π θ r ρ r ρ ω = (6) 5 h l APPROACH h/h Fig. Comrion between exct (dh-dotted line) nd roximte (olid line) dimenionle dheion otentil. Dming. Dming coefficient γ in the eqution (9) cn only be etimted. Knuden vicoity. Motion of the rticle i lowed down by the reence of n mbient medium. With r mller thn the men free th of mbient g, γ cn be etimted : N m kt ρ v g g ~ ~ ~ 6 γ () π π ρ r ρ r Here m i the m of g molecule nd N number denity. Norml vicoity. With bigger rticle nd/or liquid lyer t the urfce γ cn be etimted from the Stoke formul: 6 g πηr vr 5 γ = ~ ~ () m r

3 where η i the dynmic vicoity nd r tomic rdiu. Thi, together with thermohorei, my be imortnt fter the detchment, i.e., for the roblem of redeoition. Abortion of ound. The rte of energy diition for ound wve generted by the therml exnion tht include reflection from the boundrie yield βv 8 γ ~ mx ν, D βt ~ c d () where d ~ min( r, v τ, v / ω, Dτ) i ome chrcteritic length, ν nd D re the kinemtic vicoity nd therml diffuivity of the mteril, c it ecific het. Thi gree with the logrithmic decrement of given in. Emiion of ound by the ocillting rticle into the ubtrte my be rimry dming mechnim. It yield: ρ v 9 γ ~ () ρ r + ( v / ωr ). Therml exnion The reult mot relevnt for DLC rely on clicl thermoelticity 7. The derivtion will be reorted elewhere. In the roblem of ubtrte exnion there exit hierrchy of til cle. Uully xil (z) extenion of the therml field l T nd bortion length l α re much mller thn lterl (x-y) dimenion of ler ot w, even for wekly borbing ubtrte lα + lt < w If the ound doe not leve the heted region in xil direction v τ < ( l α + lt ) < w one h to conider dynmic unilterl exnion. With free boundry nd contnt eltic rmeter the urfce dilcement i v t + σ β l( t) = T ( z, t z / v ) dz () σ With v one recover the ttic reult. If the ound leve the heted re in xil direction, but i till within the lterl extenion of the het ource, ( l + lt ) < vτ < w we del with qui-ttic α unilterl exnion. Thi ce i the mot relevnt for DLC with n ler ule. Here, qui-ttic comreive tree exit in x-y lne. They influence the exnion in z direction vi the Poion rtio σ. It i oible to by olution of het eqution lying integrtion over z. For the urfce dilcement l nd urfce velocity one obtin: + σ βφ ( t) + σ βi ( t) l( t) =, l& = (5) σ cρ σ cρ Here φ nd I re the borbed fluence nd intenity. Both therml exnion nd het content within the mteril re roortionl to the borbed energy. Thi reult i vlid even for temerture deendent rmeter if β(t) i the differentil therml exnion coefficient, the rtio β/cρ cont (within % for Si) due to Grüneien reltion. The tyicl urfce dilcement, velocity nd ccelertion for relitic excimer ler ule t t I ( t) = I ex (6) τ τ re hown in Fig.. With thi definition φ=i τ nd the full width hlf-mximum ule durtion τ FWHM.5τ. When the ound leve the irrdited ot in lterl direction, w < v τ the lterl comreion ignificntly relxe. The eltic roblem i D, while het conduction i till D. Generl reult for D qui-ttic exnion with D het conduction re different from the qui-ttic unilterl exnion βφ ( t) βi ( t) l( t) = ( + σ), l& = (+ σ) (7) cρ cρ Although w nd the til rofile of the bem do not enter thi formul exlicitly, the conidertion i imlicitly bed on the umtion tht tree nd dilcement dier t infinity due to the D relxtion. Dilcement t thi tge i lwy lrger thn the unilterl qui-ttic one, the mteril whole i "le comreed". EXPANSION l[nm] VELOCITY v[cm/] v dv/dt 6 TIME t [n] φ =. J/cm l.5. ACCELERATION dv/dt [ 9 cm/ ] Fig. Surfce dilcement l (dhed line), velocity v (olid line) nd ccelertion dv/dt (dotted line) for Si ubtrte. Ler ule (fluence φ=. J/cm ) i given by (6). Other rmeter re lited in Tble. Finlly, when the het diffue out of the irrdited ot w < l T, het conduction become D nd the het content long the z direction deend on the ler bem rofile. One cn obtin for the Fourier comonent of generl D quittic exnion ~ ( + σ) kz ~ l ( k) = e T ( z, k) dz β (8) Thi hould be ued with time deendent D temerture ditribution, for exmle relted to field enhncement by the rticle.

4 With ttionry temerture ditribution nd emi-infinite ubtrte urfce dilcement i infinite everywhere it require infinite energy to be umed into the ytem. Thi w overlooked in ref. where the exreion for dilcement logrithmiclly diverge. Dimenionle coefficient tht enter different roximtion cn eily differ by fctor of two. Prticle influence on the exnion of the ubtrte. Sometime the therml tre t the urfce ued to clculte clening force i etimted 8 σ zz ~ βte. Thi tre would hve exited if the ubtrte (rticle) w not llowed to exnd. The exnion, however, i retricted only by the elticity nd quite mll inerti of the rticle. The ubtrte i not recibly lowed down by the rticle. Thi doe not men tht the ubtrte i not deformed. Totl deformtion h include rticle nd ubtrte contribution h=h +h (ee Fig. ), which re in reltion 7 σ σ h : h = :. Thu, "oft" ubtrte will hve n E E indenttion of the order of h, not l. Therml exnion of the rticle. Temerture of mll hericl rticle i homogeneou long D t>>r, i.e., with r~ -5 cm nd D ~. cm /, for t>> n. The incree in it rdiu i given by r& = β T & r /, it temerture cn be roximted by cmt& = σ I K ( T T ) (9) where σ πr A i the bortion cro ection (for mll rticle the exreion i different), i the contct rdiu, nd we ued (8..) from for loe into the ubtrte. Indice nd refer to rticle nd ubtrte reectively, T being the temerture of the ubtrte "fr from the rticle". Thu we obtin for n borbing rticle without therml contct β rσ β I r& = I () c m c ρ which i imilr to the exreion (5) for the ubtrte. Let u now ume tht the temerture of the rticle i equl to tht of the ubtrte (idel het contct, uer-end etimtion). Subtituting n energetic etimtion (7.5.8b) from, for the urfce temerture into the exreion for chnge in rticle rdiu we get for trnrent rticle in therml contct with the ubtrte r βi r& lα l () + T c ρ Thi exreion gin h tructure imilr to (5). The rtio r/(l α +l T ) i uully le thn. Thi cn be incororted into the coefficient C in (7) below. Mximum velocity of ejected rticle. Let u etimte the mximum velocity, which hevy rticle cn cquire. Similr etimtion not reclculted into ler rmeter were done in. Fr bove threhold the exnion reult in comreive eltic energy nd i trnformed into kinetic energy lter. Energy blnce (including rticle exnion) yield for the ejection velocity v vi n eltic mechnim: h 5/ / r v = m 5θ () 5/ / 5/ Eh l + r βφ v ~ ~ v ~ v C cm/ 5/ r ρ r cρr Here we ued (5), () nd (7), nd umed comrble roertie of rticle nd ubtrte. Uully l, r<<r, nd the velocity of ejected rticle i rther mll. It i even mller for mll rticle, they move whole during the exnion. The velocity for the inertil mechnim cnnot exceed the combined exnion velocity, which (ee (7)), reult in n ejection velocity v: I v ~ C β ~.5 cm/ () cρ The eltic mechnim yield higher velocitie. If the meured velocitie exceed both etimtion, other mechnim (e.g., bltion) re involved.. Clening threhold Short clening ule. If ler ule τ<<τ, one cn neglect dming nd dheion force in (9) during the ule. Then h ( τ) h + l + r, h& ( τ) () nd the ccumulted energy i determined by chnge in h. Clening will occur if thi energy exceed the totl dheion energy U. Thi i eltic energy clening regime. With otentil () thi reult in / l + r > ( 5/ ) h.8h ~ h (5) ( ) where the lt roximtion refer to rbolic otentil. Long clening ule. If τ>>τ, ocilltion re wekly excited nd one cn olve (9) in qui-ttic roximtion. A reult, t ech moment the clening force blnce the totl VdW-eltic force of dheion. Thu, one h to overcome the dheion force during the ule. Thi i the inertil force clening regime. For the otentil () the force i mximl with h= nd i oitive in our nottion. Thi reult in: m ( l&& + r&& > F (6) ) mx Thu, detchment occur in the decelertion he 7 due to the inerti of the lredy ccelerted rticle. The me hold for trong dming. Deendence of the clening threhold on rticle rdiu nd ule durtion. Rewritten in term of the rticle rdiu r, ule durtion τ nd fluence φ the condition (5), (6) yield clening threhold. We combine (5) with () for the overll exnion of ubtrte nd n borbing rticle. 5/

5 σ β A β A βa l r + + = + φ C φ (7) σ cρ c ρ cρ For the trnrent rticle with therml contct the econd term will be of the order of (), etc. In the lt roximtion we introduced verge rmeter where the mteril with the bigget βa dominte, nd C~.5- i dimenionle coefficient. Rewriting (5),(6) in dimenionl quntitie with h from () nd ω from (6) we obtin the following threhold fluence (for the ule (6) miniml negtive velocity occur t t=τ/): / /.8( πϕθ) r τ >> τ > cρ φ C τ ϕ (8) βa τ << τ π r ρ Intermedite regime cn be clculted numericlly. Numericl coefficient deend on the temorl rofile of the ler ule. The deendence on ule durtion i monotonou -- horter ule re more fvorble. With τ<τ ny further decree in ule durtion i not dvntgeou. With αv τ one h to conider ound relted effect. Fig. Movement of the rticle for ubtrte exnion APPROACH h/h τ FWHM =.τ The deendence on the rticle rdiu i non-monotonou. There exit n otiml rdiu for given ule durtion with τ (r)~τ. With bigger rdii the eriod τ (r)>>τ, the clening force i much horter thn the ocilltion cycle nd clening roceed in the "eltic energy" regime. Hevy rticle lmot doe not move during the ule hence the ubtrte urfce move much fter thn the center of the rticle. Thi led to n incree in eltic energy (comreion of ubtrte nd rticle) nd detchment fter the end of the ule. Detchment occur in the firt bckwrd wing of the ocilltion. Thi i hown in Fig.. From the hyicl oint of view, r / incree in threhold i due to bigger equilibrium h nd higher overll dheion energy () for lrger rticle. With mller rticle τ (r)<<τ the reone of the ocilltor to the "low frequency" force i inefficient. Clening roceed in the "qui-ttic" regime, with mll ft ocilltion in h uerimoed on the low "drift" in h tht obey force blnce. Thi regime i hown in Fig. b. Strong incree in threhold for mller rticle demontrte inefficiency of "inertil force" clening regime. Figure 5 how the movement of the rticle for τ~τ when no imle roximtion exit. Initilly urfce dilcement l i fter thn the rticle movement (comreion) nd lter the rticle detche with contnt velocity. Fig. 5 Movement of the rticle lightly bove clening threhold. Potentil nd ule he in Fig. with ENERGY U/ U - τ FWHM =τ ) DISTANCES l/h, h/h, (x-x )/h τ FWHM = τ x-x l h - - APPROACH h/h bove the clening threhold. Ler ule i given by (6). ) Eltic energy clening regime for big rticle -- hort ule τ FWHM =.τ b) Inertil force regime for mll rticle -- long ule τ FWHM =τ. b) TIME t / τ τ FWHM =τ. Solid line - evolution of the roch h. Dhed line - urfce exnion l. Dotted line - rticle center x in the lbortory reference frme referred to it initil oition x. 5. Exmle of SiO rticle clened from Si wfer Exerimentl. Clening of SiO rticle (rdii -585 nm) from () Si wfer w tudied with KrF excimer ler (8 nm, ule durtion n FWHM) nd frequency doubled Nd-YAG ler (5 nm, 7 n FWHM) rdition. The ler ot on the trget h circulr to-ht rofile with mm dimeter. The mle w fixed in vcuum chmber ( -5 5

6 mbr) to minimize humidity nd redeoition. Prticle were deoited by in-coting. Oticl microcoy nd imge roceing oftwre were ued to evlute the clening efficiency. Picture of the clened re before nd fter irrdition were tken nd comred to monitor the behvior of cluter nd rticle redeoition. Figure 6 comre theoreticl nd exerimentl reult. Emloyed rmeter re lited in Tble. Their choice i not unmbiguou. Si i niotroic, vitreou SiO doe not ccurtely follow the Grüneien reltion, etc. Abortion nd exnion of fued ilic re much mller thn tht of Si, nd were neglected, well dming. In the reence of ntive oxide, the contct i SiO -SiO, which reduce the work of dheion ϕ. Thi vlue w ued in the clcultion for the Nd-YAG ler. The urfce roughne nd reidul moiture cn further chnge dheion. Hving thi in mind we lo reent clcultion for time mller ϕ. Though the clening threhold incree with decreing rticle ize with both the excimer ler (circle) nd Nd-YAG ler (tringle) dt, the greement with the theoreticl reult i quite different. With the KrF-ler dt both the oberved vlue nd the loe of φ cl =φ cl (r) re much lower thn redicted, while for Nd-YAG ler rdition the greement i reonble. THRESHOLD φ cl [J/cm ] - force (inerti) τ /r - - RADIUS r [cm] SiO /Si eltic energy Fig. 6 Exerimentl (ymbol) nd clculted clening threhold fluence function of rticle rdiu for SiO rticle on Si. Circle - KrF ler, tringle - Nd-YAG ler. Solid line - clculted threhold for KrF ler. Dh-dotted line - threhold for time mller dheion. Dhed line - threhold for Nd-YAG ler. Dotted line - threhold for "rigged" KrF ler ule. Tble. Prmeter ued in the clcultion. Pule durtion τ (ee (6)).7 n (KrF).86 n (Nd-YAG) Subtrte Si Secific het c.7 J/gK Volumetric therml exnion β K - r / Poion rtio σ.7 Young modulu E.6 dyne/cm Denity ρ. g/cm Abortion coefficient α.67 6 cm - (KrF) 9 cm - (Nd-YAG) Abortivity A.9 (KrF).6 (Nd-YAG) Prticle SiO Secific het c J/gK Volumetric therml exnion β.65-6 K - Poion rtio σ.7 Young modulu E.7 dyne/cm Denity ρ. g/cm Work of dheion ϕ Si-SiO SiO -SiO erg/cm (KrF) 76 erg/cm (Nd-YAG) One oible exlntion for thi dicrency i the "bd qulity" of the excimer ler ule. It i too long for mll rticle nd they re removed in the inefficient "force" regime. Sike in intenity, when in reonnce with τ, my trongly decree the threhold. Clcultion for the rigged ule with ngulr frequencie u to ~/τ re hown by the dotted line in Fig. 6. The urfce dilcement i lmot the me for the mooth ule (Fig. ), but the velocity nd eecilly the ccelertion differ ignificntly (Fig. 7). Another reon my be the effect of field enhncement by the rticle 5,. EXPANSION l[nm] VELOCITY v[cm/] 6 Fig. 7 Surfce dilcement l (dhed line), velocity v (olid line) nd ccelertion dv/dt (dotted line) for the rigged ule (dhed line in Fig. 6). All other rmeter re in Fig.. Note the difference in cle for ccelertion comred to Fig.. 6. Exerimentl uggetion v dv/dt TIME t [n] φ =. J/cm One cn try to utilize reonnce effect to remove mller rticle with the me fluence but lower heting. A n excimer ler ule i "too long" for clening ub-µm rticle. If it i modulted with the frequency tht l 6 ACCELERATION dv/dt [ 9 cm/ ] 6

7 mtche the "dheion frequency" (6), one cn exect reonnce incree in ocilltion mlitude. Clcultion how tht if the totl durtion of ule ty contnt, nd the eriod of ocilltion i bout. of the overll ule durtion, the clening threhold cn be decreed by - order of mgnitude. With non-liner otentil () reonnt growth turte fter 5- ocilltion. Without dming there i no difference between the clening by the ingle reonnt ule τ=τ nd longer modulted ule with n reonnt "uhe" τ=nτ with the me totl fluence. The dmge threhold, however, will decree for the longer ule. In thi wy one cn incree the window for dmge-free clening. Shorter ule re more efficient. With ule, the dmge threhold i determined by l α nd i much lower thn with n ule. One cn relce ingle ule by everl ule with fixed dely τ in between. Mode locked ler re nturl cndidte for uch exeriment. Clening will be comrble, while dmge will be determined by the overll durtion nτ of the trin of n ule, rovided tht l T ~(D nτ ) / >>l α. 7. Concluion We formulted the DLC roblem with n ule n ece from the dheion otentil under the ction of clening force relted to therml exnion. Model exreion for thi otentil nd dming force re uggeted. Therml exnion of the ubtrte nd the rticle re treted on unified bi. Exreion for therml exnion tht do not require olution of the het eqution nd re vlid for temerture-deendent rmeter re dicued. In ddition to the ull-out force F, rmeter of the dheion otentil mot imortnt for DLC re the eriod of ocilltion τ nd equilibrium deformtion h. Their deendence on rticle ize r nd mteril roertie i rovided. The ler ule durtion τ hould be comred with τ, nd the overll therml exnion l+ r with h. Simle formul for the clening threhold φ cl re derived. With τ<τ (big rticle) clening tke lce in the "eltic energy" regime, which require l+ r>h reulting in φ cl r /. With τ>τ (mll rticle) clening occur in the "inertil force" regime, which require decelertion m ( l&& + r&& > F, leding to φ cl τ /r. ) mx Therml exnion mechnim cnnot fully exlin exeriment with SiO rticle on Si urfce. Threhold oberved in exeriment with KrF ler re too low. Poible exlntion re ft til-temorl vrition in intenity of excimer ule nd field enhncement effect. Utiliztion of reonnce effect by modultion of n ler ule or by emloying ule with dely equl to τ (r) i uggeted. Acknowledgment. We thnk Prof. B. Luk'ynchuk, HD Dr. J. Boneberg nd Dr. B.-U. Runge for ueful dicuion. Finncil uort by the EU TMR roject Ler Clening n o ERBFMRXCT98 88, nd the Fond zur Förderung der wienchftlichen Forchung in Öterreich roject P7- TPH i grtefully cknowledged. Reference W. Zk, W. Ziemlich, nd A. C. Tm, Al. Phy. Lett (99) The ntionl Technology Rodm for Semiconductor (Semic. Indutry Aocition), Sn Joe, CA, 6 (99) D. Bäuerle: Ler Proceing nd Chemitry, rd ed., Sringer, Berlin, S.J.Lee, K.Imen, S.D.Allen Al.Phy.Lett. 58 (99) 5 M. She, D. Kim nd C. P.Grigorooulo J. Al. Phy., (999) 6 R.D. Hlfenny, D.M. Kne, J.Al.Phy (999) 7 V. Dobler, R. Oltr, J.P. Boquillon, M. Mobcher, J. Boneberg, nd P. Leiderer, Al. Phy. A, 69 5 (999) 8 Y. F. Lu, W. D. Song, B. W. Ang, M. H. Hong, D. S. H. Chn, T. S. Low, Al. Phy. A, 65 9 (997) 9 V. P. Veiko, E. A. Shkhno, in Proc. SPIE, () Y. F. Lu, Y. W. Zheng nd W. D. Song, Al. Phy. A, (999) Y. F. Lu, W. D. Song, M. H. Hong, B. S. Teo, T. C. Chong nd T. S. Low, J. Al. Phy., 8 99 (996) Al.A. Kolomenkii, H. A. Schueler, V. G. Mikhlevich nd A. A. Mznev, J. Al. Phy., 8 (998) Y. F. Lu, Y. W. Zheng, nd W. D. Song, J. Al. Phy., () G. Vereecke, E. Röhr, nd M. M. Heyn, J. Al. Phy., (999) 5 P. Leiderer, J. Boneberg, V. Dobler, M. Mobcher, H.-J. Münzer, T. Fourrier, G. Schrem, D. Bäuerle, J. Siegel, N. Choui, J. Soli, C. N. Afono, Proc. SPIE 65 9 () 6 Y. F. Lu, Y. W. Zheng, nd W. D. Song, J. Al. Phy., 87 5 () 7 L. D. Lndu nd E. M. Lifhitz, Theory of elticity, Pergmon Pre, New York, 986, 6,7 8 K. L. Johnon, K. Kendll, nd A. D. Robert, Proc. R. Soc. London Ser. A., (97) 9 B. V. Derjgin, V. M. Muller, nd Yu. P. Toroov, J. Colloid Interfce Sci., 5 (975) D. E. Gry (ed.), Americn Intitute of Phyic Hndbook, McGrw-Hill, New York, 97 A.A. Mznev, J. Hohlfeld, J. Güdde, J.Al.Phy., 8 58 (997) B. Luk'ynchuk, Y.W. Zheng, Y.F. Lu, Proc. SPIE, () 7

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