Effect of solidification on solder bump formation in solder jet process: Simulation and experiment

Available online at www. sciencedirect.com●IENOE doimecr.Transactions ofNonferrous MetalsSociety of ChinaScienceTrans. Nonferrous Met. Soc. China 18(2008) 1201-1208Presswww.csu.edu.cn/ysxb/Effect of solidification on solder bump formation in solder jet process:Simulation and experimentTIAN De wen(田德文), WANG Chun-qing(王春青), TIAN Yan-hong(田艳红)School of Materials Science and Engineering, Harbin Institute of Technology, Harbin 150001, ChinaReceived 12 December 2007; accepted 4 May 2008Abstract: To investigate the influence of the solidification on the solder bump formation in the solder jet process, the volume of fluid(VOF) models of the solder droplets impinging onto the fluxed and non-fluxed substrates were presented. The bigh speed camera wasused to record the solder impingement and examine the validity of the model. The results show that the complete rebound occursduring the process of the solder droplet impinging onto the fluxed substrate, whercas a cone-shaped solder bump forms during theprocess of the solder droplet impinging onto the non-fluxed substrate. Moreover, the solder soldification results in the lift-up of thesplat periphery and the reduction in the maximum spread factor.Key words: solder bump; solder jet; solidification; simulation; volume of fluid(VOF)kinetic and solidification effects to predict the solder1 Introductionbump formation under nonequilibrium conditions.Development of the free surface flow modelingSolder jet is widely used to fabricate bumps on chiptechnique provides feasibility for modeling the dropletin electronic packaging[1-3]. It is well-known that theimpingement onto the substrate. At present, the studiesbump shapedeterminesthereliabilityduringon the prediction of the molten metal dropletservice[4- -6]. Accordingly, it is crucial to predict theimpingement are almost limited in the field of thermnalsolder bump shape in microelctronic componentspraying of liquid metal droplet[12- -15]. The processpackaging.parameters for thermal spaying, such as the dropletIn recent years, various theoretical models, such asmaterials, the droplet diameter, the impact velocity andthe truncated sphere model, the force-balanced solutionthe substrate materials, are completely different fromand the energy- based method, have been developed tothose in the solder jet bumping process. Only a fewpredict solder geometry in electronic packaging[7-8].studies are about the solder bump formation, but are stillAmong these models, the surface evolution based on therestricted either to the SnPb[16 -17] and pure indiumminimum energy is most frequently used to evaluate andsolders[18]，or topartial computationalluidoptimize the packaging processing[9- -11]. However,dynamics(CFD) models based on a lot of unrealisticthese models are based on the static or quasi staticassumptions[19]. The global trend of lead free solderingtheories, and can only predict the final bump shape rathermakes lead-free solders, especially the SnAgCu solder,than the solder shape evolution. They are competent forgradually substiute for the Sn-Pb solder in solder jetpredicting the bump formation under the equilibriumpackaging. However, few studies have been devoted toconditions, such as the hotair reflow bumping, which issimulating the SnAgCu solder bump formation duringlong enough for the solder to reach its wetting balance onthe solder jet process.the substrate. For the solder jet bumping process, theThe aim of the present work is to develop a fullsolder will solidify during the impingement because theCFD中国煤化工to predict the soldersolder droplet itself has a small amount of heat. It isbump: process, which willY片necessary to develop a model that accounts for theprovcNMHGhgoftheroleoftheFoundation item: Project(50675047) supported by the National Natural Science Foundation of ChinaCorreponding author:TIAN De-wen;n; Tel:51-86418359; E mail: tiandw@hit edu.cnCorn1202TIAN De wen, et al/Trans. Nonferous Met. Soc. China 18(2008)solidification in the solder jet bumping process.enthalpy. .Here, energy is assumed to be a linear function of2 Computational modeltemperature and can be expressed asH=c0+(1-f)L(6)2.1 Mathematical formulationThe goverming equations for impressible fluid flowwhere c is the specific heat, fo is the solid fraction and Lcan be written as follows using two-dimensionalis the latent heat. The latent heat associated with thecylindrical coordinates. The equation of mass continuitymelting or freezing can be defined by specifying thesolidus temperature; 0s, the liquidus temperature, o, andthe specific energy of the phase transformation will occur(urA,)+。(wA.)=0(1)between these two temperatures, L. In this case, thlatent heat is removed linearly with temperature betweenwhere u and W represent the velocity components in theQ and 0。radial and axial directions, respectively, and A, and Azrepresent the fractional areas open to flow in coordinate2.2 Boundary conditions, initial conditions, assump-directions r and z. The momentum equations for thetions and gridradial component and the axial component can beThe boundary conditions needed to specify the fluidrespectively written asflow problem are1) Symmetry about the centerline.u1{u. u+w4. u__l亚+f, +Fe +S,2) Free surface: the surface tension force is replacedr or死}= - ρorby an equivalent surface pressure using continuum(2)surface force(CSF) method[20]. The equivalent sufaceow.1-{u4, ar +w4.onowl.! apf2+pressure can be witen asat”' arρ0rVP )|aFg+Fs+Sw(3)Fg=-o(7)In the above equations, Vr denotes the fractional。( VF]|aFvolume open to flow, ρ is the fuid density, p is the(8)pressure, g is the gravitational acceleration,fr and f2 are可己the viscous accelerations, Fyr and Fx are the surfaceIn addition, the tangential stresses on the freetension terms, and S is a temperature-dependent sourcesurface are set .to be zero.. term required for the solidification model, which is based3) No slip at the solid boundaries.on the drag concept. S is equal to zero, when the solder is4) Wall adhesion: The wall adhesion was modeledfully molten, which becomes a very large value whenin a manner similar to that of the surface tension in thesolidification is completed, and will have a finitecase of a gas/liquid interface, except that the unit normalintermediate value depending on the solidification in then in this case was evaluated using the contact angle θ asmushy zone. .follows:The free face of fluid is tracked using a volume ofi=niw cosθ+isin θ9)fluid function, F, which has a value between zero andunity, satisfying the conservation equation:whereiw and iw are the unit vectors normal andtangential to the wall.aF. 1[1 a(FA,nu)+ °(FA2川) =0(4)The boundary conditions pertaining to thet VpLrardzheat- transfer problem are1) Symmetry about the axial centerline;The energy conservation equation can be expressed2) Adiabatic free surface;in terms of a macroscopic enthalpy balance as3) The rate of heat extraction by the chill at the18(pFfuA,r)+-((HwA.)=-p.droplet/substrate interface is given in terms of ar(0H)+,20z (convective heat-transfer coefficient h:[1 Cnud,r. O0wA.>+0ks,r0+k4. '(5)q=h.0.-0)(10)Dz.中国煤化工is the contact areawhere H is macroscopic intemal energy, k is heatbetweCNMHGe,andOwistheconductivity. In this formulation, we follow a customarysubstrYHprocedure of treating the melt and the solid as aIn addition, the initial temperature of solder dropletcontinuum, which may be represented in terms of their is 250 C, and the initial temperature of substrate is 25 'C.TIAN De wen, et al/Trans. Nonferrous Met. Soc. China 18(2008)The principal assumptions made in the modeling areas follows: 1) the contact angle between the wall and thetangent to the interface at the wall is assumed to beconstant; 2) no undercooling or recalescencephenomenon is considered; 3) the interfacial heat transfercoeficient is assumed to be constant; and 4) all materialproperties are assumed to be independent fromtemperature.The equations are solved using a code based onVOF finite-difference technique. Most terms in theequations are solved using an explicit computationalscheme, but the coupling between the pressure andvelocities is implicit. This semi- implicit formulation issolved using the successive over-relaxation(SOR)method, with a modified altermating direction-implicit(SADI) iterative scheme to accelerate convergence. Fig.lFig.1 Definition of fluid region (dark region) and typicalshows the typical definition of the flow region, as well ascomputational domain mesh for calculations of dropletthe spatially uniform grid used in the simulation ofimpingement onto substrate (z-r plane: 60X 120 grids)droplet impingement on the substrate. Table 1 lists thesolder properties used in the model.heat the Sn3.0Ag0.5Cu solder to the molten state and apressure-driven unit to squeeze molten solder droplets3 Experimentalout of the nozzle. The droplet would fall in the chamberfilled with ambient gas and Ar, for a distance before itIn order to examine the validity of the simulation, aimpacts on the substrate. The substrate is placed on thehigh speed videography system was designed to capturexy work stage to reach the intended location precisely.the solder profile at each moment. The main componentsThe flling height can be adjusted to achieve an intendedof the apparatus are a translation stage, a solder dropletimpinging velocity. The high speed camera (DALSAgenerator, a gas chamber, an x-Y precision work stage,0256) is capable of recording 955 frames per second andand a high speed camera with data acquisition system. Iis ftted with a Japan AVENIR CCTV 16 mm lens toschematic drawing of the experimental setup is shown inmagnify tbe small solder droplet throughout theFig.2. The solder droplet chamber is fitted with thespreading process. The rapid motion involved in thetranslation stage at the top of the gas chamber. The soldersolder impingement was captured by EPIX videodroplet generator utilizes a temperature controlled unit toacquisition system. The XCAPTM image analysis systemTable 1 Physical properties of Sn3.0Ag0.5Cu_p/(kgm3)____ u山(Pas)_a/(Nm~)O/Ck(Wm^'"C) (/(Jkg-c-) LUkg^)_7 5000.0020.431221_2167325064 762ThermocouplePressure controllerHeater中5SolderreservoiroTemperature controllerAHigh回Chamberspeed camerWindow中国煤化工SubstratelY片CNMHGxY stagc .Computer with data acquisition systemFig.2 Schematic diagram of experimental setup1204TIAN De-wen, et a/Trans. Nonferrous Met. Soc. China 18(2008)was used to control the beginning of the capture and substrate at a velocity of 0.5 m/s, the values of the fouranalyze the pictures captured to achieve some usefulnumbers are as follows: Re=4 125, We=9.57, Car-0.002 3,data.Bo=0.825. It is obvious from the above values of theTwo kinds of substrates, coller clad (CCL) platedimensionless parameters that the inertial and surfacecoated with RMA flux and CCL plate coated withouttension forces dominate the solder impingement process,flux, were used as the experimental substrates. It iwhereas，the viscous and gravitational forces areknown that flux is often used to remove the surface oxidenegligible.of the substrate in electronic manufacturing. However,Fig.3 shows the simulated solder shape evolution ofherein, the flux does not remove the oxide but provides aa 2.2 mm-diameter solder droplet impingement on fluxedcomparison case without solidification for solder bumpsubstrate at a velocity of 0.5 m/s in the absence offormation. No solidifcation occurs in the case of dropletsolidification. Here, we examined the calculated resultsimpingement on the fluxed substrate because the fluxwith different contact angles and found a good agreementwill be heated to vapor as the droplet touches thebetween the calculated and the experimental data whensubstrate, which efficiently prevents the heat dissipationthe contact angle is equal to 140*. The average contactfrom the solder to the substrate. So the fluxed substrateangle measured by MEGARIDIS et al[21] in the partialhas a low interfacial heat transfer coefficient. Threbound of molten metal droplet impinging on a solidnon-fluxed substrate contrarily has a high heat transfersubstrate is 145", which is very close to the value used inceofficient due to a high heat conduction of pure copperhis work. Heat transfer and solidification werefoil on the suface of substrate. The substrates must benegligible in this analysis for no solidification wascleaned in the ultrasonic machine to remove the surfaceobserved in the impingement process. In the dropletspreading process, the inertial and gravitational forcescontaminants before the experiment.are the driving forces, while the viscous and surfacetension forces are resistance forces. Because the driving4 Results and discussionforces are far greater than the resistance ones at thebeginning, the spread diameter increases greatly and the4.1 Solder droplet impingement onto fluxed substratesurface energy increases correspondingly. The outflowThe dimensionless parameters, Reynolds numbermolten solder will accumulate at the periphery to form aRe=pdow/I，Weber number We=pdowo2/a, Capillarytoroidal rim. The spread diameter reaches the maximumnumber Ca puwo/o, and Bond number Bo= pgd'/o, arevalue at the moment t=3.1 ms, when most of the kineticused to impart a measure of generality and qualify theenergies are converted into the surface energy and partlyrelative importance of each force in the dropletdisspated by the viscous force. Subsequently, theimpingement spreading process. Here, do is the initialspreading lamella will recede toward the center to releasedroplet diameter; and Wo denotes the impact velocity. Forthe surface energy. The surface and the remaining kineticthe case of a 2.2 mm-diameter droplet impinging on theenergy in the liquid lamella at the end of the spreadingPmshe-119931832510729178-187112w40-133a)(b)(c)2202516341697682.026- 6507一20中国煤化工(0HYHCNMHGFig.3 Simulated deformation and pressure distribution of 2.2 mm-diameter solder droplet impingement onto fluxed substrate atvelocity of0.5 m/s: (a) =0 ms; (b) =1.1 ms; (c) =2.1 ms; (d) =3.1 ms; (e) =5.2 ms; (I =6.3 ms; (g) 1=8.4 ms; (h) =10.5 msTIAN De-wen, et al/Trans. Nonferrous Met. Soc. China 18(2008)1205stage may be sufficiently large but not to be fullyupward by vapor at its base. Although the substrate isdissipated at the receding stage. In such case, the kineticcold in this work, the flux will be evaporated during theenergy may suffice to squeeze liquid upward from thesolder droplet impinging, and this serves the samesurface to form a rising liquid column. And then thefunction with the Leidenfrost ffect. The difference ofdroplet is elongated and detaches from the surface as anthe last picture in Fig.3 and Fig.4 is just ascribed tointact drop (complete rebound). The subsequent dropletaction of the fux vapor to the droplet impingement. Tobehaviors are impossible to be observed for thepredict the completely rebound behavior more accurately,visualization limitations of high speed camera. So onlya vapor flow by flm boiling must be incorporated in thethe first spreading cycle was studied.model[23]. However, the rebound behavior is not theFig.4 shows a series of pictures captured by highfocus in the present study. It is primary as a comparisonspeed camera of a 2.2 mm-diameter solder dropletof the case with soldification. Although the action of theimpinging onto the fluxed substrate at a velocity of 0.5flux vapor on the droplet is not considered in the presentm/s. Clearly, the calculated solder profile is in goocmodel, the predicted results are in good agreement withagreement with that from the experiment by comparingthe experimental ones except that the moment of theFig.3 with Fig.4 except the last one, which correspondsdroplet completely rebounds. It can be concluded that theto the completely rebound stage. MEGARIDIS et al[21]vapor plays only a minor role at the early stages of theused Froude number, Fr=wo /(dog), a number scales thedroplet spreading.importance of inertia compared with gravity, as a partialrebound criterion, and found that partial rebound will4.2 Solder droplet impingement onto non-fuxed sub-ccur if Fr> 144. As a complete rebound scenario, thestrateimpingement droplet should be with a higher value ofFr.Predictions from the computer model of dropletIn the above case of droplet impinging onto the fluxedimpact are sensitive to the values of two input parameters:substrate, the value of Fr is equal to 11.58, which doesthe liquid-solid contact angle(0), and the thermal contactot agree with the MEGRAIDIS's criterion. Thisresistance(Rc) at the droplet/substrate interface. Due toindicates that factors other than inertia and gravity maythe similar initial spreading behaviour compared with theaffect the rebound behavior in the present study. Previouscase impingement onto the fluxed substrate, the sameresearch[22] has shown that rebound is facilitated byvalue of 0=140° was used in the simulation. The thermalelevated surface temperatures, especially when thcontact resistance is caused by the roughness of the solidLeidenfrost effect sets in and the drop is propelledsurface and gas entrapment. It is expressed as the reci-a6dg中国煤化工MHCNMHGFig.4 Experimental results of 2.2 mm-diameter solder droplet impingement onto tuxed substrate at velocity of 0.5 m/s: (a) t=0 ms;(b) =1.1 ms; (c) t=2.1 ms; (d) -3.1 ms; (e)←5.2 ms; (①t←6.3 ms; (g) =8.4 ms; (h) =l0.5 ms .1206TIAN De-wen, et a/Trans. Noferous Met. Soc. China 18(2008)procal of an interfacial heat transfer coefficient. The ratesolder. Some ripples will form on the bump surface.of the heat transfer from the molten metal to the substrateBecause the maximum capturing speed of high speedis often limited by the thermal contact resistance.camera used in the present study is 955 frame/s, which isHowever, as a practical matter, interfacial heat transfertoo low to capture the rapid oscillatory motion. Incoefficient is quite dificult to be evaluated directly fromaddition, due to a low resolution of high speed camerathe experiment. The usual solution method is to fit theand the solidification shrinkage, the ripples are notexperimental results to either a numerical[24] (evident in the captured pictures. The total solidificationanalytica[25] model. In this work, the convective heattime of the droplet in the case is 15.8 ms and the finaltransfer coefficient is determined to be 1 X 10* W/(m2.K)bump is approximately cone-shaped. Fig.6 shows theby ftting the instant solder profiles captured by highcaptured solder droplet evolution process. It is found thatspeed camera with the numerical predictions.the predictions are in excellent accordance with theFig.5 shows the evolution of the solder bumpexperiment.formation onto the non fluxed substrate. As a result ofThe spread factor variation with time was used todirectional heat removal, the lower layers of the dropletqualitatively examine the validity of the prediction. Here,solidify at a planar mode after it contacts with thethe spread factor is defined as 5 =d/do, where d denotessubstrate. The deformation behaviours of the solderthe dynamic contact diameter. Fig.7 shows thedroplet at the first 3 ms are similar to those in the case ofcomparison of the predicted spread factor with theimpingement onto the fluxed substrate. Soldificationexperimental one. This figure clearly indicates that theseems to play a minor role in the early stages of dropletmaximum spread factor of the droplet impingement ontospreading. However, the solidification leads to a lift-upthe non-fluxed substrate is less than that of theof the periphery of the splat compared with the tightimpingement onto the fluxed substrate due to the kinetictouch with substrate in the case of droplet impingementenergy loss by solidification. The predicted results ofonto the fluxed substrate. In addition, the loss of kineticdroplet impingement onto the non-fluxed substrate showenergy due to the solder solidification will cause athat the spread reaches its maximum at about 2.1 ms, anddecrease of the maximum spread factor. Afterwards, thethen remains at a constant contact value. But theaccumulated molten solder at the periphery will recedeexperimental results illustrate that the spread reaches itsunder the surface tension forces, and then bridges at themaximum at about 2.1 ms, and then recedes, after 3 ms itcenter of the splat (5.2 ms). The receding molten solderremains at a constant value. The difference between thewill fill the gap between the bridge and the bottomresults predicted and those of the experiment is becausesolidified solder, and finally a very thin gap remains. Thethat the spread factor here is defined using contactlift at the splat periphery diminishes with the proceedingdiameter, not the maximum diameter of the solder profile.of the receding process. Moreover, the solidificationOwing to the poor resolution of the captured pictures, itdirection in this stage is not vertical but from the side tois optically blury in the region between the equatorcenter. And then the molten solder rises from the center.diameter and the substrate. It is difficult to recognize theSubsequently, a spreading and recoiling oscillationcontact boundary from the picture. So the measurementprocess occurs coupled with the solidification of theerrors are unavoidable. However, in general, the model can50I 05030.11a)(b)(c)d)”os07中国煤化工c)(DFig.5 Simulated deformation and soldification of 2.2 mm-diameter solder drYHCNMHGsubstrate at velocityof0.5 m/s: (a) =0 ms; (b) =1.1 ms; (c)=2.1 ms; (d) =3.1 ms; (e) r=4.2 ms; (f) r=5.2 ms; (g) =6.3 ms; (h) =15.8 msTIAN De-wen, et al/Trans. Nonferrous Met. Soc. China 18(2008)12076CC)g)Fig.6 Experimental resuts of 2.2 mm-diameter solder droplet impingement onto non-fluxed substrate at velocity of 0.5 m/s: (a) t=0ms; (b) =1.1 ms; (c) =2.1 ms; (d) =3.1 ms; (e) =4.2 ms; (1) t=5.2 ms; (g) t=6.3 ms; ([) =15.8 ms1.8- Simulated, non-fluxed substrateReferences. Simulated, fluxed substrate1.5-[1] LIU Q, ORME M. High precision solder droplet printing technologynd the state of-he-art [J]. Jounal of Materials ProcessingTechnology, 2001, 115(3): 271-283.2] GALLAGHER C, HUGHES P I, TASSE R, RODGERS K,BARTON 1, JUSTICE J, CASEY D P. Solder jet technology foradvanced packaging [CV/ Poceding of SPIE on Optoelectronics,50.6Photonic Devices, and Optical Networks. Dublin, Ireland: SPIE,2005: 615 621.。Experimental, non-fluxed0.3substrate3] HSU Y Y, CHIANG K N. Double-layers wafer level chip scale●Experimental, fluxed substratepackage (DL-WLCSP) solder joint shape prediction, reliability andparametric study [C]/ The 9th Intersociety Conference on Thermal80 12and Thermomechanical Phenomena in Electronic Systems. New York:Time/msIEEE, 2004: 310 -316.Fig.7 Comparison of experimental and numerical spread4] HSU Y Y, CHIANG K N. Double-layers wafer level chip scalepackage[DL-WLCSP) solder joint shape prediction, reliability andfactors for 2.2 mm-diameter solder droplet impinging ontoparametric study [C]/ The 9th Intersociety Conference on Thermnalfluxed and non-fluxed substrate at velocity of 0.5 m/sand Thermomechanical Pheomena in Electronic Systems. New York,2004.give an accurate prediction of the spread factor as a5] PENGC r, LIUC M, LNJC, CHENG H C, CHIANG K N.function of time.Reliability analysis and design for the fine-pitch fip chip BGApackaging 0 IEEE Transations on Componeats and PackagingTechnologies, 2004, 27(4): 684- 693.5 Conclusions6] TIAN Y H, WANG c Q. Shape prediction and rliabilitty design ofball gid aray solder joints切Key Engineering Materials, 2007,1) The model can give an accurate prediction of the353: 2944-2947.solder bump formation during solder jet process.I7] HEINRICH S M, LEE P S. Solder geometry prediction in ectronie2) The solder droplet will rebound completely whenpackaging: An overview []. Advances in Electronic Packaging, 1997,it impacts on the fluxed substrate.19(2): 1371-1376.3) The final solder bump is cone-shaped after the8]中国煤化工”hoeoew of solder bump shapesolder droplet impinging on the non-fluxed substrate.4) Solidification leads to a lift-up of the splatCHCNM H G2.periphery during the spreading process and a reduction inopimizaion of package processing and design through solder jointthe maximum spread factor.profile prediction [小IEEE Transactions on Elecronics Packaging1208TIAN De-wen, et al/Trans. Nonferrous Met. Soc. China 18(2008)Manufacturing, 2003, 26(1): 68-74.295- -309.geometry of solder joint in fiber atachment soldering [CV1solder jet packaging process [J. IEEE Transactions on ComponentsInternational Conference on Electronic Materials and Packaging.and Packaging Technologies, 2006, 29(3): 486-493.Hong Kong, China, 2006: 1-4.[19] YOUNG-SOO Y, HO-YOUNG K, JUNG-HOON C. Spreading and[1] CHEN W H, LIN s R, STUDENT G CHIANG K N, FELLOW A.solidificaion of a molten microdrop in the solder jet bumpingPrdicting the liquid formation for the solder joints in flip chipproess [印IEEE Transactions on Components and Packagingtechnology []. Jourmal of Electronic Packaging, 2006, 128(4):Technologies, 2003, 26(1): 215-221.331-338.[20] BRACKBILLJ U, KOTHE D B, ZEMACH C. A continum method[12] PASANDIDEH-FARD M, CHANDRA s, MOSTAGHIMI J. Afor modeling surface tension [0 Joumal of Computational Physics,three-dimensional model of droplet impact and soldifcation [J].1992, 100(2): 335-354.Intemational Joumal of Heat and Mass Transter, 2002, 45011):[21] MEGARIDIS C M, BOOMSMA K, BAYER 1 s. Partial rebound of229-2242.2molten-metal droplets impacting on solid substrates [] AIChE[13] KAMNIS s, GU s. Numerical modeling of droplet impingement [].Joumal, 2004, 50(7): 1356- 1363.Jourmal of Physics D: Applied Physics, 2005, 38(19): 3664-3673.[22] YARIN A L. Drop impact dynamics: Splashing, spreading, reeding,[14] XUE M, HEICHAL Y, CHANDRA s, MOSTAGHIMI J. Modelingbouncing [] Annual Review of Fluid Mechanics, 2006, 38:the impact of a molten metal droplet on a solid surface using variable159-192.interfacial thermal contact resistance [0 Joumal of Materials Science,[23] YANG G LIANG-SHIH F. Numerical study of the velocity efetst2007, 42(1): 9-18.on the impingement of an acetone droplet on a high-temperature[15] GHAFOURI-AZAR R. SHAKERI s, CHANDRA s, MOSTAGHIMIsurface [0 Journal of the Chinese lstitute of Engineers, 2005, 28(7):J. Interactions between molten metal droplets impinging on a solid1077-1087.surface小Intemational Joumal of Heat and Mass Transfer, 2003,[24] PASANDIDEH-FARD M, BHOLA R, CHANDRA s,46(8);: 1395-1407.MOSTAGHMI J. Deposition of tin droplets on a steel plae:[16] DIETZEL M, HAFERL s, VENTIKOS y, POULIKAKOS D.Simulations and experiments [D]. lnternational Jounal of Heat andMarangoni and variable viscosity phenomena in picolier size solderMass Transfer, 1998, 41(19): 2929-2945.droplet deposition []. Journal of Heat Transfer, 2003, 125(2):[25] AZIZ s D, CHANDRA S. Impact, recoil and splashing of molten365-376.metal droplets 小International Joumal of Heat and Mass Transfer,[17] WALDVOGELJ M, POULIKAKOS D. Solidifcation phenomena in2000, 43(16): 2841-2857.picoliter size solder droplet deposition on a composite substrate [0](Edited by L Xiang-qun)International Joumnal of Heat and Mass Transfer, 1997, 40(2):中国煤化工MYHCNMHG