spreading and solidification of liquid metal droplets … and solidification of liquid metal...

© International Microelectronics And Packaging Society

The International Journal of Microcircuits and Electronic Packaging, Volume 23, Number 4, Fourth Quarter, 2000 (ISSN 1063-1674)

Intl. Journal of Microcircuits and Electronic Packaging

386

Spreading and Solidification of Liquid MetalDroplets on a Substrate:Experiment, AnalyticalModel, and Numerical Simulation

M. R. Predtechensky, Yu. D. Varlamov, and S. N. Ul’iankinInternational Scientific Center of Thermophysics and EnergeticsInstitute of Thermophysics SB RASav. Lavrentyeva,1, Novosibirsk,630090 Russia

A. N. Cherepanov and V. N. PopovInstitute of Theoretical and Applied Physics SB RASstr. Institutskaya 4/1, Novosibirsk,630090 Russiae-mail: [email protected]

Abstract

The main motivation for this work was in the connection with the novel solder-drop-printing process as an alternative and addition topresently available solder bumping processes for Flip Chip application. In this process, the liquid droplets are deposited directly onthe wettable bond-pad metallization. The shape of solidified droplet produced on surface of substrates including the multilayermicrochip substrates is affected by fluid dynamics and the heat transfer processes occurring at the collision of liquid droplets withsolid surface. How precisely the final shape of solidified solder droplets can be predicted is crucial for the application of thistechnology to microelectronic packaging. The present work is focused on the experimental study of the factors determining the finaldeposit shape, the development of analytical model of droplet solidification, the numerical simulation of the fluid dynamics, and theheat transfer phenomena occurring during the impingement of a liquid solder droplet upon a substrate. The original design dropletgenerator for dispensing the 30-150 µm diameter molten solder droplets was used in experiments. The obtained results allow toexplain the multiformity of the solidified droplets shapes observed in experiments and to analyze the effects of deposition conditionsand properties of used materials on the final shape of solidified droplets. It is demonstrated that the developed analytical model andsoftware for numerical simulation can be used for the prediction of final solder bump shape at the optimization of solder-drop-printing technology.

Key words:

Solder-Drop-Printing, Droplet-on-Demand Device, Solder BumpShape, Impingement, and Solidification.

1. Introduction

Well established trends of integrated circuit development pointto the fact that advanced IC packaging techniques, such as FlipChip (FC), and Chip Scale Packages (CSPs) will be a potentialcandidates for interconnect technology (see for example Refer-ences1,2). Flip Chip technology offers the highest density inter-connects. Wafers with the pitches down to 150 µm for Flip Chipapplication can be achieved and current developments are tar-

Spreading and Solidification of Liquid Metal Droplets on a Substrate Experiment, Analytical Model, andNumerical Simulation


© International Microelectronics And Packaging Society 387

geting to ultra fine pitches (down to 100 µm). The solder bumpstructure for all Flip Chip Interconnection Technologies whichare used in industry today consists of two major components;Under Bump Metallurgy (UBM) and Solder Bump (SB).

The UBM, a multilayer alloy of thin film interface metals, isrequired to provide good adhesion between the pads and the bumpsand also serve as a diffusion barrier, a solder wettable layer, andan oxidation barrier. The semiconductors, ceramic, and flexiblematerials are used as substrates.

The commonly used deposition technology for solder bumps(evaporation or electroplating or stencil printing) requires a mask-ing step for the structuring of the solder. The reflow process isessential for generating smooth, spherical bumps. For Flip Chipapplication, the height distribution of bumps on a wafer is animportant parameter. The creation of masks imposes a limit tothe amount of material between apertures (minimal pitch require-ment) that can be achieved. The ambiguity of paste amount andreflow process might influence the distribution of the bump height.All of these concerns prompt an interest in pursuing an alterna-tive bumping solution. One such solution that is currently beingpursued is solder jet printing, the software-driven, maskless pro-cess in which liquid droplets are deposited directly on the wet-table bond-pad metallization3-5. Since the solder jet device dis-penses bumps individual, it is capable of meeting ultra fine pitchrequirements.

With a reference to this application, it is important that eachdroplet have the definite, reproducible shape. The shape of so-lidified droplet produced on surface of substrates is affected bydynamics of impact, as well as the heat transfer processes, orother words, by the conditions of droplet deposition and the physi-cal properties of used materials (including the multilayer micro-chip substrates). Thus, how precisely the final shape of solidi-fied solder droplets can be predicted is crucial for the applicationof this technology to microelectronic packaging.

During impingement of liquid droplets on solid surface, thefluid-flow phenomena are followed or accompanied by heat trans-port and phase transition. Some of the experimental works per-formed to date have addressed to studying the spreading phe-nomena of ordinary liquid droplets under two limiting condi-tions: impact at high Weber and Reynolds numbers, where thespreading is determined by inertial forces (see for example Ref-erence6), or very slow droplet spreading driven by capillary forces(see for example Reference7). The spreading of highly viscousliquid droplet is considered in works7,8 where it is shown that theviscous damping time is short, and droplet spreading finishesquickly before solidification. However, for solder droplet depo-sition, the reproducible final shape of solidified metal droplets isachieved at the regime of deposition corresponding to the mod-erate Reynolds and Weber numbers. The influence of viscousforces during the spreading of liquid metal droplets with a diam-eter of 50-100 µm is insignificant with respect to forces of inertiaand surface tension. Peculiarities of fluid dynamics, cooling andsolidification of small liquid metal droplets, were considered inseveral works (see for example References9-13) where the numeri-cal simulation of processes occurring during the droplet impinge-ment was carried out. Particularly, results of these efforts dem-

onstrated that the intricate final shape of solidified droplets is asequence of a strong coupling between fluid dynamics and thesolidification process. Therefore, to distinguish the main pro-cesses determining a shape of solidified droplets, and to checkthe developed models, it is necessary experimentally to investi-gate both the effect of droplet spreading dynamics and heat transferconditions between a droplet and a substrate. On the other hand,the use of numerical methods allows one to track down the se-quence of the droplet shape change up to the solidification mo-ment. However, to predict the droplet final shape, one shouldknow the functional dependencies that reflect the effect of depo-sition parameters.

Taking into account the above mentioned issue, the compre-hensive approach to the solution of this problem was implementedin the present work. This approach is based on experimentalstudy of the factors determining the shape of solidified droplets,the development of analytical model of droplet solidification, andthe numerical simulation of droplet spreading upon surface ofsubstrate and its cooling and solidification.

2. Droplet Generator andExperimental Procedures

The main element required to jet solder is the droplet genera-tor. The known design of droplet generator on the base of tubu-lar piezoelectric (PZT) actuator has same limitations (see for ex-ample Reference4,5). In the present work, the novel design ofdroplet generator is offered in which the diverse principle of op-eration to eject the liquid metal droplet has been used. A simpli-fied scheme of experimental apparatus and appearance of 50 mlvolume droplet generator head are shown in Figure 1. The de-sign styling of droplet generator and its sizes are similar to ink-jet print head. The design includes the following elements: areservoir with molten metal, a heater for metal heating and keep-ing a constant temperature, and a droplet ejector that is able tooperate either in the regime of a single droplet ejection or in thecontinous regime with a frequency of ejection assigned by thecontrol unit. The design of the generator allows to carry out thedeposition of droplets with the maximum frequency of dropletejection more than 300 Hz using materials of droplets such astin-lead solder and other metals, solders and alloys with the fu-sion/melting temperature more than 500oC. (The last item israther important in connection with the tendency to use leadlesssolders that takes place in Flip Chip application for memory cellsproduction).




388

Figure 1. Schematic and main parameters of dropletgenerator, and appearance of 50 ml volume droplet generatorhead.

The main investigations were carried out with a tin-lead sol-der of eutectic composition (63%Sn-37%Pb with the fusion/melt-ing temperature Tsol=183oC). The molten solder temperature Toin the ejection zone of generator was controlled by a thermo-couple and was varied in a range of 210-350°C. To prevent themolten metal oxidation, the droplet generator was placed into ahermetic chamber filled with carbon dioxide. A diameter ofejected liquid droplets in the present experiments was varied from40 µm up to 110 µm by changing a size of the droplet generator’snozzle. Analysis of the shape and size of solidified droplets wasperformed with an Optical and Electron Scanning Microscopes.The droplet velocity was determined by the time-of-flight methodin which the time interval between moments when the dropletintersects the two laser beams was measured. The golden cop-per, the silicon plates, and the polyimide films, covered by a goldfilm with the nickel sublayer, have been used as substrates. Tovisualize the stages of droplet spreading, the CCD camera withmicroscope objective lens and stroboscope system with the dura-tion of light pulses about 1 µs have been used. The experimentalstudy was based on the analysis of the final shape of solidifieddroplets produced at various deposition conditions: droplet ini-tial diameter, velocity and temperature prior to impact, tempera-ture and material properties of substrate (the different coefficientsof heat accumulation and wetting conditions).

3. Numerical Model and Software

The mathematical model is formulated to simulate the impactof initially spherical liquid droplet on solid surface beginning atthe instant of contact. It is based on the Navier-Stokes equationsapplied to axisymmetric coordinate system10-11. Laminar flow ofa constant property incompressible fluid is assumed. Boundaryconditions for fluid along solid surfaces are the no-slip and no-penetration. At the liquid free surface, the stress tensor compo-

nents determined the surface tension coefficient and the totalcurvature of the interface. A change of temperature fields andthe solidification front penetration in a spreading droplet are de-termined from the conjugated heat transfer problem in liquidand solid phases of the droplet and in the substrate. Emission ofthe latent heat of solidification during the phase transition is cal-culated by the efficient thermal capacity, which characterizes theheat transfer near the interface. The numerical solution of theproblem is based on a Finite Element method using implicit dif-ference scheme.

Input parameters of the developed software are the bondingpad geometry and the composition and properties of multilayersubstrate. The parameters that have to be optimized are the di-ameter, the velocity, and the temperature of droplet prior to im-pact and the temperature of the substrate. Output parameters(the time sequences) are droplet configuration, velocity distribu-tion, field of temperatures, and solidification front location.

4. Experimental Results andDiscussion

As example of multiformity of final droplet shapes observedin experiments14,15, the Scanning Electron micrographs of thefinal shape of solidified droplets deposited on the gold andpolyimide/gold substrates are shown in Figure 2 for different drop-let velocities and substrate temperatures. It should be noted thata change in the ejection droplet velocity vd in a range of 0.7-5.6m/s was accompanied by the alteration in the droplet diameterDd from 74 µm to 108 µm.

Figure 2. The Scanning Electron micrographs of the solidifieddroplets deposited at different values of droplet velocity andsubstrate temperature (parameters of deposition: To=275°C,Dd=74-107µm).




According to experimental data the following generalities canbe highlighted. With an increase in the droplet velocity prior toimpact, the visible splat diameter of solidified droplets increasesalso. The shape of droplets varies from almost spherical to aring-like shape for the substrates with high heat accumulationability and to the pancake-like shape for the substrate materialswith low value of heat accumulation coefficient. Droplets depos-ited at low substrate temperatures clearly exhibit the surface per-turbations observed as ripples. A size of ripples decreases withan increase in the substrate temperature. This process is moredistinct during solidification of droplets on the gold substrate.The data on the experimental condition variation14,15 show thatthe velocity and the size of droplets before the impact, as well asheat accumulation ability of substrate materials and the substratetemperature, are crucial parameters that determine the final drop-let shape. The wetting conditions do not significantly effect thefinal shape of droplets deposited on the surface of substrates thathave the high thermal conductivity. The overheating of dropletsupper the fusion/melting temperature Tsol and the variation ofsubstrate temperature in the range 20-160oC cause a change inthe splat diameter within the limits of 20-30%.

To interpret experimental data by the observed multiformityof final shapes of solidified droplets the time sequence of theafter-collision alteration of the liquid droplet shape that is pre-sented qualitatively in Figure 3 using the data of experiments onvisualization of droplet impingement should be analyzed. As anexample, the numerical simulation results of the time consequenceof the droplet shape change, velocity distribution and solidifica-tion front location during droplet impingement on polyimide/gold and copper substrates at conditions of deposition corre-sponded to a and d variants in Figure 3 are presented also.

Figure 3. Spreading and solidification of droplets (experimentand numerical simulation). a, c and d – wetted substrates,different heat removal conditions. b – non-wetted substrate.The examples of droplet shapes and comparison ofcharacteristic time scales.

After the droplet impact with the substrate surface the liquiddroplet, originally in spherical shape, begins to spread out.During this stage, the kinetic energy of the droplet is mainlyused for the droplet deformation and the formation of an addi-tional surface. The splat diameter increases. Characteristic timescale of the spreading stage can be estimated as !spr = Dd/ vd ~ 10 -5s(here Dd , vd are the initial diameter, and the velocity of a droplet,respectively). If the droplet does not freeze during the spreadingstage, the inertial movement of liquid metal at the substrate slowsdown and, finally, ceases by the action of surface tension forces.The researchers did not observe any significant effect of heatremoval conditions on the visible splat diameter of solid dropletsfor a wide range of experimental conditions. Thus, one can con-clude that the time of droplet solidification is more than the timeof initial spreading (!sol >!spr), and the splat diameter of dropletscomes to the maximal value Ds!"Dsmax (see Figure 3 and Figure4).

Figure 4. The main geometric parameters characterizing theshape of solidified droplets and the examples of numericalcalculation on the time dependencies of droplet spreadingdiameter and height change during droplet impingement.

After the spreading stage, the reverse droplet motion starts.The liquid droplet begins to recoil. For this stage, the liquiddroplet motion is governed by heat transfer conditions. In thecase of intensive heat transfer to the substrate, the liquid metalmotion nearby the substrate surface is arrested by the local so-lidification. As a result, the visible splat diameter of solidifieddroplets is about Dsmax. Then, the liquid metal has no contactswith the substrate and the final shape of the solidified dropletswill not depend on the wetting conditions. If a droplet will havetime to solidify completely during the recoiling process, the drop-lets have a ring-like shape (Figure 3, variant c).

If during recoiling, the droplet does not start to solidify, thedroplet shape evolution strongly depends on wetting conditions.In case of the non-wetted substrates, the size of splat decreasesduring the recoiling and the droplet shape tends to be spherical.




390

In this case, the splat diameter of droplet is determined by thecontact angle. Moreover, if the energy loss due to viscous fric-tion is low, the droplet can bounce from the surface like a ball.As an example, the ball effect has been observed at the dropletdeposition on the silicon substrates at the temperatures TS>160oCand on the polyimide substrates without gold covering at tem-peratures TS>20oC (see Figure 3, variant b).

If the substrate is wetted by the droplet’s material, the bottomlayer of liquid metal contacts with the substrate and it cannottake off during the recoiling due to strong adhesion interaction.As a result, the droplet splat size never reduces in the followingstages. The visible splat diameter of solidified droplets is closeto the maximum diameter of droplet’s spreading as it was ob-served in the case of droplet solidification on a substrate with ahigh thermal conductivity. Moreover, the contact spot size canincrease due to capillarity force imbalance at the contact line.However, this effect was only observed on the wetted substratesat the temperature of substrate TS #Tsol. Therefore, it can be con-cluded that under the current experimental conditions, when TS<Tsol , the time of droplet solidification was much less than thetime of capillary spreading (!sol << !cap).

The stages of droplet spreading and recoiling can be inter-preted as the first cycle of droplet oscillations. If a droplet hasnot solidified completely during this first cycle, the droplet oscil-lations will continue (see Figure 3 and Figure 4). The oscillationperiod of liquid droplets on a substrate !osc =1/"o can be esti-mated by the formula (see References11,17) !osc=(#DdWe1/2)/4vd ,where We=(pdlvd2Dd)/$% is Weber number, $ is surface tensioncoefficient. Without solidification, the oscillation of liquid drop-lets is damped by viscous effect. As the time scale of the damp-ing, the viscous diffusion time !visc=Dd

2/&d can be used (here &d isthe kinematic viscosity of molten solder). Typical values of !oscand% !visc are ~10-4s and 10-2s correspondingly for the conditionsof the current experiments.

The droplet’s oscillations stop before the most part of dropletbecame solid if the viscous damping time !visc is small comparedwith solidification time !sol. In this case, the droplets will have asmooth surface. The pattern is different for !sol <%!visc. The liquidabove the solidification front oscillates up and down while it movesfrom the substrate plane into the oscillating liquid. This resultsin formation of ripples on the surface of solidified droplets. Theheight of ripple is equal to the shift of the solidification frontoccurring during one oscillation. The number of oscillationsmade by the droplet before bulk solidification and the number ofripples on the surface of solidified droplet will increase as thesolidification time (!sol ) increases. Under this condition, a heightof ripples will decrease and the droplet surface will becomesmooth. Clearly, !sol becomes longer than the temperature ofsubstrate TS or/and the droplet temperature Td goes up, or thanthe substrates with a low thermal conductivity are used (see Fig-ure 3, variant a).

Thus, for conditions to correspond to solder-drop-printingprocess, it is possible to conclude the following. The shape ofsolidified droplets is determined basically by the number of os-cillations made by a droplet up to a moment of complete solidifi-cation or, in other words, by a relation of the solidification time

!sol and oscillation period !osc. To characterize the solidified dropletshape, the following geometric parameters can be used14,16: thevalue of the splat diameter DS of the solidified droplet, the drop-let height H, the number of the droplet oscillations before thecomplete solidification, and the height hn of ripples formed onthe surface of droplets (see the Figure 4). Examples of numericalcalculation on time dependencies of droplet spreading diameterand height change during droplet impingement are shown inFigure 3 too.

One can introduce the dimensionless number Pd= ωωωω %!sol thatcharacterizes the number of oscillations performed by the drop-let before the moment of complete solidification (or the numberof ripples formed on a surface of solidified droplets). In thiscase, ωωωω is the characteristic frequency of the droplet oscilla-tions.

In the moment when the splat diameter reaches its maximalvalue, the kinetic energy of the droplet transforms into the poten-tial energy of deformation. Using this approximation, the splatdiameter can be estimated as follows,14-16

D D v6

D We6s

dl d3

d2

d=

=

ρσ

12

12

(1)The solidified droplets height H can be estimated, if one as-

sumes that the solidified droplets have a shape close to the shapeof a spherical segment with the splat diameter determined byEquation (1). This assumption is in agreement with the mostpart of droplet shapes observed in the experiments. Then, usingthe condition of the droplet volume conservation, the followingequation for estimation of droplet height can be obtained as fol-lows,

H = D We6

sh 13

arcsh 4 We6d

−12

32

(2)

For the case of purely conductive heat transfer with substrateto estimate the time of droplet solidification%!cond, the task of one-dimensional crystallization of the metal layer with effective thick-ness L=Vd /Ss (in this case, the Ss is the area of the droplet-sub-strate contact surface defined by Equation (1)) was solved). Inaccordance with the results from References14,16, the time of dropletsolidification can be defined as a function of droplet and sub-strate parameters,

( )

∆+−

+∆

×=2

d

S

eff

ds

2

S

d

ds

eff

22ddlds

effds2

cond

bb

qTc211

bb

cqT

1

v

q8

ρλ

ρστ

(3)

where%'T=Tsol-TS, bd=((ds)dscds)1/2 and bS=((S)ScS)

1/2 are the coef-ficients of heat accumulation of the droplet and substrate materi-als, (ds and (dl, )ds and )dl, cds and cds are the thermal conductivity,the density, and the specific heat capacity of the droplet materialin the solid and liquid states, (S, )S, and cS are the thermal con-ductivity, the density, and the specific heat capacity of substratematerial, respectively, and TS is the initial temperature of the




substrate, qeff=q+cdl(Td-Tsol)/2 is the effective crystallization heat,where q is the latent heat of fusion, and Td is the temperature ofdroplet prior to the impact with the substrate.

During the solidification process, as the solidification frontmoves from the substrate, the volume of the droplet liquid partdecreases, and the frequency of its oscillations increases in ac-cordance with expression for "o (see above) as "(t)= "o[1-Vsn(t)/Vd]

-0.5, where Vsn(t) is the volume of solidified part of the dropletat the moment t. Then, following the definition of the Pd num-ber, as the number of oscillations made by the droplet during thesolidification time t=!cond, one can obtain that for the case of con-ductive heat transfer with the substrate,

condo38Pd τω= (4)

The height of the first lower, most distinct ripple, can be esti-mated as the ratio of the volume of metal solidified during firstperiod of oscillations to the area of the droplet-substrate contactsurface Ss. In accordance to the results from References14,16, theheight of first ripple can be defined as follows,

hH1 = −

−+

83

14

1 1

343

3

22D

HDPdd

scos

arccos( )π

(5)

Figure 5 shows the examples of solidified droplet shapes thatare accompanied the results of numerical simulation and calcu-lated values of parameters describing the droplet shape. It isseen that the values of these parameters correlate with the realshape of the solidified droplets and the results of numerical simu-lation.

Figure 5. The micrographs of solidified droplets, data ofnumerical simulation, experimental and calculated valuesof the geometrical parameters.

5. Conclusion

The present solder droplet generator is a drop-on-demandsolder jet device and can be used to dispense picoliter volumesolder droplets in a developed packaging processes of microelec-tronic.

It is clear that the variations in bond pad under bump metal-lurgy (UBM), bond pad size, density of bond pad array, underly-ing/surrounding circuit structure, and number of layers all effectthe formation of the bump and how well the droplet “sticks” tothe UBM. With reference to this problem, the data of experi-mental and theoretical study including the numerical simulationof the fluid dynamics and heat transfer phenomena occurringduring the impingement of a liquid solder droplet upon a sub-strate are presented. The experimental data demonstrate that afeatures of droplet’s final shapes (including the number of ripplesand their scale) is determined by ratio of the time of the dropletssolidification and the period of oscillations for a liquid droplet.The analytical model for describing of the final shape of the dropletsolidified during its impingement on the cold substrate for differ-ent deposition parameters and heat removal conditions has beendeveloped. The foundation of this approach is the estimation ofthe solidification time and calculation of the dimensionless num-ber Pd (a characteristic of the number of droplet’s oscillationsbefore the complete solidification). It is demonstrated that thedeveloped analytical model and software for numerical simula-tion can be used for the prediction of final solder bump shape atthe optimization of solder-drop-printing technology.

References

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3. D. J. Hayes, D. B. Wallace, M. T. Boldman, and R. M. Marusak,“Picoliter Solder Droplet Dispensing”, International Journalof Microcircuits and Electronic Packaging, IJMEP, Vol. 16,pp. 173-180, 1993.

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About the authors

Mikhail R.Predtechensky – Head of Physics of molecular struc-ture department of Institute of Thermophysics of Siberian BranchRussian Academy of Science. Dr. M.R.Predtechensky receivedhis Ph.D. Degree and Doctor of Science Degree (Physics andMathematics) from the Institute of Thermophysics of Russian

Academy of Science. His efforts centered upon the research ondynamics of laser plume expansion in ambient gas, cluster for-mation in laser plume, deposition of thin films, plasmachemicalprocesses, and fluid dynamics and heat transfer phenomena dur-ing impingement of liquid microdroplets on solid surface.

Yuri D.Varlamov – Senior Researcher, Head of research groupof Institute of Thermophysics of Siberian Branch Russian Acad-emy of Science. Dr. Yu. D.Varlamov received his Ph.D. Degreefrom the Institute of Thermophysics of Russian Academy of Sci-ence. The scope of his research activity are the deposition of thinfilms, the growth conditions, microstruture and properties of epi-taxial multicomponent films, and dynamics of spreading, heat-and mass transfer processes during collision of liquidmicrodroplets with solid surface, and the design of novel equip-ment for microdrop deposition technology.

Sergey N. Ul’yankin – Research Engineer of Physics of mo-lecular structure department of Institute of Thermophysics of Si-berian Branch Russian Academy of Science. His efforts centeredupon the research on fluid dynamics and heat transfer phenom-ena during impingement of liquid microdroplets on solid sur-face, and the design and implementation of novel equipment formicrodrop deposition.

Anatoliy N. Cherepanov – Head of Laboratory of Institute ofTheoretical and Applied Physics of Siberian Branch RussianAcademy of Science. Dr. A.N.Cherepanov received his Ph.D.degree and Doctor of Science Degree (Physics and Mathematics)from the Institute of Thermophysics of Russian Academy of Sci-ence. His efforts centered upon the research on nonequilibriumprocesses of crystallization, numerical modeling, and heat- andmass transfer processes.

Vladimir N.Popov - Senior Researcher of the Institute of Theo-retical and Applied Physics of Siberian Branch Russian Acad-emy of Science. Dr. V. N. Popov received his Ph.D. Degree fromthe Institute of Thermophysics of Russian Academy of Scienceand Doctor of Science Degree (Physics and Mathematics) fromthe Institute of Theoretical and Applied Physics of Russian Acad-emy of Science. His efforts centered upon the development ofnumerical procedures and numerical simulation ofnonequilibrium processes of crystallization and heat- and masstransfer processes.

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