nonlinear thermal stress and flow modeling in various ... linear thermal stress analysis with simple...

© International Microelectronics And Packaging Society

The International Journal of Microcircuits and Electronic Packaging, Volume 23, Number2, Second Quarter 2000 (ISSN 1063-1674)

Intl. Journal of Microcircuits and Electronic Packaging

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Nonlinear Thermal Stress and Flow Modeling inVarious Electronic Packages

R. Panneer Selvam and A. ElshabiniHigh Density Electronic Center (HiDEC) &The Computational Mechanics Laboratory4190 Bell Engineering CenterUniversity of ArkansasFayetteville, Arkansas 72701Phone: 501-575-5356Fax: 501-575-7168e-mails: rps, aicha @engr.uark.edu

Abstract

A survey of the status of computer modeling in electronics industry is presented in this work. For three-dimensional analysis ofelectronic packages having nonlinear material properties, in-house computer programs are preferable than standard packages. Inthis publication, details of the implementation of three-dimensional in-house Finite Element program UASTRESS (University ofArkansas –STRESS) for thermal stress analysis and Finite Difference program for heat transfer analysis are presented. Thermalstress analysis of two electronic packages with elasto-plastic and creep properties is conducted using the Finite Element programUASTRESS. The computed stress is compared to the actual performance of the package during the assembly stage. Next, the heattransfer in a complex micro jet array assembly used to cool the electronic chip is modeled using the Finite Difference method. Thecomputed temperature is compared with measurement results, and shows good agreement. In all these models, computer visualizationis utilized to understand further the process.

Key words:

Finite Element Method, Finite Difference Method, Thermal StressModeling, Heat Transfer, MEMS, Micro-Jet Array, and Compu-tational Fluid Dynamics.

1. Introduction and Background

The trend in the development and realization of electronicpackages in industry is low cost, small size, high reliability, moreinput/output, and faster speed. The smaller the package size, thesevere is the thermal and mechanical issues to be addressed. Forsafer and efficient design of the packages, computer modelingbecomes an efficient tool. Using computer modeling, one can

select an efficient and proper package for manufacturing. Com-puter modeling serves as an efficient and vital tool for predictingelectrical, thermal, and mechanical performance of multichipmodules, especially with increasing complexity and functionaldensities of these electrical circuitries.

For linear thermal stress analysis with simple geometric con-figurations in electronic packages, Suhir 1, 2 , Lau 3, Zeyfang 4

and Kuo 5 are among many researchers using these analyticalprocedures. Suhir and Lau used the structural analysis approach,and Zeyfang and Kuo used the theory of elasticity approach. Theadvantage of this procedure is less computer intensive. On theother hand, this method is not easy to apply for materials withnonlinear material properties. In addition, the structural analy-sis technique is two-dimensional, not applicable for three-dimen-sional problem. Therefore, for complex electronic industry prob-lems with three-dimensional and nonlinear material characteris-tics, the Finite Element method (FEM) and the Finite Differencemethod (FDM) are the preferred logical numerical procedures toaddress these situations.

Currently, the majority of the researchers use commercial pro-

Nonlinear Thermal Stress and Flow Modeling in Various Electronic Packages


© International Microelectronics And Packaging Society 225

grams such as ANSYS, ABACUS, NASTRAN, among otherpackages, for example, Chandran et al. 6 used ANSYS and Payderet al. 7 used ABAQUS. These programs are very convenient touse for linear static problems and simple geometric structure.When the material properties are nonlinear and time dependent,very rarely three-dimensional modeling is done due to restric-tion in storage and computer time. In these situations, in-houseprograms designed for specific problem, are very efficient tool touse. Also, management of data is more reasonable. The pro-grams can be suited for parallel and other high performance-computing environment.

In this work, nonlinear thermal stress modeling of a complexelectronic package with three layers and nonlinear flow and heattransfer modeling in a micro jet array assembly is presented. Inthe thermal stress modeling, the Finite Element method (FEM)is used. The material properties are considered to be elasto-plas-tic and creep. In this case, aluminum nitrate (AlN) or Nickel isbrazed to Diamond substrate using Cusil as the brazing material.The melting point of Cusil is about 700°C. Also, Cusil haselasto-plastic and creep properties. In this work, the detail of theFEM implementation and the solution procedures used are pro-vided. Comparison of computer model results to the actual per-formance of the package is also discussed.

The cooling of high power electronics is becoming increas-ingly important to the Air Force and commercial industry as thepower capacity of microchips increase 8, 9 . Some proposed de-vices by these industries have projected waste heat flux levels inexcess of 300 W/cm2. The Air Force is further interested in em-ploying air cooling where possible. Although air is a poor heattransfer fluid, it has many advantages. There are no logisticsissues; no inventory problems, no environmental concerns, nosafety issues involved, and no special training associated withthe use of air. Thus, the use of different fluids other than aircome at great cost, as reported by Leland et al. 9. In order to usean air-cooling device for high power electronic packages, Lelandet al. 8 developed a micro-electromechanical systems (MEMS)called Micro-Jet Array (MJA) impingement cooling device. Theresearchers studied the performance of the cooling device bymeasuring temperature distribution at the bottom of the MJAversus mass flow rate for various ranges of heat flux.

To understand the flow features inside the MJA and to im-prove the heat transfer of the MJA, a numerical modeling studyis conducted in that regard. The computed temperature distribu-tion at the bottom of MJA is compared with Leland et al. 9 ex-periments. The computed results are in good agreement with theexperimental measurements. The Finite Difference method(FDM) is used for the heat transfer analysis due to its efficiencyin implementation. The details of the computer modeling andthe comparison with available experimental results are providedin this publication.

2. Numerical Procedure for Thermaland Mechanical Issues

The numerical procedures commonly used, in the electronicindustry are Finite Element method (FEM) 10 and Finite Differ-ence method (FDM) 11. In the FEM, the governing partial differ-ential equations (PDE) are converted to integro-differential equa-tion using weighted residual or minimum energy principle. Then,these equations are approximated numerically. In the FDM, thePDE is directly approximated numerically. The FEM is suitablefor any complex geometry and the implementation of boundaryconditions are reasonable. For the same grid system, the FEMtechnique is more accurate than the FDM technique. The disad-vantage of FEM as compared to FDM is the need for more com-puter storage and computer time. For example, to solve theLaplace equations in a 3D rectangular mesh, the FEM needsfourteen storage spaces and the FDM needs only four storagespaces for each equation. Hence, the FEM increases the storagespace by more than three times compared to FDM to solve thisproblem. As the number of variables in the PDE increases, amore storage space is required. Also, as the number of variablesin each equation increases, the number of multiplication increasesand hence more computer time is clearly needed. With the ad-vancement in computers and computational technology, this prob-lem is minimized. On the other hand, due to intensive comput-ing and storage requirements, FEM is not that prevalent in com-putational fluid dynamics (CFD). The FDM can be implementedreasonably in simple geometry. The technique requires less stor-age and computing in assembling the equations. The major draw-back is the difficulty in implementing the boundary conditions incomplex regions. FDM is still popular in the area of CFD. TheFEM is much accurate in approximating the convection term inthe Navier-Stokes equations compared to FDM as illustrated bySelvam12. For complex flow or stress problems in electronic in-dustry, adaptive technique13 and parallel computing can certainlybe considered as possibilities for future investigation.

In this work, two different packages are considered for ther-mal stress analysis. In the first one, an aluminum nitride (AlN)ringframe is brazed to a diamond substrate. In the second one, aNickel leadframe is brazed to diamond. For both packages, Cusilis used as the brazing material. Cusil yields at about 160 Mpa atroom temperature and then enters the plastic range. Also, Cusilcreeps at high temperatures and thus has the ability to relax thestresses. Hence, elsto-plastic-creep FEM model is used for theanalysis 14, 15 . For the thermal stress analysis, the in-house FEMprogram UASTRESS is used.

For the flow and heat transfer inside the micro jet array (MJA),the FDM is used. The flow region is considered to be in a rectan-gular region and the FDM is applied in a rectangular grid sys-tem. Hence, the procedure saves computing time and storage.The Navier-Stokes (NS) equations are assumed to be incompress-ible at this time. In the actual experiment, the flow reaches com-pressible region for certain cases. The three-dimensional NS




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equations for incompressible fluid in general tensor notation areas follows,

Continuity equation: Ui,i = 0 (1)

Momentum equation:Ui,t + UjUi,j = -(p/ρ),i+ [ν(Ui,j + U j,i)],j (2)

Energy equation:T,t + UjT,j = (aT,j ),j+(ν/cv ) Φv (3)

Dissipation term: Φv = (Ui,j + U j,i)2

The variables Ui, T, and p are the mean velocity, the temperature,and the pressure, respectively, “a” is the thermal diffusivity, ν isthe kinematics viscosity, and ρ is the fluid density. In this case, acomma represents differentiation, t represents time and i = 1, 2 and3 mean variables in the x, y and z directions, respectively. Thedetails of the derivation are reported in Arpaci and Larsen16.

3. Computer Modeling for Stress andFlow Modeling

3.1. Thermal Stress ModelingA Finite Element model to perform thermal stress analysis is

developed in-house. The program is named UASTRESS. Thisprogram has the capability of considering elasto-plastic and creepmaterial behavior. The details of modeling for elasto-plastic arereported in Peng et al.14,15. The general procedure for elastic andviscoplastic behavior of material is briefly reported in this publi-cation. The method is based on the work of Zienkiewicz andCormeau 17.

KδDi = δF (4)

where K is the structural stiffness matrix, δDi is the incrementalnodal displacement vector for the ith iteration, and δF is the loadvector including the effect of thermal strain, creep and viscoplasticstrain. The element stiffness matrices are computed as follows,

k = BT E BdΩ (5)

where E is the material matrix, and B is the element strain-dis-placement matrix. The load vector δF is computed as follows,

δF = δFth + δFc + δFvp (6)

δF = BT Eδεth δΩ (7)

δFc = BT Eδεc δΩ (8)

δFvp = BT Eδ εvp δΩ (9)

where δεth, δεc and δεvp are the increments in thermal, creep, andviscoplastic strain, respectively. To compute the increment in creepor viscoplastic strains, the following equation, similar to Bathe 18 ,is used,

dte

din

σσεδε 2

3.= (10)

where δε -Inelastic strain, δεc for creep and δεvp for viscoplastic·εin -Minimum strain rate,ε c is for creep and · εvp is for viscoplasticσd -Deviatoric stress,σe -Equivalent stress, anddt -Time interval.

The minimum creep strain rate is computed using any of theequations established from experiment. In this case, Garofalosinh equation is used for creep and viscoplastic 14,15. After solv-ing for the displacements from Equation (4), the element stressin ith time step is computed as follows,

σi = σi=1 + δσ (11)

where σi - The element stress in ith time step,and σi=1 - The element stress in (i-1) th time step.The incremental stress δσ is calculated as follows,

δσ = E(δε - δεth - δεc) (12)

where δε is computed as δε = BδD .The UASTRESS uses eight node brick elements. The non-

zero upper triangular part of the K matrix in Equation (1) isstored in a compact column vector and the equations are solvedby the preconditioned conjugate gradient (PCG) procedure. Theimplementation of the solution procedure is given in Selvam etal.19. The current PCG method reduces the computing time andstorage. At this time, the UASTRESS can run on a personalcomputer or workstation. Currently, work is under progress toconvert the program for parallel platforms.

3.2. Flow and Heat Transfer ModelingA Finite Difference model to compute the flow and heat transfer

in the MJA assembly is formulated in-house 20. The three-di-mensional Navier-Stokes (NS) equations (1) to (2) for incom-pressible fluid are considered in the flow region. A nonstaggeredrectangular grid system is used in this work. All variables aresolved at the nodes. The NS equations are approximated by Eulerbackward in time. In the momentum and energy equations, theconvection term is approximated by upwind procedure while therest of the terms by central difference. The NS equations aresolved using an unsteady implicit procedure. The implicit methodused to solve NS equations is proposed by Selvam 21. Implicittreatment of the convective and diffusive terms eliminates thenumerical stability restrictions. In this implicit solution proce-dure, the time step is kept for CFL (Courant-Frederick-Lewis)number less than one.




3.2.1. Solution Procedure and ConvergenceCriterion

First, the continuity and momentum equations are solved intime until steady state is reached. Once the velocity field is com-puted, then the energy equation is solved for temperature as asteady-state equation in space. Through numerical computations,it is concluded that about 900 iterations are sufficient to reachsteady state. The momentum equation is solved using point it-eration with an under-relaxation factor of 0.7 for each time step.Usually, about 10-20 iterations are sufficient to reduce the abso-lute sum of the residue to be less than 0.01. The pressure equa-tions take considerable computer time. In this work, a precondi-tioned conjugate gradient (PCG) procedure is used. The itera-tion is performed until the absolute sum of the residue of theequation reduces to 1x10-5 times the number of nodes for eachtime step. Once the steady state is reached for the flow, the en-ergy equation is solved using point iteration with an under-relax-ation factor of 0.7. For this step, about 2000 iterations are usedto solve the equation.

4. Computed Results

4.1. Thermal Stress Modeling in ElectronicPackages

4.1.1. Computer Modeling of Brazing a Die toDiamond Substrate

The brazing of ringframe or leadframe to diamond substrateis modeled using only one quarter assembly as shown in Figures1 and 2.

Figure 1. Three-dimensional quarter model of ringframe.

Figure 2. Three-dimensional quarter model of leadframe.

The ringframe consists of an AlN die on the top and a Dia-mond substrate on the bottom. The Cusil is in the middle layer.The thicknesses of the top, middle, and bottom layers are0.6096mm, 0.0254mm, and 0.889mm, respectively. The sub-strate has a 13mm width in the x-direction and a 10.16mm widthin the y-direction. The widths of Cusil and AlN in the x and ydirections are 1.2446 mm, and 1.7272 mm, respectively. Theringframe has 18,408 nodes and 15,974 elements. The grid spac-ing is kept equal along the x and y directions. In the verticaldirection, finer spacing near the interface of each layer is kept.The smallest grid spacing in the vertical direction is 0.0085 mm.

In the leadframe, Cusil is used to braze Nickel and Diamond.The thicknesses of the top, middle, and bottom layers are 0.1016mm, 0.0254 mm, and 0.889 mm, respectively. The substrate hasthe same dimension in the x and y directions as in the ringframepackage. The widths of the leadframe in the x and y directionsare 9.652 mm and 1.6002 mm, including the 2.921 mm x 0.762mm hollow part on either side as shown in Figure 2. Theleadframe has 13,535 nodes and 11,713 elements. The grid spac-ing is kept equal along the x and y directions. The grid spacingis finer around the interface of each layer in the vertical direc-tion. The smallest grid spacing is 0.0085mm in the vertical di-rection.

During the assembly stage, both packages are subjected to atemperature cooldown procedure of 780 °C to 20 °C, with a cool-ing rate 0.833 °C per second. The effect of plasticity beyondyield is considered for Cusil and Nickel. The creep behavior inCusil is also considered. To compute the increments in creepstrain components, the Garofalo sinh equation is used as sug-gested by Stephen et al. 22. The details of the equation is alsoreported in Reference 14 .

The material properties of each layer in the ringframe pack-age is presented in Table 1. The yield stress and the Young’smodulus of plasticity (Ep) change with temperature for Cusil asreported in Reference 22. These values are presented in Figure 3and Figure 4. The authors assumed that the coefficient of ther-mal expansion (CTE) for Cusil does not change with tempera-ture. For leadframe package, the material properties of AlN andDiamond are the same as the ringframe. The properties of Nickelare as follows: E=207e3, ν =0.31, CTE=13e-6 and σy =59 MPa. In




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the Table, E=Young’s modulus, ν=Poisson ratio, CTE-Coefficientsof thermal expansion, and σy =Yield stress. The Ep for Nickel isnot available at this time. Hence, different values of Ep are consid-ered for this analysis.

Table 1. Material properties for the ringframe package.

Figure 3. Yield stress versus temperature for cusil.

Figure 4. Young’s modulus versus temperature for cusil.

4.1.2. Discussion on Computed Stresses

The three-dimensional ringframe model is analyzed consid-ering the plasticity and creep effects of Cusil. The normal stress

σy is considered for this analysis. The point is selected close tothe corner of the ringframe along the y axis. The stress for diamondis reported on the top of the layer at (1.67 mm, 3.73 mm, 0.855 mm).The stress for Cusil and AlN are reported at the bottom of eachlayer at the coordinate of (6.23 mm, 4.71 mm, 0.8932 mm) and (5.23mm, 3.723 mm, 0.92 mm). The normal stress σy in each layer isreported in Table 2. In the elasticity case (EL), all materials areconsidered to be linear and elastic. In the elasto-plasticity case(EL-PL), the plasticity effect of Cusil is considered. The effect ofcreep in Cusil is considered in the elasto-creep case (EL-CR). Theplasticity and creep effects of Cusil are considered in the elasto-plastic and creep case (EL-PL-CR). For creep analysis a coolingrate of 0.833 °C/s is used. The computing time is about 16 hoursfor EL-PL-CR case in the SUNsparc20. The normal stress in thediamond layer reduced from 497 MPa in the case of EL to 227 MPafor EL-PL-CR case. The normal stress σy in AlN layer is 315 MPafor EL-PL-CR case and 414 MPa for EL case. Similar trends areobserved for other normal stresses for each case. The authorsalso find that the normal stress σy exceeds the yield stress of 310MPa in EL-PL-CR case. Hence, as observed experimentally, theringframe cracks. For further details on these results, the reader isreferred to Peng et. al. 14.

Table 2. The normal stress (MPa) developed in each layerfor ringframe.

In the leadframe package, in addition to considering the plas-ticity and creep effects of Cusil, the plasticity effects of Nickel arealso considered. The maximum and minimum principal stressesin each element are considered for the analysis in this package.Since the maximum tensile stress is critical in each layer for thesurvival of the package, the absolute maximum principal stressin each layer is reported as critical stress. The point is selectedclose to the corner of the leadframe along the y axis. The stressanalysis is done for the following cases. In the case of EPC-P1the plasticity effect in Nickel is considered in addition to consid-ering the elasto-plastic and creep effects in Cusil. In this case,the Ep of Nickel is considered to be 30,000 MPa. The EPC-P2case is same as EPC-P1 except that the Ep is considered to be15,000 MPa. The same cooling rate of 0.833 °C/second is usedin this package. Since the actual value of Ep for nickel is notknown at this time different values are considered to study theeffect. The critical stresses are reported for each case in Figure 5to Figure 6, respectively.

The critical stress in the top layer for the case EPC-P1 is about75% smaller than the EL-PL-CR case. When the elasto-plasticbehavior in Nickel is not considered, the critical stress of2,000MPa exceeds the allowable stress of 310 MPa. If plasticityis considered in Nickel, the maximum stresses of 450 MPa in the




case of EPC-P1 is reasonably close to the allowable stress. In thecase of EPC-P2 (Ep = 15,000 MPa), the slope of the Nickel stresscurve is much lower than the EPC-P1(Ep =30,000 MPa). Hence,the stresses are further reduced.

Figure 5. Critical stress developed in time for each layer inthe leadframe model (EPC-P1).

Figure 6. Critical stress developed in time for each layer inthe leadframe model (EPC-P2).

In Figure 9, the authors report the critical stress within therange of 600 s. Results for Nickel beyond 600 seconds were notobtained due to numerical instability, but the trend is quite ap-parent. The researchers are examining a better solution proce-dure to resolve this problem. According to experimental obser-vations, there are no cracks in the Nickel layer and hence theleadframe package survives. Thus, the Ep on Nickel is likelynear 15,000 Mpa can be concluded.

4.2. Heat Transfer in the MJA Array

4.2.1. Computational Grid and Boundary Conditions

The micro jet array (MJA) cooler is shown in Figure 7. Airenters the device plenum and is distributed over the orifice plate.The air then flows through the orifice plate creating a high heat

transfer zone under each of the 221 jets. Then, the air is exhaustedfrom two opposite edges of the cooler. More details about theMJA are given in Leland et al. 9. Only one quarter of the MJA isconsidered for computer modeling due to symmetry in the hori-zontal plane. A computer program is written to generate a grid forthis complex region. The grid has 381,024 (84x84x50) points. In thevertical direction, an equal spacing of 0.025 mm is used. In thehorizontal direction, unequal spacing is used to consider the holeand no-hole regions of the plate. The diameter of the hole in theorifice plate is discretized using five points.

Figure 7 7. Schematic of micro-jet array cooler.

The quarter model plan in the x-y plane is shown in Figure 8.Along boundary AB and AD, a symmetric boundary condition isimposed. Thus, normal velocities are zero and the normal gradi-ent of other velocities is zero as well. On the wall, no slip bound-ary condition is introduced. A velocity of 21 m/s is kept at the5.0mm diameter inlet. This is equal to the case of mass flow rateof 0.5 g/s in Leland et al. 9. The temperature at the inlet is alsoassumed to be 20° C. The pressure at the exhaust is consideredto be zero and at all other boundaries where the velocity is known,the normal derivative of the pressure is considered to be zero.The normal derivative of the velocities are also considered to bezero at the exhaust. The material properties for air are assumedto be as follows: u = 10x10-6 m2 /s, thermal diffusivity, a = 22x10-6 m2 /s,and cp=0.001 J/(Kg-K).




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Figure 8. solution region and boundary conditions. Topview of the quarter model of micro-jet array.

At the bottom of MJA, Leland et al. 9 used 2.31 mm copperplate. At the middle of the copper plate, the researchers embed-ded the thermocouples. Through this technique, they could in-put the heat. In this analysis, a heat flow rate of 15 W is consid-ered at the bottom of the plate. In the current modeling, the groovesin Figure 1 are not considered due to lack of refinement in thegrid. Instead, the thermal diffusivity “a” is increased to be 44x10-6 m2 /swhich is equivalent to the ratio of grooved area to the plane areatimes the thermal diffusivity of air. To consider the diffusion inthe silicon plate at the bottom of MJA, four extra layers withthickness of 0.025 mm are considered in the solution of tempera-ture distribution. Hence, the grid for temperature solution be-comes 84x84x54. Since the thermal diffusivity of silicon is veryhigh, it is hard to solve the equations together for both air andsilicon. Hence, a value of a =1000x10-6 m2 /s for silicon is used atthis time. The diffusion in the copper plate is not considered inthis work.

4.2.2. Computational Observations

The micro jet array (MJA) described in the previous section iscomputed for an inlet velocity of 21 m/s and an input power of 15W at the bottom of the MJA. The computation is performed for900 time steps; it took about 2 days in SUN Ultra 10 system. Inthe first 200 iterations, the momentum error reduces very fast.In this case, the error is referred to the initial absolute sum of theresidue of the momentum equations. Numerical experiment isconducted running up to 1500 time steps. The reduction is verysimilar to the 900 iterations and the flow features are almost thesame. For further discussion on numerical issues, one can referto Selvam et al. 16. The maximum velocity computed for thiscase is 89.9 m/s in the vertical direction, which is lower than100m/s, and hence the incompressible flow assumption is rea-sonable. This maximum velocity is located at the exit of themicro jet, located about 0.939 mm from the center.

Once the flow is obtained, the temperature equation is solvedas a steady state equation. When the silicon plate at the bottomof MJA is considered, the temperature equation is difficult tosolve for silicon thermal diffusivity “a” greater than 1000x10-6

m2/s. The equation at the interface region between air and sili-

con becomes very stiff. At this time, a =1000x10-6 m2/s is used andthe solution is obtained by running for 7000 iterations. Whenlower thermal diffusivity of the order of 100x10-6 m2/s is used,the maximum temperature at the bottom of the plate is higherand the hot spot in Figures 9 and 10 becomes narrower. For theactual diffusivity of silicon, the hot spot region will be wider andthe temperature in that region will be lower than 98° C.

Figure 9. Contour diagram for temperature at the bottomof the plate (at the point of zero velocity).

Figure 10. Contour diagram for temperature at the bottomof the plate (at the point of zero velocity) with temperatureabove 55°C is plotted.

4.2.3. Comparison Between Numerical and Experi-mental Results

The computed velocities and temperature are visualized. Thecomputed temperature distributions at the bottom of the plate areshown in Figures 9 and 10. The maximum temperature com-puted in the solution region is 124°C. As seen in Figure 9, thetemperature near the exhaust is computed to be about 98°C.However, this high temperature will not exist in the experiment.In the computer modeling, the micro-jets in the orifice plate close




to the exhaust are not considered, since these holes are very closeto the outflow region. Therefore, it will be very hard to solve theequations accurately having such a complex flow close to theoutflow region. Also, in reality, heat can dissipate by convectionand radiation at the edges, but these factors are not considered inthe computer model. Hence, for comparison, temperature at theedges is neglected. In the experiment conducted by Leland et al. 15,the temperature at 16 points is measured. Leland averaged the16 points and reported the temperature to be about 57° C. It isshown in Figure 10 that right below the micro jets, the computedtemperature is below 55° C and it agrees well with the experi-mental measurement of Leland et al. 15.

Between the second and the fifth holes from the center, a heatpatch of above 90° C is spread out. A similar pattern is alsoobserved in the experiment results. For comparison, a figurereported by Leland et al. 15 is reproduced in this publication asFigure 11. This heat patch region is due to flow re-circulationoccurring between the jets. This phenomenon can be explainedby visualizing the temperature contours and velocity vector dia-grams in Figures 12 to 14. In Figure 12, one can see the spreadof the hot spot in the vertical direction along the centerline. Fig-ure 13 shows the re-circulation regions between the second andthird hole and between the third and fourth hole from the center.The close up view of the re-circulation region between the sec-ond and third hole is shown in Figure 14. From this illustration,it can be concluded that the re-circulated air retains the heat inthose regions and hence a higher temperature distribution isformed at the bottom plate. This phenomenon may be very hardto measure or visualize in the experiment due to the small geom-etry. Hence, numerical modeling has proved to be a useful tool tounderstand the flow phenomena.

Figure 11. Photograph of micro-jet cooler target plate.

Figure 12. Contour diagram for temperature along thecenterline at the exhaust.

Figure 13. Velocity vector diagram along the centerline atthe exhaust.

Figure 14. Close-up view of velocity vector diagram alongthe centerline at the exhaust around the third hole fromthe center.




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The computed temperature is in agreement with the measure-ment result. The flow visualization is helpful in order to under-stand the heat transfer phenomena in the MJA. The flow visual-ization revealed the hot spot region due to flow circulation. Al-ternative design of the MJA to improve the efficiency of the heattransfer is currently underway.

5. Conclusions and Future Directions

The importance of computer modeling in electronic packagesis illustrated with few applications in thermal stress modelingusing Finite Element method (FEM), and flow and heat transferin a micro jet array (MJA) using Finite Difference method (FDM).The current status of computing in electronic packages and thefuture possibilities are also discussed in this work. The FEMtechnique is applied to compute the thermal stress in a ring andlead frame. The brazing material assumed to have elasto-plasticand creep behavior. The predicted failure of ring frame and thesurvival of lead frame from computer model are in accordancewith experimental work. For further capabilities of the model,one can refer to Peng et al. 15. In that work, a five layer modelwith two layers of Ball Grid Array (BGA) is analysed. In one ofthe BGA layer, underfill is considered. Next, the computed tem-perature distribution at the bottom of MJA is compared with theexperimental measurement of Leland et al. 9. The computedtemperature distribution is in reasonable agreement with themeasurement.

Further work is under progress in the MJA heat transfer con-sidering the compressible effect of the air. Techniques to im-prove the efficiency of the heat transfer in MJA changing thesize of the holes are under investigation. To improve the compu-tational time, the FEM code UASTRESS is modified for parallelcomputing environment. Work is under progress to model theinteraction of stress, thermal, and electromagnetic effect in powerelectronic packages.

Acknowledgments

The authors would like to acknowledge the work they haveinteracted with Dr. S. Ang, Dr. W. Brown, Dr. L. Schaper, Dr.M. Gordon, and Dr. H. Naseem from HiDEC, University of Ar-kansas. Graduate students, Mr. Y. Peng and J. Khater’s, help inproviding some of the Figures, is also acknowledged.

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7. N. Payder, Y.Tong, and H.U. Akay, “A Finite Element Studyof Factors Affecting Fatigue Life of Solder Joints”, ASMEJournal of Electronic Packaging, Vol. 116, pp. 265-273, 1994.

8. J. E. Leland , D.C. Price, B.P. Hill, and H.E. Collicott, “Cool-ing Down Hot New Electronics”, Aerospace America, Vol.33, pp. 40-44, 1995.

9. J. E. Leland , R. Ponnappan, and K. S. Klasing, “Experimen-tal Investigation of an Air Micro Jet Array Impingement Cool-ing Device”, AIAA-99-0476, 37th AIAA Aerospace Sciences,Reno, Nevada, 1999.

10. O.C. Zienkiewicz, and R.L. Taylor, “The Finite ElementMethod”, Vol. 1 & 2, McGraw-Hill, New York, New York,1991.

11. J. D. Anderson Jr., “Computational Fluid Dynamics: TheBasics with Applications”, McGraw-Hill, New York, NewYork, 1995.

12. R. P. Selvam, “Computational Procedures in Grid BasedComputational Bridge Aerodynamics”, Bridge Aerodynam-ics, Larsen, A. and Esdahl (eds), Balkema, Rotterdam, pp.327-336, 1998.

13. R. P. Selvam, “Computation of Flow over Circular CylinderUsing P-Adaptive FEM”, International Symposium on Windand Structures for the 21st Century, Chejudo, Korea, January26-28, 2000.

14. Y. Peng, R. P. Selvam, W. F. Schmidt, M. H. Gordon, K.V.Lohrmann, and R.R. Reynolds, “Nonlinear Finite ElementModelling of Brazing a Die to a Diamond Substrate”, The 31st

International Symposium on Microelectronics, IMAPS ‘98,San Diego, California, October 31 to November 4, pp. 485-490, 1998.

15. Y. Peng, R. P. Selvam, and W. L. Schaper, “Reliability Analysisof a SLIM/SHOCC Package”, The International Conferenceon High-Density Interconnect and System Packaging, MCC‘2000, Denver, Colorado, April 25-28, 2000.

16. V.S. Arpaci, and P.S. Larsen, “Convection Heat Transfer”,Prentice-Hall Inc, New Jersey, 1984.




neering at Cairo University, Egypt in 1973 in both Electronics andCommunications areas (five years academic program), a MasterDegree in Electrical Engineering at University of Toledo, Ohio in1975, in Microelectronics, and a Ph.D. Degree in Electrical Engi-neering at the University of Colorado, at Boulder, Colorado in 1978in Semiconductor Devices and Microelectronics. Currently, she isserving the position of Professor and Department Head for theElectrical Engineering Department at University of Arkansas. Dr.Elshabini is a Fellow member of IEEE/CPMT Society (1993) Cita-tion for Contribution to The Hybrid Microelectronics Educationand to Hybrid Microelectronics to Microwave Applications, a Fel-low member of IMAPS Society (1993), The International Micro-electronics and Packaging Society, Citation for Continuous Con-tribution to Microelectronics and Microelectronics Industries fornumerous years. Dr. Elshabini was awarded the 1996 John A.Wagnon Technical Achievements Award from The InternationalMicroelectronics and Packaging Society (IMAPS). The award isin recognition of significant contributions to the Microelectronicsindustry in the fields of Microwave Hybrids and Thin Film Tech-nology; and for commitment to the dissemination of knowledge asa Professor, and as Editor of the IMAPS Journal.

17. O. C., Zienkiewicz, and I. C. Cormeau, “Visco-Plasticity-Plastic-ity and Creep in Elastic Solids – A Unified Numerical SolutionApproach”, International Journal for Numerical Methods inEngineering, Vol. 8, pp. 821-845, 1974.

18. K. J. Bathe, “Finite Element Procedures in EngineeringAnalysis”, Prentice-Hall, Inc., Englewood Cliffs, New Jersey,Chapter 6, pp. 386-396, 1982.

19. R. P. Selvam, R. P. Elliott and A. Arounpradith, “PavementAnalysis Using ARKPAV”, S.C. Burns (Ed.), Proceedings ofthe 45th Highway Geology Symposium, Portland, Oregon,pp. 241-249, 1994.

20. R.P. Selvam, J. Khater, J.E. Leland, and R. Ponnappan, “Com-puter Modeling of Flow and Heat Transfer in a MEMS BasedAir Micro-Jet Array Impingement Cooling Device”, 1999International Symposium on Microelectronics, IMAPS ‘99,Chicago, Illinois, October 26-28, pp. 201-206, 1999.

21. R.P. Selvam, “Computation of Pressures on Texas Tech Build-ing Using Large Eddy Simulation”, Journal of Wind Engi-neering and Industrial Aerodynamics, Vol. 67 & 68, pp. 647-657, 1997.

22. J. J. Stephens, S. N. Burchett, and F. M. Hosking, “ResidualStresses in Metal/Ceramic Brazes: Effect of Creep on FiniteElement Analysis Results”, Metal-Ceramic Jointing, P. K.Kumar and V. A. Greenhut, ed., TMS. Warrendale, Pennsyl-vania, pp. 23-41, 1991.

23. R.P. Selvam, J. Khater, J.E. Leland, and R. Ponnappan, “Com-puter Modeling of Flow and Heat Transfer in a MEMS Basedair Micro-Jet Array Impingement Cooling Device”, Report,Department of Civil Engineering, 4190 Bell EngineeringCenter, University of Arkansas, Fayetteville, Arkansas72701,1999.

About the authors

R. Panneer Selvam received his BE in Civil (1978) and MEin structural (1980) from the University of Madras, MSCE (1982)from South Dakota School of Mines and Tech. and Ph.D. (1985)from Texas Tech University. He is currently a Professor of CivilEngineering and the Director of the Computational MechanicsLaboratory at the University of Arkansas. His expertise is incomputer modeling of thermal stress, flow and heat transfer inelectronic packages, nonlinear finite element and finite differ-ence modeling, adaptive finite elements, computational fluiddynamics, parallel computing, modeling in MEMS structures,nonlinear dynamic analysis, fluid-structure modeling of airplanewings and bridges, computational wind engineering and controlsystem using structural dynamics. Dr. Selvam has more than120 publications. He is also recognized for his work on com-puter modeling of tornado effects on buildings. He is a memberof ASCE, IMAPS and AIAAJ.

Aicha Elshabini is a Professor of Electrical and ComputerEngineering. She obtained a B.Sc. Degree in Electrical Engi-

nonlinear thermal stress and flow modeling in various ... linear thermal stress analysis with simple...

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