Collaborating components in mesh-based electronic packaging

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1 Scentfc Programmng 12 (2004) IOS Press Collaboratng components n mesh-based electronc packagng P. Chow a and C.-H. La b a Fujtsu Laboratores of Europe Lmted, Hayes Park Central, Hayes End Road, Hayes, Mddlesex UB4 8FE, UK E-mal: p.chow@fle.fujtsu.co.uk b School of Computng and Mathematcal Scences, Unversty of Greenwch, Old Royal Naval College, Park Row, Greenwch, London SE10 9LS, UK E-mal: C.H.La@gre.ac.uk Abstract. From the model geometry creaton to the model analyss, the stages n between such as mesh generaton are the most manpower ntensve phase n a mesh-based computatonal mechancs smulaton process. On the other hand the model analyss s the most computng ntensve phase. Advanced computatonal hardware and software have sgnfcantly reduced the computng tme and more mportantly the trend s downward. Wth the knd of models envsaged comng, whch are larger, more complex n geometry and modellng, and multphyscs, there s no clear trend that the manpower ntensve phase s to decrease sgnfcantly n tme n the present way of operaton t s more lkely to ncrease wth model complexty. In ths paper we address ths dlemma n collaboratng components for models n electronc packagng applcaton. 1. Introducton Computatonal aded engneerng (CAE) s a key element n the desgn and analyss of electronc packagng products, from conceptual desgn to manufacturng operatons and processes. The geometrc model, commonly known as a computer aded desgn (CAD) model, facltates all the down stream phases n the CAE process for a product. Wth the product desgn and analyss occur early n the sequence of the process chan, ther success s vtal to all subsequent actvtes to eventual product fabrcaton and tme to market. For models needng computatonal mechancs analyss such as heat transfer of an ntegrated crcut chp, a model for the geometry of the sold object (and may be also the surroundng doman) s needed. Ths s frequently performed by the CAD system wth bult n sold modellng functons. Next the assgnng of materal types and boundary patches before fnte element mesh generaton of the model doman, then the analyss may begn. For a fully ntegrated CAE process the stages between the geometrc modellng to the start of analyss s generally straghtforward, but ths s not always true. Some non-trval examples are lsted. (1) A partcular knd of meshes s needed such as structured mesh solvers, whch are not so common when the geometry modeller forms part of the analyss software package. (2) CAD model not drectly sutable for mesh generaton such as those assembled components that are not merged deally leavng holes and gaps. (3) Mesh generaton dffcultes, ncludng sheer sze and complexty of the model, demandng on computng resources. Any problems encountered between the two stages requre man-tme for attenton and adjustment, and these actvtes become frequent and are extremely tme-consumng. Some of the dffcultes can be solved by more advanced technology n algorthmc, software and hardware, but the knd of models envsaged whch are much larger, more complex n geometry and modellng, and multphyscs, the man-tme s unlkely to decrease sgnfcantly. It s possble to assume the total modellng tme beng consst of geometry creaton, meshng and analyss. The analyss part may have greatly reduced ts computatonal tme, due to advances n computatonal hardware, software and numercal technques, and more mportantly the trend ISSN /04/$ IOS Press and the authors. All rghts reserved

2 66 P. Chow and C.-H. La / Collaboratng components n mesh-based electronc packagng MCM-L Motherboard S Chp Fg. 1. A multple chp geometry. Ch4 Solder Bump BGA Solder Bump s downward. However the frst two parts of the modellng tme have not been reduced to the same level, because t s professonal-manpower ntensve, and wth no clear downward trend. Therefore t s unlkely the total modellng tme wll decrease vastly n the present way of desgn operatons. The tme to market n electronc packagng s decreasng rapdly, the product desgn and analyss cycle need to be shortened to meet the challenge, not just by reducng the number of desgn cycles but smart and more effcent ways of operatons. In the sectons below, the component meshng and glung (CMG) approach s ntroduced for mult-chp module (MCM) problems n electronc packagng. Ths knd of problem s frequently makeup of basc shapes (blocks, cylnders, etc.) and when assembled together t becomes a complex geometry model to undertake; the relatve scale between the components s a key factor. Fgure 1 shows an example dagram of MCM geometry. 2. Component meshng and glung concept The component meshng and glung (CMG) approach takes a more natural approach, n the same lght as an engneer assemblng components n CAD to construct the sold model. Here, the object model s a collecton of assembled meshed components. Lke CAD systems database that uses a parametrc approach defnng the geometry component relatve to parameters such as length and thckness, for rapd model creaton. The CMG follows the same concept wth the component volume meshed, and s perhaps most suted to applcatons where models are constructed from a few basc shapes such as mult-chp module (MCM) models n electronc packagng. The model of assembled components s then glue together by ether mergng components to form one mesh model or collaboratng components usng some teratve methods. The former methodology requres the use of polyhedral type elements to combne nto one mesh model, and t s referred to as the CMG- Coupled strategy n ths paper. One dsadvantage of the CMG-Coupled strategy s that t does not apply to all solvers, for example, structured mesh solvers. Only solvers wth polyhedral element capablty can be consdered. The latter methodology requres some teratve methods to collaborate the components through the exchange of boundary condtons between the components nterface, and t s referred to as the CMG-DDM n rest of paper. The soluton of each component may be obtaned by means of exstng fast solvers. Ths s more unversally applcable to all types of solvers, but one known dsadvantage s that the computng tme to soluton s longer. Fast teratve methods n doman decomposton (thus we called ths strategy CMG-DDM) can sgnfcantly shorten the tme to soluton but t s unlkely to match the sngle mesh case. For approprate solvers, a combnaton of the two glung strateges s possble. The new approach vrtually removed the dffcultes n the prevous operaton and speedup the model creaton and meshng processes. The tools for model creaton and meshng n the process-chan are very much for constructng components for the meshedcomponent database. And any assembled models can be added to the database as meshed-components for use n other models. The volume-meshng element s not fgured n the assembled model constructon process, thus removng a potental manpower ntensve element from the procedure. The only meshng related element that perhaps needng manpower nput s the component s nterface, ths s not envsage because t s a surface-meshng type problem and s one degree of dmenson less than volume meshng thus full automaton s expected. The downsde n CMG-DDM s the expected longer analyss tme, but f ths s not too excessve the reducton tme ganed n model assembly could well offset the extra computng tme and acheve a reduced overall modellng tme. Ths s the ultmate goal, but untl then when the analyss tme s too excessve, we do have the parallel computng armaments to address the longer analyss tme remember the trend for the analyss part s downward.

3 P. Chow and C.-H. La / Collaboratng components n mesh-based electronc packagng Numercal technques Provded that the solvers can take polyhedral elements, the CMG-Coupled strategy does not requre extra effort to put nto the solvers. It s the mesh-model that needs to be connected at the fnte-element mesh topology level, glung the nterfaces of the mesh components. Ths s essentally a fnte-element mesh connectvty problem. In the CMG-DDM strategy, the doman decomposton method (DDM) [1] s deally suted for the assembled-component model, wth the non-overlappng class the most approprate. A nonoverlappng approach allows flexblty n the mesh processng, the methods of numercal soluton, the handlng of dfferent physcs, and the adopton of numercal solvers n each of the model components. Ths choce also makes the defect equaton technque as developed n [2] an deal method for CMG-DDM. The algorthmc methodology for the CMG-DDM by the defect equaton technques s as: Let Lu = f be defned n the doman Ω and u = g on Ω, where L may be a nonlnear operator that depends on u, and g s a known functon. The doman Ω s parttoned nto M non-overlapped sub-domans such that M =1 Ω =Ωand Ω Ω j = φ, for j. Each sub-doman s assocated wth a sub-model defned by L u = f. The boundary of each subdoman, Ω, subtractng the part of boundary whch overlaps wth the boundary of the entre problem s n essence a part of the nterface. Therefore the nterface, whch attached to Ω, may be defned as γ = Ω \ Ω. The boundary condtons defned on γ may be denoted by and t satsfes a defect equaton, such as D(u γ )= 0 [2]. Usng superscrpts to denote the number of glung process, the CMG-DDM algorthm may be wrtten as follows. Intal value : n =0; u (0) gven. Repeat {n := n +1; For =1,...M Do to u (0) u (n) := {Solve L u (n) = g on Ω Ω and u (n) γ = u γ }; End-Do Solve D(u γ )=0;} Untl Convergence acheved =1, 2,...M are = f n Ω subject When the model conssts of a sngle doman (meshed component) then the For loop and the defect calculaton, D(u r )=0, are redundant, thereby revertng back to the conventonal soluton procedure. The CMG- Coupled cases are performed n ths way. From the above algorthm the For loop may be run n parallel and on homogeneous computng systems the soluton wll be dentcal between parallel and scalar computatons. 4. Numercal experments The partcular problem to be consdered n ths paper s governed by the 2-D energy equaton, lmted to conducton only, n temperature u. The varables n (2) are densty (ρ), specfc heat (c), thermal conductvty (k), tme (t) and the source term (S). ρc u = (k( u)+s(u) (1) t The nonlnearty s ntroduced n the form of a materal phase-change n the source term. For soldfcaton usng the enthalpy source-based method ths s gven by S(u) =Lρ f(u) (2) t where L s the latent heat and f s the lqud fracton. The algorthm for solvng these knds of problems may be found n papers by Chow and Cross [3] and Voller and Swamnathan [4] and s not dscussed n ths paper. Readers nterested n obtanng more nformaton are drected to these references. In ths study, the numercal stable method of Voller and Prakash [5] soldfcaton algorthm s used. A nonlnear problem wth phase-change occurrng nsde the doman, geometry as that of Fg. 1, was used to conduct our numercal experments and nvestgatons. Three experments conducted were; 1) A steady state heat transfer (no phase-change) where the top surface s at a temperature of 10 C and bottom surface of 100 C. The left sde of the model s symmetry and for all other boundares, a convectve heat boundary condton of ambent temperature of 25 C wth a heat transfer coeffcent of 10.0 W/m 2 C. 2) A transent heat transfer problem that has the same boundary condtons as the frst experment wth an ntal temperature of 100 C. The tme step sze taken was 10 seconds nterval and smulaton tme end at 120 seconds. 3) The fnal experment s a heat transfer wth the small solder bumps (Ch4 Solder Bump n Fg. 1) undergong soldfcaton. The boundary condton s essentally the same as the

4 68 P. Chow and C.-H. La / Collaboratng components n mesh-based electronc packagng Table 1 Geometry dmenson of components n test model Length (mm) Heght (mm) Gap nterval (mm) S chp Ch4 Solder bump MCM-L BGA solder bump Motherboard Table 2 Materal propertes Densty Specfc Heat Conductvty Lqudus temp. Soldus Latent heat kg / m 3 J / kg C W / mm C C temp. C J / kg Board Solder Table 3 Total energy n system and computng tmes (Computng Platform: Wndow 2000, 2GHz Pentum 4, 1 GB RAM) Conformal mesh Non-conformal mesh Coupled computaton Collaboratng components Coupled computaton Collaboratng components Steady State Results (obtaned wth resdual L2-norm tolerance of 1.0e-6) Total energy Relatve error E E E-05 Computng tme Iteraton number Transent Results (obtaned wth resdual L2-norm tolerance of 1.0e-6) Total energy Relatve error E E E-04 Computng tme Max. Iteratons 2 75 (1st) 2 75 (1st) Mn. Iteratons Soldfcaton Results (obtaned wth resdual L2-norm tolerance of 1.0e-6) Total energy Relatve error E E E-03 Computng tme Max. Iteratons 78 (1st) 79 (1st) 77 (1st) 78 (1st) Mn. Iteratons prevous two experments wth both top and bottom surfaces now have the convectve heat boundary condtons. The ntal temperature s at 183 C wth tme step sze of 2 seconds nterval and smulaton tme end at 600 seconds. Table 1 shows the dmenson of the components n the experment model, the materal propertes data used n the experments are gven n Table 2. In the experments, only for convenent, the S-Chp, MCM-L and motherboard takes on the materal property of the Board dataset, and both the Ch4 and BGA solder bumps takes on the Solder dataset. For the thrd experment, only the Ch4 solder bumps are soldfyng, the lqudus and soldus temperatures for BGA solder bumps are set above that gven thus no soldfcaton occurs. Fgure 2 shows two dfferent meshes used n present experments. Fgures 3 to 5 shows the cell nvarant temperature dstrbuton of the coupled computaton and collaboratng components for the three experments. The plots are ndstngushable between the coupled computaton and collaboratng components. Where as the temperature profle on the two meshes (conformal and non-conformal) s vrtually mpossble to tell apart. Table 3 gve the total energy n the system doman and computng costs for the smulaton, together wth teraton numbers requred. The coupled conformal mesh result s used as the reference gude towards measurng accuracy and computng performance. In the transent problems, the teraton numbers shows the frst tme step has the hghest teraton counts, ths s obvous due to the cold startng the smulaton, whereas lowest s found n tme steps towards end of smulaton. The coupled computaton for lnear problems, Experment 1 and 2, requre 2 teratons for both steady state and per tme step n transent to acheve convergence on temperature. The largest dev-

5 P. Chow and C.-H. La / Collaboratng components n mesh-based electronc packagng 69 Conformal Mesh Non-conformal Mesh Fg. 2. Two dfferent meshes used n experments. Coupled System Collaboratng Components Fg. 3. Comparson of the temperature dstrbuton of steady state results. Coupled System Collaboratng Components Fg. 4. Comparson of the temperature dstrbuton of transent results. aton of the soluton from the referenced data s under 0.2% n Experment 3, and under 0.07% and 0.01% respectvely for Experments 2 and 1. Computng tmes for collaboratng components for the two meshes (conformal and non-conformal) are 72.1 and 65.0 n Experment 1, 44.5 and 40.2 n Experment 2, and 2.1 and 2.0 n Experment 3, tmes more expensve respectve to the referenced coupled conformal mesh cases. Based on these results the collaboratng component approach for lnear problem s not compettve, but non-

6 70 P. Chow and C.-H. La / Collaboratng components n mesh-based electronc packagng lnear problem s a dfferent proposton. Assumng 25% of overall tme s used for analyss, ths mples the projected total modellng tme of 197 for coupled computaton n Experment 3, whch suggests there s possblty for the collaboratng component approach to be compettve n non-lnear phase-change problems n electronc packagng. 5. Summary Numercal experments of solder soldfcaton based on the enthalpy method [3,4] for multple chp module shows the potental advantage of the method n electronc packagng applcatons. References [1] Doman Decomposton Methods n Scences and Engneerng, proceedngs of nternatonal conference seres on doman decomposton methods, publshed by DDM.org, URL: [2] C.-H. La, A.M. Cuffe and K.A. Percleous, A defect equaton approach for the couplng of subdomans n doman decomposton methods, Computers Math. Applc. 6 (1997), [3] P. Chow and M. Cross, An enthalpy control volumeunstructured mesh (cv-um) algorthm for soldfcaton by conducton only, Internatonal Journal for Numercal Methods n Engneerng 35 (1992), [4] V. Voller and C. Swamnathan, General source-based methods for soldfcaton phase change, Numercal Heat Transfer 19 (1991), [5] V. Voller and C. Prakash, A fxed grd numercal modellng methodology for convecton-dffuson mushy regon phase change problems, Internatonal Heat Mass Transfer 30 (1987),

7 Industral Engneerng Multmeda The Scentfc World Journal Appled Computatonal Intellgence and Soft Computng Internatonal Dstrbuted Sensor Networks Fuzzy Systems Modellng & Smulaton n Engneerng Submt your manuscrpts at Computer Networks and Communcatons Artfcal Intellgence Internatonal Bomedcal Imagng Artfcal Neural Systems Internatonal Computer Engneerng Computer Games Technology Software Engneerng Internatonal Reconfgurable Computng Robotcs Computatonal Intellgence and Neuroscence Human-Computer Interacton Electrcal and Computer Engneerng

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