a hybrid optimization approach for chip placement of multi-chip module packaging

9
A hybrid optimization approach for chip placement of multi-chip module packaging Ping Yang a,b, , Xiangnan Qin a a Laboratory of Advanced Design, Manufacturing & Reliability for MEMS/NEMS, School of Mechanical Engineering, Jiangsu University, Zhenjiang 212013, China b Laboratory of Materials & Micro-Structural Integrity, School of Mechanical Engineering, Jiangsu University, Zhenjiang 212013, China article info Article history: Received 24 May 2008 Received in revised form 28 April 2009 Accepted 4 May 2009 Available online 12 June 2009 Keywords: Chip placement Hybrid model Thermal characteristics Parameters Optimization Multi-chip module abstract The aim of this article is to provide a systematic method to perform optimization design for chip placement of multi-chip module in electronic packaging. Based on the investigation of the structural and thermal characteristics of multi-chip module, the key performance indexes of multi-chip module that include the lowest internal temperature objective, thermal-transfer accuracy, chip placement are analyzed. A hybrid model is presented by using genetic algorithm and response surface methodology for optimization. Furthermore, some design processes for improving the performance are induced. Finally, an example is discussed to apply the method. & 2009 Elsevier Ltd. All rights reserved. 1. Introduction A multi-chip module (MCM) is a package combining multiple chips into a single system-level unit. The resulting module is capable of handing an entire function. MCMs provide a very high level of system integration, with hundreds of bare chips that can be placed very close to each other on a substrate. Therefore, systems based on MCM architectures can achieve much denser circuits and much shorter interconnect distances among the chips than those in which chips are packaged in a single-chip module and placed on printed circuit board (PCB). However, this denser integration results in higher heat flux densities at the substrate and creates a very challenging thermal management problem. If the dissipated heat is not properly transferred, higher operating temperatures can occur. A higher temperature not only affects circuit performance directly by slowing down the transistors on chips, but also decreases their reliability. As a result, thermal management is equally an important aspect in multi-chip module. In general, the real relation function of the internal temperature of MCM cannot be obtained because of the nonlinearity of these factors. So, it is necessary to develop a random algorithm to search the optimum design scheme for validity in engineering applica- tion. More recently, some references to investigate the thermal design problem of electronic packaging system. For example, Yang [1] discussed the numerical analysis on thermal characteristics for chip scale package by integrating 2D/3D models. The objective of this paper is to investigate stress and strain of a special scale package-substrate on chip for reliability evaluation or manufac- ture strategy in deep-seated situation. A two-dimensional model (2D model) with one-half of cross-section and a three-dimen- sional (3D model) model with one-fourth of whole package were built, respectively, to simulate the thermal stress and strain of CSP–SOC under the condition of the standard industry thermal cycling temperature. The analysis by integrating the 2D and 3D model can get a more comprehensive profile for the thermal investigation of chip scale package (CSP) than by using any single model. The investigation built a basis for improving reliability in engineering design of CSP product. Kaija and Heino [2] discussed transient thermal characterization of a stacked multi-chip package (SMCP). This paper is a case study of the thermal behavior of a stacked multi-chip package. The aim is to measure temperature responses when heat is dissipated on different dice and to characterize the behavior with a compact thermal model (CTM) that accurately models steady-state and transient re- sponses with a simple thermal RC-network. The measured package consists of three stacked layers, where each layer has one thinned flip chip attached die on an aramid interposer. The package’s thermal responses were measured with thermal test dice that contain heaters and temperature sensors. The package was modeled with a finite element method (FEM) and the ARTICLE IN PRESS Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/mejo Microelectronics Journal 0026-2692/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.mejo.2009.05.002 Corresponding author at: Laboratory of Materials &af0 Micro-Structural Integrity, School of Mechanical Engineering, Jiangsu University, Zhenjiang 212013, China. Tel.: +86 51188790779. E-mail addresses: [email protected], [email protected] (P. Yang). Microelectronics Journal 40 (2009) 1235–1243

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ARTICLE IN PRESS

Microelectronics Journal 40 (2009) 1235–1243

Contents lists available at ScienceDirect

Microelectronics Journal

0026-26

doi:10.1

� Corr

Integrit

212013,

E-m

journal homepage: www.elsevier.com/locate/mejo

A hybrid optimization approach for chip placement of multi-chipmodule packaging

Ping Yang a,b,�, Xiangnan Qin a

a Laboratory of Advanced Design, Manufacturing & Reliability for MEMS/NEMS, School of Mechanical Engineering, Jiangsu University, Zhenjiang 212013, Chinab Laboratory of Materials & Micro-Structural Integrity, School of Mechanical Engineering, Jiangsu University, Zhenjiang 212013, China

a r t i c l e i n f o

Article history:

Received 24 May 2008

Received in revised form

28 April 2009

Accepted 4 May 2009Available online 12 June 2009

Keywords:

Chip placement

Hybrid model

Thermal characteristics

Parameters

Optimization

Multi-chip module

92/$ - see front matter & 2009 Elsevier Ltd. A

016/j.mejo.2009.05.002

esponding author at: Laboratory of Mate

y, School of Mechanical Engineering, Jia

China. Tel.: +86 51188790779.

ail addresses: [email protected], yangp

a b s t r a c t

The aim of this article is to provide a systematic method to perform optimization design for chip

placement of multi-chip module in electronic packaging. Based on the investigation of the structural

and thermal characteristics of multi-chip module, the key performance indexes of multi-chip module

that include the lowest internal temperature objective, thermal-transfer accuracy, chip placement are

analyzed. A hybrid model is presented by using genetic algorithm and response surface methodology for

optimization. Furthermore, some design processes for improving the performance are induced. Finally,

an example is discussed to apply the method.

& 2009 Elsevier Ltd. All rights reserved.

1. Introduction

A multi-chip module (MCM) is a package combining multiplechips into a single system-level unit. The resulting module iscapable of handing an entire function. MCMs provide a very highlevel of system integration, with hundreds of bare chips that canbe placed very close to each other on a substrate. Therefore,systems based on MCM architectures can achieve much densercircuits and much shorter interconnect distances among the chipsthan those in which chips are packaged in a single-chip moduleand placed on printed circuit board (PCB). However, this denserintegration results in higher heat flux densities at the substrateand creates a very challenging thermal management problem. Ifthe dissipated heat is not properly transferred, higher operatingtemperatures can occur. A higher temperature not only affectscircuit performance directly by slowing down the transistors onchips, but also decreases their reliability. As a result, thermalmanagement is equally an important aspect in multi-chip module.In general, the real relation function of the internal temperature ofMCM cannot be obtained because of the nonlinearity of thesefactors. So, it is necessary to develop a random algorithm to searchthe optimum design scheme for validity in engineering applica-

ll rights reserved.

rials &af0 Micro-Structural

ngsu University, Zhenjiang

[email protected] (P. Yang).

tion. More recently, some references to investigate the thermaldesign problem of electronic packaging system. For example, Yang[1] discussed the numerical analysis on thermal characteristics forchip scale package by integrating 2D/3D models. The objective ofthis paper is to investigate stress and strain of a special scalepackage-substrate on chip for reliability evaluation or manufac-ture strategy in deep-seated situation. A two-dimensional model(2D model) with one-half of cross-section and a three-dimen-sional (3D model) model with one-fourth of whole package werebuilt, respectively, to simulate the thermal stress and strain ofCSP–SOC under the condition of the standard industry thermalcycling temperature. The analysis by integrating the 2D and 3Dmodel can get a more comprehensive profile for the thermalinvestigation of chip scale package (CSP) than by using any singlemodel. The investigation built a basis for improving reliability inengineering design of CSP product. Kaija and Heino [2] discussedtransient thermal characterization of a stacked multi-chippackage (SMCP). This paper is a case study of the thermalbehavior of a stacked multi-chip package. The aim is to measuretemperature responses when heat is dissipated on different diceand to characterize the behavior with a compact thermal model(CTM) that accurately models steady-state and transient re-sponses with a simple thermal RC-network. The measuredpackage consists of three stacked layers, where each layer hasone thinned flip chip attached die on an aramid interposer. Thepackage’s thermal responses were measured with thermal testdice that contain heaters and temperature sensors. The packagewas modeled with a finite element method (FEM) and the

ARTICLE IN PRESS

Fig. 1. Structure scheme and chip position. (a) Structure scheme of a multi-chip

module (MCM). (b) Cartesian coordinates and chip position variables (X, Y) on

substrate.

P. Yang, X. Qin / Microelectronics Journal 40 (2009) 1235–12431236

simulated temperature responses showed reasonable agreementwith measured data. The FE model was further used to providereference thermal data under different boundary conditions forCTM synthesis. The obtained CTM models can simulate thesteady-state and transient behavior and can be used as simplifiedmodel of the measured SMCP for further thermal analysis.Mathias, Balandraud and Grediac [3] discussed a genetic algo-rithm (GA) for the optimization of composite patches. This paperdescribes the application of genetic algorithms to the optimiza-tion of a composite patch bonded on a metallic structure. Theobjective is to reduce the stress level in a given area under someconstraints, such as a maximum surface of the patch and someforbidden zones which cannot be covered by the patch. GAs arepresently used for optimizing ply orientations of the stackingsequence as well as for the location and the shape of the patchwhich is modeled with a spline function. The design variables areply orientations and coordinates of interpolation points whichdefine a closed plane spline curve. Stress field calculations in thestructure are carried out using the ANSYS finite element package.The structure considered in this study is an aluminium plate witha circular hole around which the stress level must be reduced bybonding the composite patch. Shapes and ply stacking sequencesresulting from the optimization procedure enable a local reinfor-cement in the neighbourhood of the patch and also a long-distance effect, which consists in a deviation of the stress flowadjoining the area over which the stress level must be reduced.Yang [4,5] discussed the microstructure property by usingmolecular dynamics model. These microstructure propertiesinclude parametric analysis for stress of PBGA solder joint undershock load and characteristics of interfacial heat transportbetween two kinds of materials using a mixed MD–FE model forMEM/NEMS packaging. The thermal performance and vibrationalperformance must be accurately predicted during the designphase to maintain satisfactory reliability. Geffroy, Mathias andSilvain [6] developed heat-sink material selection in electronicdevices by computational approach. In this work, the thermalstress and strain analyses were carried out making use of FEMLABmulti-physics software, which was used to predict the stresshistory of complex structure materials and solder joint life ofelectronic assemblies. It was also concluded that the study haddemonstrated a strategy, where computational mechanics iscoupled with heat-sink material selection for predicting thereliability electronic devices. Bonnet et al. [7] discussed 3Dpackaging technology for integrated antenna front-ends. In thiswork, a novel concept of integrated antenna feed in Ka band hasbeen developed for vertical multi-chip module packaging tech-nology. This technology enables the integration of active elementsvery close to the radiating surface, which reduces dramatically theweight and volume of the antenna. Yang [8] developed investiga-tion on the thermal conductivity of aluminium nitride (AlN) thinfilms by using molecular dynamics simulation. To investigate highthermal property of AlN ceramic, the equilibrium moleculardynamics (EMD) was used to simulate the thermal conductivityof aluminium nitride films. The Stillinger–Weber potential andGreen–Kubo’s formula were introduced to calculate thermalconductivity. The results show that the thermal conductivity ofthe thin films is much lower than that of its bulk counterpart, andthe size-effect on thermal conductivity is significant. Yang [9]discussed a mixed isomorphism approach for kinematic structureenumeration graphs based on GA for intelligent design andmanufacturing. In this work, how to get the advisable crossoverand mutation probabilities to prevent premature convergence andblind operation were discussed. Kleijnen [10] reviewed theresponse surface methodology (RSM) for constrained simulationoptimization. This article summarizes ‘generalized response sur-face methodology’ (GRSM), extending Box and Wilson’s ‘response

surface methodology’. Both GRSM and RSM estimate localgradients to search for the optimum. These gradients are basedon local first-order polynomial approximations. Moreover, thesegradients are used in a bootstrap procedure for testing whetherthe estimated solution is indeed optimal. The focus of this paper isthe optimization of simulated (not real) systems.

In this paper, a systematic method to perform optimizationdesign or evaluation for chip placement of multi-chip module inelectronic packaging was presented. Based on investigation of theparameter characteristics (about structural and thermal physicalparameter characteristics) which are originated by design andmanufacture, the key performance indexes of MCM that includethe lowest internal temperature objective, thermal-transferaccuracy and chip placement are analyzed. The mapping relationsbetween parameter characteristics of MCM are established on thebasis of systematic design point. A GA–RSM model was presentedto implement the optimization. Furthermore, some designprocesses for improving performance are induced. Finally, anexample is discussed to apply the method.

2. Description about chip placement of multi-chip module inelectronic packaging

Fig. 1a shows a structure scheme prototype of a multi-chipmodule. Fig. 1b shows the Cartesian coordinates and chip positionvariables (X, Y) on substrate. The MCM mainly comprises threeembedded chips, molding compound, die attach, Al2O3 substrate,255 solder balls for signalling and thermal transfer and

ARTICLE IN PRESS

P. Yang, X. Qin / Microelectronics Journal 40 (2009) 1235–1243 1237

dissipation. The chip attached between chips and substrate is0.29 mm thick. The right die is the main power chip, and the lefttwo dies are memories with the same size. The dimensions of themain power chip and memories are 8.5�7.62�0.65 mm3 and9.5�6.82�6.5 mm3, respectively. The diameter of the solder ballis 0.8 mm, and the center distance of them is 1.27 mm. In addition,the dimensions of substrate are 25�21�2.2 mm3. For getting agood temperature performance, chip placement of multi-chipmodule in electronic packaging is very important.

3. GA–RSM model description

3.1. The key steps of GA–RSM

A GA–RSM model for optimization design or evaluation ofmulti-chip module is built based on GA and RSM. There are somekey steps in the mixed algorithm; some vital steps are describedas following.

3.1.1. Design of experiments (DOE)

Design of experiments is used for factor screening. Thisidentifies the factors that contribute most to the responsevariables for further experimentation. A response variable y canbe modeled as a function of the factors xi, 1pipk as shown

y ¼ f ðxiÞ; i ¼ 1; . . . ; k (1)

The goal of RSM is to approximate the function f. This may be alinear or quadratic function, or involve higher order terms of thefactors. This function is then taken as objective function of GA inGA–RSM algorithm, and optimization is performed on thisfunction. The different values to which a factor can be setconstitute the levels of the factor.

An initial model relating responses to factors is obtained usingfactorial experimental designs. A factorial design consists ofexperiments with a combination of factors specified at differentlevels. A two-level factorial design varies the factors at twodifferent levels. Such designs are the most suitable in the initialstages of experimentation, where the goal is to determine theminimum number of factors that account for the maximumresponse.

Experimental designs for fitting the second-order responsesurface must involve at least three levels of each variable.Therefore, for building the second-order fitted model, the centralcomposite design (CCD) is used. CCD is frequently used for fittingsecond-order response model.

3.1.2. Regression model and test

3.1.2.1. Regression model. When a response model, which shouldbe taken into consideration for design, is determined as a functionof multiple design variables, the behavior in GA–RSM is expressedby the approximation as a polynomial on the basis of observationdata. In GA–RSM, the regression coefficients are estimated usingthe least-squares method.

First, a linear model should be constructed, and then F-testsare used to determine the accuracy of the model and R2 estimatesthe extent to which the model describes the data, i.e., itdetermines the total variation in the data explained by the factorsin percentage form. A simple linear model is given

y ¼ b0 þXk

i¼1

bixi þ �i (2)

bi denotes the coefficients of the regression model and ei denotes arandom error stemming from the inaccuracy of the model.

If the first-order model is insignificant as a result of curvature,a second-order model is used to fit the data. For a quadraticresponse function with two variables by a regression model, it isexpressed by

y ¼ b0 þ b1x1 þ b2x2 þ b3x21 þ b4x2

2 þ b5x1x2 þ � (3)

where bj (j ¼ 0, 1, 2 y 5) are the regression coefficients, and edenotes the error. When the variables are substituted in a way,such that x1

2¼ x3, x2

2¼ x4 and x1x2 ¼ x5, (3) can be converted

into a multi-variable linear equation. Similarly, a regression modelcontaining optional higher order terms can be always reducedto a linear regression model. When a regression model hascoefficients of regression, the following equation is obtained:

y ¼ b0 þ b1x1 þ b2x2 þ b3x3 þ � � � þ bkxk þ � (4)

Then, sets of observation data in correspondence with designvariables can be expressed by matrix representation in

y1

y2

..

.

yn

8>>>>><>>>>>:

9>>>>>=>>>>>;¼

1 x11 x12...

x1k

1 x21 x22...

x2k

1 ... ..

. . .. ..

.

1 xn1 xn2...

xnk

8>>>>>>><>>>>>>>:

9>>>>>>>=>>>>>>>;

b0

b1

..

.

bk

8>>>>><>>>>>:

9>>>>>=>>>>>;þ

�1

�2

..

.

�n

8>>>><>>>>:

9>>>>=>>>>;

(5)

y ¼ Xbþ � (6)

Coefficient vector is obtained by the following equation usingthe condition where the square of error is minimized:

b ¼ ðXT XÞ�1XT Y (7)

3.1.2.2. Model adequacy checking. Generally, it would be requiredto check the validity of the mathematical expression constructedfrom the regression analysis, and also the importance of the in-cluded factors. One of the possibilities is to examine the relativeand absolute errors between the exact analysis and the responsesbased on the mathematical expression. Others can be soughtthrough statistical tests. In this context, two simple statisticalhypothesis-testing procedures, including F-test and R2-test, areused to get a basic indication of the validity of the constructedmodel. The F-test that basically adopts the analysis of varianceexamines the significance of the regression model, while theR2-test provides an informal indication of how well the estimatedregression model describes the relationship between the in-dependent and dependent variables. In other words, R2 gives thefraction of variation accounted for by the regression model fit tothe observed data. Moreover, the verification of the regressionmodel is also tested by a new selected design point that is notincluded in the fit.

In statistics, the statistical index F0 is defined as

F0 ¼SSR

k

� �SSE

ðN � K � 1Þ

� �(8)

where N is the total points in the experimental design plan, k

denotes the number of independent design variables in the model,SSR expresses the sum of squares due to regression and SSE is thesum of squares due to residual. Accordingly, the total sum ofsquares SST can be expressed as

SST ¼ SSRþ SSE ¼ UTU�PN

i¼1yi

N(9)

where yi is the ith actual response. If F04Fa,k,N�k�1, where a is thespecified significance level in the F distribution, the null hypoth-esis, H0 is shown in the following two-sided hypotheses:

H0 : b1 ¼ b1 ¼ b2 ¼ � � � ¼ bk ¼ 0

ARTICLE IN PRESS

P. Yang, X. Qin / Microelectronics Journal 40 (2009) 1235–12431238

and

H1 : bja0 for some j in fj ¼ 1;2 . . . kg

is rejected, implying that at least one independent design variableis significant to the estimated response.

In the test, the coefficient of multiple determinations R2 isdefined as

R2¼

SSR

SST¼ 1�

SSE

SST(10)

Note that 0pR2p1. If bj (1, 2 y k) ¼ 0, then R2¼ 0

Furthermore, if all responses derived from the exact numericalsimulations are fully equivalent to the estimated responses, thenR2¼ 1, suggesting that the fit of the least-square line to the data

points is perfect.The formulas which are used for checking the validity of the

regression function are listed as follows.Total sum of responses

T ¼ y1 þ y2 þ � � � þ yn ¼Xn

i¼1

yi

ði ¼ 1;2; . . . ;nÞ (11)

Total sum of squares

Syy ¼ yT y� T2=n (12)

Square sum of errors

SSE ¼ yT y� bT XT y (13)

Square sum of regressions

SSR ¼ bT XT y� T2=n (14)

Coefficient of multiple determination

R2¼ SSR=Syy ¼ 1� SSE=Syy (15)

Adjusted coefficient of multiple determination

R2adj ¼ 1�

SSE=ðn� k� 1Þ

Syy=ðn� 1Þ(16)

Error of Y

s2 ¼SSE

n� k� 1(17)

Variance-covariance matrix of the b

covðbi; bjÞ ¼ Cij ¼ s2ðXT XÞ�1 (18)

3.2. Operators of gene

The optimization of GA–RSM is based on genetic algorithm,and some steps must be noticed.

3.2.1. Objective function

Objective function decides which chromosome is selected and,further, passed to next generation in GA. In GA–RSM, theregression functions which can describe the relation of designvariables to responses are defined as the objective function of GA.In this study, the mathematical expressions of the internaltemperature of MCM as function of the thermal conductivity ofmaterials and chip location serve as the objective function of GA.Based on finite element analysis of MCM, it can be observed thatthe thermal conductivity of molding compound, substrate, solderballs and attach and the location of the chips are the mostimportant parameters for heat dissipation of MCM. In this work,the thermal conductivity of structure and the location of the chipsare considered as the design variables, and the internal tempera-

ture of MCM is considered as the objective function. Theoptimization of the design variables with the aid of GA–RSM tomake the internal temperature of MCM lowest can show a reliableoptimum approach for design of MCM.

3.2.2. Encoding of a chromosome

Encoding of chromosomes is one of the important designpoints by using GA to solve the problem. Encoding very muchdepends on the problem. The chromosome should in some waycontain information about solution which it represents. There aremany other ways of encoding, such as binary encoding, permuta-tion encoding, value encoding, but the most popular method ofencoding is a binary string. Binary encodings are applied in thisinvestigation, and it can be introduced as following.

In binary encoding every chromosome is a string of bits, 0 or 1.

Chromosome A 101100101100101011100101Chromosome B 111111100000110000011111Example of chromosomes with binary encoding

Binary encoding gives many possible chromosomes even with asmall number of alleles. On the other hand, this encoding is oftennot natural for many problems and sometimes corrections mustbe made after crossover and/or mutation.

3.2.3. Operators

3.2.3.1. Selection. Chromosomes are selected from the populationto be parents to crossover. One of the important problems is howto select these chromosomes. According to Darwin’s evolutiontheory, the best ones should survive and create new offsprings.There are many methods to find the best chromosomes, for ex-ample Roulette wheel selection, Boltzman selection, tournamentselection, rank selection, steady-state selection and some others.

3.2.3.2. Crossover. Crossover selects genes from parent chromo-somes and creates a new offspring. The simplest way to do this isto choose randomly some crossover point before this point copyfrom the first parent. Crossover can be shown as following:

Chromosome 1:11011 | 00100110110Chromosome 2:11011 | 11000011110Offspring 1:11011 | 11000011110Offspring 2:11011 | 00100110110

There are other ways to make crossover, for example we canchoose more crossover points. Crossover can be rather compli-cated and very much depends on the encoding of chromosome.Specific crossover made for a specific problem can improveperformance of the genetic algorithm.

3.2.3.3. Mutation. After a crossover is performed, mutation takesplace. This goal is to prevent the solutions in population get into alocal optimum scheme. Mutation can make the new offspringchange randomly. For binary encoding, we can switch a few ran-domly chosen bits from 1 to 0 or from 0 to 1. Mutation can beshown as following:

Original offspring 1:1101111000011110Original offspring 2:1101100100110110Mutated offspring 1:1100111000011110Mutated offspring 2:1101101100110110

The mutation depends on the encoding as well as thecrossover. Fig. 2 shows the flow of GA–RSM algorithm

ARTICLE IN PRESS

Table 1The size and power of chips in the FE model.

Parameter Chip 1 Chip 2 Chip 3

Size (mm�mm�mm) 5�5�0.65 6� 4�0.65 6� 4�0.65

Power (W) 1 0.2 0.2

P. Yang, X. Qin / Microelectronics Journal 40 (2009) 1235–1243 1239

4. Optimum design of chip placement

4.1. Finite element simulation for experiments of GA–RSM

The optimization of chip placement is investigated by usingthe above-mentioned method. The coordinates of three chips inpackage are defined as design variables, and the internaltemperature is specified as response. Optimum chip placementis searched with the aid of GA–RSM to make the internaltemperature of MCM lowest. In the process, experiments ofGA–RSM are replaced with finite element simulations withANSYS. The MCM package containing three chips inside isperformed, and the chip size is herein defined by the side length,width and height of the chip. The size and power of chips aregiven in Table 1.

To understand the finite element simulation for experiments ofGA–RSM, the following is a description about the solution offinite element ANSYS (FEA). Fig. 1 shows the internal structureof a MCM.

Fig. 2. The flowchart of

4.1.1. Finite element model

To facilitate the calculation and analysis, there are severalsimplifications and assumptions of the device.

(1)

GA–R

The internal power devices of the MCM are thermal balance,and the temperature distribution is stable.

(2)

The embedded power chip and memories of the MCM are themain thermal source, and the Joule heat generated by theresistances and connections in both MCM and printed circuitboard is neglected.

SM algorithm.

ARTICLE IN PRESS

P. Yang, X. Qin / Microelectronics Journal 40 (2009) 1235–12431240

(3)

Assuming the bottom surface temperature of the MCM isconstant, for measuring with thermal infrared imager.

(4)

Assuming heat-transfer coefficient between the packaging orPCB surface and ambient is constant.

Table 2Range of coordinates of three chips.

Variable x1 (mm) y1 (mm) x2 (mm) y2 (mm) x3 (mm) y3 (mm)

Max 19.75 15.71 18.75 16.71 18.75 16.71

Min 0.5 0.5 0.5 0.5 0.5 0.5

According to the simplifications and assumptions above, a 3Dmodel was built with ANSYS. The 3D assembly finite elementmodel is composed of 209,803 elements and 45,222 nodes; the 3DPCB finite element model is composed of 235,284 elements and51,317 nodes. In the meantime, the model thermal boundaryconditions are introduced as follows: the thermal was generatedby the embedded chips in the MCM, in which the power of themain power chip is 2.6 W, and power of two memories is 15 mW,respectively. The heat transfer among the components of themodel is by conduction, and also it obeys the Fourier heat law; theheat dissipates from the surface of the model to ambient byconvection and radiation, and heat convection obeys Newton’slaw of cooling, heat radiation obeys Stephen–Boltzman law. Theambient temperature is 16 1C.

Fig. 3 shows the temperature dissipation of three embeddedchips. It shows that the highest temperature is 62.023 1C and thelowest temperature is 43.338 1C. The temperature of the mainpower chip on the side of memory is lower; the temperature ofmemory on the main power chip side is higher.

4.2. Selection of design variables

The coordinates of three chips in package are used to denotethe chip location on the substrate, as x1, y1, x2, y2, x3, y3. Inaddition, the Cartesian coordinates (X, Y), as shown in Fig. 1, areused to specify the in-plane spatial location of the small die on thesubstrate. Note that appropriate constraints are imposed on thesecoordinates, in which the chips could not exceed the edge of themolding compound and, in addition, the chips would not overlapeach other. The specific range of variation associated with theseparameters is shown in Table 2.

Fig. 3. Temperature dist

4.3. Establishment of regression model

4.3.1. Linear function

By fitting the responses at the selected points into a linearpolynomial expression, the macro model that describes theinternal temperature of the MCM associated with these designparameters is generated by using a linear regression analysis, andis shown as

T ¼ 46:0136þ 0:0024x1 þ 0:005y1 þ 0:0024x2

� 0:0088y2 þ 0:0111x3 þ 0:0047y3 (19)

where, T is the highest temperature in the package of MCM, x1 isx-axis value of chip 1, x2 is x-axis value of chip 2, x3 is x-axis valueof chip 3, y1 is y-axis value of chip 1, y2 is y-axis value of chip 2, y3

is y-axis value of chip 3.After test, it is found that the linear function cannot describe

the real function relative between internal temperature and thecoordinates of chips in MCM, so a second-order response modelshould be constructed.

4.3.2. Second-order function

Note that the method of constructing second-order function isidentical to the way mentioned previously. For building the second-order function, five levels of each variable are involved and thecentral composite design is used. A second-order function isgained according to the experiment scheme and simulation results.

ribution of the dies.

ARTICLE IN PRESS

Fig. 5. The objectives of initial population.

0 5 10 15 20Chromosomes after 10 iterations

25 30 35 40 4540

40.5

41

41.5value of objective function

valu

e of

obj

ectiv

e fu

nctio

n

Fig. 6. The objectives of chromosomes after 10 iterations.

P. Yang, X. Qin / Microelectronics Journal 40 (2009) 1235–1243 1241

As shown in

T ¼ 41:8905� 0:346x1 þ 0:1498x2 þ 0:1358x3

� 0:2795y1 þ 0:1039y2 þ 0:0786y3

þ 0:0187x21 þ 0:001x1x2 � 0:0006x1x3

� 0:0028x1y1 � 0:003x1y2 þ 0:0008x1y3

� 0:0064x22 � 0:0016x2x3 � 0:0023x2y1

� 0:0024x2y2 þ 0:0018x2y3

� 0:0078x23 þ 0:0017x3y1 þ 0:0018x3y2 þ 0:0005x3y3

þ 0:0193y21 þ 0:0015y1y2 � 0:0025y1y3

� 0:0058y22 þ 0:0003y2y3 � 0:0048y2

3 (20)

where T is the highest temperature in the package of MCM, x1 isx-axis value of chip 1, x2 is x-axis value of chip 2, x3 is x-axis value ofchip 3, y1 is y-axis value of chip 1, y2 is y-axis value of chip 2, y3 isy-axis value of chip 3.

From the F-statistics of the above mathematical expressions,the calculated indexes F0 is greater than F0.05(27, 24) underthe significance level of a ¼ 0.05. As F0 ¼ MSR/MSE ¼ 0.4877/0.1924 ¼ 2.53484F0.05(27, 24). The index R2 is close to 1, implyingthat the amount of variation observed in the internal temperatureof MCM that is explained by the quadratic regression model isalmost 100%, the fit of the least-square line to the data points isexcellent, and the independent variables (x1, y1, x2, y2, x3, y3) aresignificantly correlative to the estimated internal temperatureof MCM.

Furthermore, the quadratic mathematical expressions areverified using the four groups of newly selected design pointsthat are not included in the fit. In comparison with the FEsimulation results at the newly selected design point, there ismaximally about 0.28 1C discrepancy in the internal temperatureof MCM calculated by the regression model presented in Fig. 4. Itis concluded that the response surfaces derived from the second-order regression model can adequately predict the internaltemperature of the MCM as function of the spatial location ofthese chips.

4.3.3. Search characteristic analysis of the model

Taking the second-order function (20) as the objective functionof GA–RSM, search the optimum location of these chips whichmake the internal temperature of MCM lowest. To make sure thechips do not exceed the edge of the molding compound and not

1 1.5 2 2.5 3 3.5 440

40.5

41

41.5

42

42.5

Number

Res

ults

of G

A a

nd A

NS

YS

results of GAresults of ANSYS

Fig. 4. Comparison between results of GA and of ANSYS.

0 20 40 60 80 100 120 14039.5

40

40.5

41

41.5

42value of objective function

Chromosomes after 30 iterations

valu

e of

obj

ectiv

e fu

nctio

n

Fig. 7. The objectives of chromosomes after 30 iterations.

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P. Yang, X. Qin / Microelectronics Journal 40 (2009) 1235–12431242

overlap each other, filters are added into the GA. However, thechromosomes number of each generation may not be uniform, butit does not affect the optimization. Finite element experimentswere carried out to produce the initial population. The expecta-tion is that an initial population of reasonably structured solutionswill evolve to high-quality solutions in a relatively small numberof generations of the GA. In the meantime, the crossoverprobability is selected as 0.7, and the mutation probability isselected as 0.02. In general, when crossover probability is 0.8,mutation probability is 0.2, premature convergence occurredfrequently. We should select the advisable crossover and mutationprobabilities to prevent premature convergence and blind opera-tion. By using the method in Ref. [9], the above-mentionedcrossover and mutation probabilities are selected as 0.7 and 0.02,respectively. The results show that they are the advisable

0 20 40 60 80 100 120 14039.5

40

40.5

41

41.5

42value of objective function

Chromosomes after 50 iterations

valu

e of

obj

ectiv

e fu

nctio

n

Fig. 8. The objectives of chromosomes after 50 iterations.

0 5 10 15 20 25 30 35 40 45 5038.5

39

39.5

40

40.5

41minimal valueaverage value

Generation

The

Ave

rage

and

min

imal

val

ue o

f

obje

ctiv

e fu

nctio

n in

pop

ulat

ion

Fig. 9. The average and minimal objective of each chromosome’s generation.

Table 3The result of genetic iteration.

x1 (mm) y1 (mm) x2 (mm) y2 (mm) x3 (mm) y3

10.8422 7.6576 18.75 16.71 18.75 0.

selection. The searching characteristics about GA are shown inFigs. 5–9. Fig. 5 shows the objectives of initial population. It can befound that the distribution of objectives is wide and uniform.After 10 genetic iterations, the chromosomes which meet thecondition that chips do not exceed the edge of the moldingcompound and not overlap each other decrease a lot, and there areonly 45 chromosomes. However, the objective values ofchromosomes decrease obviously and most of the objectivevalues are between 40 and 41.5, as Fig. 6. Moreover, Figs. 7 and8 show the objective values decrease further after 30 geneticiterations, but the number of chromosomes increases a lot. Thereare 140 chromosomes in total.

The average and minimal objective values of each generationchromosomes are shown in Fig. 9. In the figure, the above curvedenotes average values of objectives, and the below curve denotesminimal values. It can be found that both the average and minimalobjective values of each chromosome decline obviously as thegenetic iterations increase. Moreover, the minimal value ofobjective becomes stable after fortieth genetic iteration, so itcan be believed that the design variables associated with thisobjective are the optimum.

After the calculation of GA–RSM, the chromosome of which theobjective value is minimal is gained, and the correlativecoordinates of chips in MCM are given in Table 3.

To verify whether the internal temperature of MCM associatedwith the location of the chips in MCM gained with GA is minimal,a large number of experiments have been done. The results ofexperiments indicate that the internal temperature of MCM isminimal when the coordinates of chips in MCM are 10.8422,7.6576, 18.75, 16.71, 18.75, 0.5, respectively (The test investigationabout this will be published in another paper for experimentalresearch). In the meantime, the numerical analysis by finiteelement method was developed. Fig. 10 shows the comparisonbetween results of ANSYS and the optimal result of GA–RSM. Itshows that the GA–RSM method can get the most optimum designresults.

(mm) The value from GA The value of simulation Error

5 39.5844 40.434 0.8496

1 1.5 2 2.5 3 3.5 440

40.5

41

41.5

42

42.5

43results of ANSYSthel result of GA

Number

resu

lts o

f AN

SY

S a

nd th

e op

timal

resu

lt of

GA

Fig. 10. Comparison between results of ANSYS and the optimal result of GA.

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P. Yang, X. Qin / Microelectronics Journal 40 (2009) 1235–1243 1243

5. Conclusions

(1)

A GA–RSM model is developed in this paper for optimumdesign of chip placement of multi-chip module in electronicpackaging. The internal temperature of MCM is specified asresponse. The experiments of GA–RSM are replaced withsimulations with the aid of ANSYS based on an appropriate-ness and applicability of the proposed FE modeling.

(2)

By the integration of the GA–RSM and the FE simulationtechniques, mathematical expressions of the internal tem-perature of MCM as function of, such as, the chip location areaccordingly constructed in this study for readily assessing thethermal performance of MCM packages. Then the chipplacement is optimized based on GA–RSM model.

(3)

From the regression analysis, it shows that both the two linearregression functions would not provide the estimated internaltemperature of the MCM as function of spatial location of thechips in MCM. However, it would be more reasonable to adoptthe quadratic polynomial expression to describe the relationof the estimated internal temperature of the MCM containingthree chips to the respective spatial location of chips. They canbe further utilized to facilitate the subsequent thermalmanagement of the MCM during initial design stage withoutrepeated efforts on time-consuming FE simulations.

(4)

An example is illustrated where the GA–RSM model can beused well for optimum design of chip placement of multi-chipmodule. It lay a basis for engineering design of chip placementof multi-chip module in electronic packaging.

Acknowledgments

The authors would like to acknowledge the support of NationalNatural Science Foundation of China (50875115), the support ofNatural Science Foundation of Jiangsu Province of China(BK2008227), the Special Science Foundation for Middle-Youngacademic leader of Jiangsu high education in China (QinglanGongcheng Project), the Natural Science Foundation for QualifiedPersonnel of Jiangsu University (04JDG027) and the SpecialNatural Science Foundation for Innovative Group of JiangsuUniversity during the course of this work.

References

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[2] Kimmo Kaija, Pekka Heino, Transient thermal characterization of a stackedmulti-chip package, Journal of Microelectronics and Electronic Packaging 4(1) (2007) 23–30.

[3] Jean-Denis Mathias, Xavier Balandraud, Michel Grediac, Applying a geneticalgorithm to the optimization of composite patches, Computers andStructures 84 (12) (2006) 823–834.

[4] Ping Yang, Jie Zhang, Research on parametric analysis for stress of PBGAsolder joint under shock load, International Journal of Materials and ProductTechnology 31 (3) (2008) 293–304.

[5] Ping Yang, Ningbo Liao, Research on characteristics of interfacialheat transport between two kinds of materials using a mixed MD-FEmodel, Applied Physics A: Materials Science & Processing 92 (2008)329–335.

[6] Pierre-Marie Geffroy, Jean-Denis Mathias, Jean-Franc-ois Silvain, Heat sinkmaterial selection in electronic devices by computational approach, AdvancedEngineering Materials 10 (4) (2008) 400–405.

[7] Barbara Bonnet, Philippe Monfraix, Renaud Chiniard, Jerome Chaplain,Claude Drevon, Herve Legay, Pascal Couderc, Jean-Louis Cazaux. 3Dpackaging technology for integrated antenna front-ends, in: Procee-dings of the 38th European Microwave Conference, EuMC 2008,pp. 1569–1572.

[8] Ping Yang, Min Shen, Investigation on the thermal conductivity of AlN thinfilms by using molecular dynamics simulation, International Journal ofMaterials & Product Technology 34 (3) (2009) 323–329.

[9] Ping Yang, Ningbo Liao, A mixed isomorphism approach for kinematicstructure enumeration graphs based on intelligent design and manufacturing,International Journal of Advanced Manufacturing Technology 31 (9–10)(2007) 841–845.

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Yang Ping is currently a professor in Jiangsu University in China, also is currentlyan editorial Member of Microsystem Technologies, an editorial Member ofInternational Journal of Materials and Product Technology, Associate Editor inChief of International Journal of Materials and Structural Integrity, a directorof China Precision Machine Society and a senior member of Chinese Instituteof Electronics. He received his Ph.D. in mechanical engineering from HuazhongUniversity of Science & Technology (HUST) in 2001. He engaged in sciencesresearch in Concordia University. His research interests focus on thetheoretical aspect and CAD of mechanical system for the purposes of designand control. He has authored over 60 professional and scholarly publicationsin famous international journal in the very specialized field of the theoreticalaspect and CAD of micro/nano-mechanical system for the purposes of designand control.