the thermal resistance of solder joints in high brightness light emitting diode (hb led) packages

IEEE TRANSACTIONS ON COMPONENTS AND PACKAGING TECHNOLOGIES, VOL. 32, NO. 4, DECEMBER 2009 825

The Thermal Resistance of Solder Jointsin High Brightness Light Emitting

Diode (HB LED) PackagesYoung-Bok Yoon and Jin-Woo Park

Abstract—We present a framework to calculate the thermalresistance of Au–Sn eutectic solder joint (Rth,Au–Sn joint) in highbrightness light emitting diode (HB LED) packages whose heatextraction capability controls the optical efficiency and reliabilityof HB LEDs. Using the transient thermal measurement combinedwith the structure function based analytical method and the finiteelement method, we find that the thermal conductivity (k) of thethin solder joint becomes significantly smaller than the Au–Snalloy after joining; hence, Rth,Au–Sn joint constitutes a large portionof the total Rth of the package (RPKG

th ).

Index Terms—Finite element method, LED package, structurefunction, thermal resistance.

Nomenclature

k Thermal conductivity (W/m·°C).kA k of a material A (W/m·°C).keffB Effective k of a joint or material B after

joining (W/m·°C).ki k of the ith element from the junction in

the equivalent resistance–capacitance (RC)network (W/m·°C).

Rth Thermal resistance (°C/W).Rth,n Rth of the nth component from the junction

in the package (°C/W).Rth,A Rth of the component, A (°C/W).RPKG

th Total thermal resistance of a HB-LED pack-age (°C/W).

RMDLth Total thermal resistance of a HB-LED mod-

ule (°C/W).RFEM

th,� Total Rth from the calculated thermal re-sponses (°C/W).

RFEM,eff.th,� Total Rth from the calculated thermal re-

sponses and effective k (°C/W).RTTM

th,� Total Rth from the measured thermal re-sponses (°C/W).

Manuscript received March 12, 2008; revised December 30, 2008. Firstversion published October 30, 2009; current version published November20, 2009. Recommended for publication by Associate Editor S. Tonapi uponevaluation of reviewers’ comments.

Y.-B. Yoon is with the Computer-Aided Engineering Group, CorporateResearch and Development Institute, Samsung Electro-Mechanics Company,Ltd., Suwon 443-743, Korea (e-mail: [email protected]).

J.-W. Park is with the Department of Materials Science and Engineering,Yonsei University, Seoul 120-749, Korea (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TCAPT.2009.2033414

RCth Cumulative thermal resistance (°C/W).

RCth,k RC

th up to the kth element from the junction(°C/W).

RCth,Fic.n RC

th system having the first to nth componentsout of N components in total (°C/W).

CCth Cumulative thermal capacitance or structure

function (W·s/°C).Cth,n Structure of the nth component from the

junction (W·s/°C).Kth Differential structure function

(dCC

th

dRCth

)(W2 ·

s/°C2).(RC

th–Kth)FEM RCth–Kth curve from the calculated thermal

responses.(RC

th–Kth)TTM RCth–Kth curve from the measured thermal

responses.εc Conversion efficiency from electrical to op-

tical power of LED.εe

PKG Heat extraction efficiency of HB LED pack-ages.

Tj Junction temperature of LED (°C).T0 Ambient temperature (°C).ri Thermal resistance of an ith element from

the junction in the equivalent RC network(°C/W).

ci Capacitance of an ith element from the junc-tion in the equivalent RC network (W·s/°C).

ρi Density of the ith element from the junctionin the equivalent RC network (kg/m3).

Cp Specific heat (J/kg·°C).Cp,i Cp of the ith element from the junction in

the equivalent RC network (J/kg·°C).Ai Cross-sectional area of the heat conduction

path of the ith element from the junction inthe equivalent RC network (m2).

hi Height of the ith element from the junctionin the equivalent RC network (m).

I. Introduction

IN THE LAST decade, a light emitting diode (LED) ofhigh light output, which is called a high brightness LED

(HB LED), has taken great attention as next-generation generallightings due to its environment-friendly, energy-saving

1521-3331/$26.00 c© 2009 IEEE

826 IEEE TRANSACTIONS ON COMPONENTS AND PACKAGING TECHNOLOGIES, VOL. 32, NO. 4, DECEMBER 2009

Fig. 1. Schematic descriptions of (a) transient temperature profile measurement system, and (b) an equivalent RC network to the system in (a).

characteristics, and longer life [1]. The light output of HBLEDs has already surpassed the incandescent and halogenbulbs [2]. However, the conversion efficiency from electricalto optical power (εc) has not been improved as much as thelight output [2]. Therefore, the junction temperature (Tj) ofthe chip increases with increasing input power due to the heatgenerated in the junction during operation [3].

Most of the reliability issues retarding the commercializa-tion of the HB LEDs are closely related to the temperaturerise in the junction. Tj affects not only the color of the lightbut also further degradation of εc significantly [1]–[3]. Asan alternative to increasing εc, engineers have addressed thethermal issues by improving the heat extraction efficiencyof HB LED packages (εe

PKG) [3], which is described by theconcept of thermal resistance (Rth) [3], [4]. RPKG

th is definedas the difference between Tj and ambient temperature (T0)divided by the input power [4]. As the electrical resistance isinversely proportional to electrical conductivity, so to k is Rth

[4]. RPKGth is the summation of Rth of the components con-

stituting the package like the concept of electrical resistance[4]. Hence, efforts have been made to find highly conductivematerials for the components, such as a heat sink [Fig. 1(a)]to decrease RPKG

th [3]. However, as far as the manufactur-ing cost is concerned, the selection of the materials is solimited [5].

The joint between HB LED and the heat sink constitutesthe smallest volumetric portion in the package, but has beenconsidered as an important heat conduction pathway from thejunction [3]. For further improvement of εe

PKG by decreasingRth of the joint, epoxies with low k that were generally used forLED of low output have been replaced by metal solders and,instead of ball bonding, die bonding has been used to increasethe conduction area [6]. These replacements decreased RPKG

th

in a degree, but not as much as the degree expected from theincreases in k and the area [2], [3].

k of the joint is strongly related to the joint and interfacemicrostructures [5]. In our previous paper on the HB LEDjoint of a few-micrometer-thick Au–Sn eutectic solder, whichis the most popular solder alloy for HB LED packages, wefound that thick Au–Sn–Ni intermetallic compound layers andthe large number of defects are formed at the interfaces andin the joint, respectively [7]. According to our investigation[7], the poor joint microstructure is due to the large aspectratio of the interface area to the thickness of the joint, whichis inevitable in joining HB LED [7]. As a consequence, kof the joint is expected to become smaller than k of thealloy [8].

Because, currently, there is no direct measurement techniqueof k and Rth of the thin solder joint with such a complexmicrostructure [6], [9], [10], quantitative analysis results havebeen often argued [3], [8]. As an alternative to the directmeasurement, transient thermal measurement (TTM) and thestructure function-based analytical method (SFM) by Székelyet al. [9], [10] have been used most frequently. In this method,the temperature changes of the junction on heating [Fig. 2(a)]is calculated inversely from the measured functional relation-ship of the forward voltage (Vf ) of HB LED at fixed inputcurrent (I) with temperature [9], [10]. Using the transformationalgorithms by Székely et al., an equivalent RC network thatgenerates the same transient thermal response of the HB LEDpackage is found [Fig. 1(b)] [9], [10].

Based on the equivalent RC network, cumulative thermalcapacitance

(CC

th

), which is called structure function, or dif-

ferential structure function (Kth), which is(dCC

th/dRCth

), as a

function of cumulative thermal resistance(RC

th

)is generated

along the heat conduction path from the junction to the air [9].

YOON AND PARK: THERMAL RESISTANCE OF SOLDER JOINTS IN HB LED PACKAGES 827

Fig. 2. (a) Calculated with effective k, and measured temperature changes in the junction on heating. (b) RCth–Kth curves transformed from (a).

RCth–CC

th and RCth–CC

th curves are, so-called, graphic represen-tations of the 1-D equivalent RC network [10]. Theoretically,if we know the material properties of each component con-stituting the package and an approximate 3-D shape of theconduction path, Rth of each component can be estimated fromthe RC

th–CCth or RC

th–Cth curve based on (1), (2), and (3) [4],[9], [10]

RCth =

M∑n=1

Rth,n =N∑i=1

ri =N∑i=1

hi

ki · Ai

(1)

CCth =

M∑n=1

Cth,n =N∑i=1

ci =N∑i=1

Cp,i · ρi · hi · Ai (2)

Rth,n = RCth,k − RC

th,l =k∑

i=1

ri −l∑

i=1

ri, k > l (3)

where Rth,n and Cth,n are Rth and the structure of the nthcomponent from the junction [Fig. 1(a)], respectively. ci andri are the capacitance and resistance of an ith element fromthe junction in the equivalent RC network consisting of Nelements, respectively [Fig. 1(a)] [4], [10]. Cp,i,ρi, ki, Ai, and

hi are specific heat, density, thermal conductivity, the cross-sectional area of heat conduction path, the height of the ithelement, respectively [4], [10]. RC

th,k and RCth,l are RC

th up tothe kth and lth elements from the junction, respectively, thatare assumed to correspond to the interfaces with two othercomponents [10].

In reality, however, there is no theoretical background indetermining the element matching to an interface, which hasoften led to contradictory conclusions on Rth,n as well as Rth

of the joint from the same RCth–CC

th curve [3], [10]. In addition,in many opto-electronic device packages where Rth is oneof the most important issues, heat conduction path and thejoint thermal properties are unknown in practice [9], [10].Nevertheless, TTM–SFM is still considered as an attractiveindirect measurement technique of Rth,n because its detectionaccuracy of the changes in Cp,i, ρi, ki, and Ai along theconduction path depends not much on the size scales of theinhomogeneity but on the degree of the changes [3], [9]–[11].

In this paper, Rth of Au–Sn eutectic solder joint(Rth,Au–Sn joint) in HB LED packages whose microstructure hasbeen analyzed in our previous paper [7] is investigated using


TABLE I

Size and Material Properties of the Components of the Model System in Fig. 1

Size [Width (mm) × Thickness (mm) × Height (mm)] k (k∗) (W/m·°C) ρ (kg/m3) Cp (J/kg · °C)Au–Sn solder joint 0.7 × 0.7 × 0.004 57 (4.0) 14 510 200Si heat sink 5.0 × 5.0 × 0.3 124 2329 702TG joint #1 5.0 × 5.0 × 0.05 1.0 (0.5) 800 2000MCPCB 25 × 25 × 1.5 200 2707 896TG joint #2 25 × 25 × 0.05 1.0 800 2000

k∗: effective thermal conductivity.

TTM, but, to overcome the limitations in interpreting the re-sults transformed by SFM, we use FEM. The transient thermalprofile of the same HB LED package is both measured byTTM and calculated using FEM. Two profiles are transformedto RC

th–KCth curves by SFM and the factors determining the

differences in the two curves are investigated using sensitivityanalysis by FEM. Based on the FEM results, the effective kof the joint (keff.

Au–Sn) and other components can be deduced.Instead of estimating Rth,n as well as Rth,Au–Snjoint by

partitioning the RCth–Kth curve based on (1)–(3), we calculate

the difference in RCth between when the model system has

up to nth component from the junction and only up to the(n−1)th component using FEM with the effective k, which isconsidered as Rth, n. For these calculations in the model systemof this paper [Fig. 1(a)], removing one component by onecomponent from the thermal grease #2 to the Au–Sn solder,five fictitious model systems are created. Then, Rth,n can becalculated as

Rth,n = RCth,Fic.n − RC

th,Fic.(n−1) =n∑

i=0

Rth,i −n−1∑i=0

Rth,i (4)

where RCth,Fic.n and RC

th,Fic.(n−1) are RCth of the fictitious systems

having the first to nth components and having the first to(n − 1)th components from the junction, respectively. Rth,0 isRth of HB LED. Based on the calculation results, the commonmistakes in estimating Rth,n from RC

th–Kth curves in previousstudies [12], [13] are discussed.

II. Experimental and Numerical Procedures

A. Transient Thermal Analysis

The schematic descriptions of the model package and theconfiguration for TTM used in this paper are described inFig. 1(a). The model package consists of the commercial HBLED of 1 W input power [14], Au–Sn solder joint, and a Siheat sink [7]. The joining process of HB LED to the Si heatsink can be found in our previous paper [7]. The package isbonded to a metal-core printed circuit board (MCPCB) using aconductive thermal grease (TG) for electric connections, whichis generally called an HB LED module [Fig. 1(a)]. Twenty fivemodules are made for TTM. The size and material propertiesof the components constituting the module in Fig. 1(a) aredescribed in Table I.

For measuring temperature changes of the junction, eachmodule is again bonded to thermo-electric cooler (TEC) using

the same TG for isothermal cooling. The dependence of Vf

of HB LED on temperature is measured under pulsed modeinput current of 10 mA by changing the temperature of TEC.Based on these data and measured changes in Vf of HBLED on heating during operation at 350 mA for 5 min, thetransient thermal responses are obtained. These responses aretransformed into a structure function as a function of RC

thusing T3ster (MicRED Ltd.), the thermal transient tester, andcomputer program. Using this procedure, RC

th–Cth curves areobtained for 20 HB LED modules. Several of the samples aremounted and polished for optical microscope and scanningelectron microscope analyses to measure the size of thejoints.

B. Numerical Analysis

The measurement system described in Fig. 1(a) and Sec-tion II-A is modeled to simulate the transient cooling of theHB LED module. Considering the symmetry, a quarter ofthe system is modeled. Temperature and time-independentmaterial properties are used (Table I). The heat generatedin the junction is assumed to be 0.85 W, which is 85%of the input power [2], [7]. The temperature of the bot-tom of the HB-LED module in Fig. 1(a) is fixed at 25 °C.The numerical calculations are done using ANSYS computerprogram [15]. The calculated transient thermal responsesare transformed into RC

th–Kth curves using a commercialprogram.

The effects of thermal properties of each component on thethermal responses and RC

th–Kth curves are calculated varyingone property with others fixed. Among 20 curves [(RC

th–Kth)TTM] mentioned in Section II-A, the curve with averagetotal Rth is selected and compared with the RC

th–Kth curvefrom the calculated temperature changes ((RC

th–Kth)FEM). Thematerial properties determining the difference between (RC

th–Kth)TTM and (RC

th–Kth)FEM are found based on the sensitivityanalysis results and the effective values of the propertiesthat make two curves the most corresponded are calculated.With the effective properties, thermal responses and RC

th–Kth

curves of the five fictitious systems mentioned in Section I arecalculated. From the curves, Rth,n is calculated using (4).

III. Results and Discussion

The transient temperature responses and (RCth–Kth) curves

transformed from them are shown in Fig. 2(a) and (b). Theconstant temperature of TEC [Fig. 1(a)] is equivalent to air of


Fig. 3. Changes in Kth–RCth curves varying (a) k/kAu–Sn and (b) k/kSi (where kAu–Sn is k of Au–Sn and kSi is k of Si in Table I).

infinite Cp [9], [10]. Therefore, the slope of RCth–Kth curves

increases infinitely at the end of the module, as shown inFig. 2(b). RTTM

th,� and RFEMth,� indicated in Fig. 2(b) are the total

Rth from the temperature data measured and calculated byFEM using the material properties in Table I, respectively,and they are the summation of Rth,0 to Rth,5. The increasingslope in the RC

th–Kth curves in Fig. 2(b) indicates that there isa rapid increase in Cth or decrease in Rth along the conductionpath and vice versa for the decreasing slope [9], [10].

As shown in Fig. 2(b), RFEMth,� is larger than RTTM

th,� by3.9 °C/W. According to the sensitivity analysis, for the samedegree of change, k of the components of a larger volume suchas the Si heat sink and MCPCB in Fig. 1(a) affect the totalRth greater than k of smaller components, such as the solderand TG joints as shown in Fig. 3(a) and (b). As k of large

volume components increases, the profile of conduction path[Fig. 1(a)] represented by Ai and hi in (1) to (3) seems tochange. The effect of varying k of the TG joint #1 [Fig. 1(a)]on the total Rth is as much as that of the solder, but the effectof the same TG joints #2 is negligible because

∑i hi/Ai in

(1) of the joint #2 is almost a hundred times larger than thejoint #1 as shown in Table I. The effect of k of HB LED isalso negligible.

k of materials cannot be controlled without changes in Cp

in practice. As expected from (1) and (2), varying Cp and ρ

of the components do not affect the total Rth, but affect Cth

and Kth, that is, the time to reach a steady state. However,considering that the ranges of variations in the magnitudes ofCp and ρ between materials are much smaller than those of k,the sensitivity analysis results show that the effects of varying


TABLE II

Calculated Rth,n in Fig. 4

Rth,n (°C/W)Au–Sn solder joint 2.0Si heat sink 1.8

RPKGth 3.8

TG joint #1 4.38MCPCB 0.17

RMDLth 8.34

Cp and ρ on Cth and Kth are negligible compared to k of thecomponents.

In reality, the material properties of the Si package andMCPCB in Fig. 1(a) change little during the joining processexcept the very narrow region of the Si heat sink close tothe interface with the solder joint, which is verified in theFEM calculations. According to the FEM calculation results,decreasing k of the Si heat sink or MCPCB by a certainmagnitude, RFEM

th,� increases up to RTTMth,� . However, there is large

discrepancy in two Kth, which cannot be reduced by varyingCp and ρ of the two components, either. Based on the transienttemperature data in Fig. 2(a), it can also be deduced that thedifferences between (RC

th–Kth)TTM and (RCth–Kth)FEM do not

result from the changes in Cp and ρ after joining, affectingthe time to reach a steady state.

According to our previous paper [7], it is reasonable toassume that k of the solder joint (kAu–Sn joint) becomes smallerthan kAu–Sn because of the joining defects. k of the TG joints isdecreased if there is pore formation or partially unwetted areaduring curing. FEM calculation results verify our assumptionthat the difference between (RC

th–Kth)FEM and (RCth–Kth)TTM

result mostly from the deterioration of the thermal propertiesof the joints during joining. When kAu–Sn joint is only 7% ofkAu–Sn in Table I and k of the TG joint #1 (kTG joint#1) becomesa half of kTG, transient temperature curves and RC

th–Kth curvesby TTM and FEM become almost identical as shown inFig. 2(a) and (b). Out of the total difference of 3.9 °C/Wbetween RFEM

th,� and RTTMth,� in Fig. 2(b), 1.9 °C/W is due to the

difference between kAu–Sn joint and kAu–Sn and 2.0 °C/W is dueto the difference between kTG joint#1 and kTG.

The RCth–Kth curves of the fictitious systems mentioned in

Sections I and II-B are calculated and the results are shownin Fig. 4 and Table II. As Rth,LED and Rth,TG#2 are negligible,only Rth,n of four other components are described in Fig. 4.As shown in Fig. 4, Rth,Au–Sn joint constitutes 52% of RPKG

th ,which is larger than Rth,Si comprising 48% of RPKG

th . This resultshows that considering that the input current should be morethan 10 W per LED for the general lighting applications, a fewtens of degree of the junction temperature can be reduced byimproving the quality of the solder joints. In the HB LEDmodule, Rth,TG#1 constitutes more than a half of RMDL

th asshown in Fig. 4. Regarding that multiple HB LED packagesare connected to a MCPCB in the general lighting applications,it should be considered seriously to replace the conventionaluse of thermal grease or the conductive epoxy in most of thepackages and modules having thermal issues by using moreconductive materials despite the cost increase.

Fig. 4. RCth–Kth curves of four fictitious systems and the calculated Rth,n

based on (4).

As shown in Fig. 4, the interfaces do not necessarilycoincide with the peaks and valleys, which is contradictory tothe previous analysis by other [3], [9], [10]. The small peaksand valleys in the latter part of the RC

th–Kth curves in Fig. 2 andRC

th,Fic. 4–Kth and RCth,Fic. 3–Kth in Fig. 4 seem to be generated

in converting the transient thermal responses to structurefunction [9]–[11]. Hence, it will lead to erroneous results toconsider every peak and valley as indicating discontinuities inproperties and geometry along the conduction path [11].

IV. Conclusion

The effect of microstructural changes of an Au–Sn eutecticsolder during joining on the thermal property of the solderjoint has been investigated using TTM, the indirect transienttemperature measurement technique, numerical analysis usingFEM, and analytical transformation procedure using structurefunction. The results confirmed the thermal conductivity dete-rioration of the joint due to the joint defects and intermetalliccompounds at interfaces observed in our previous paper [7],and its important effect on RPKG

th · keff.Au–Sn joint was found to be

less than 7% of kAu–Sn, which makes Rth,Au–Sn joint 13 timeslarger than Rth of the alloy with the same size and constitutemore than a half of RPKG

th . Considering the small volumetricportion of the solder joint in the package, the result verifiedthe highly important role of the joint as a conduction pathway.However, to improve the thermal capability of the HB LEDpackages and modules by optimizing the joint microstructures,the individual effect of different types of compounds andjoining defects on the decrease in k should be analyzedcarefully. This is our ongoing paper.

By using FEM, the limitations in estimating Rth,n from RCth–

Kth curves obtained by TTM and SFM could be overcomeand a new framework for the quantitative analysis of Rth,n hasbeen proposed. According to our calculation results of Rth,n,the peaks and valleys in RC

th–Kth curves do not necessarilycorrespond to the interfaces between components, which arecontradictory conclusions to the previous papers by others[3], [9], [10]. With fundamental understandings of the thermal


resistance concept and the mathematical transformation pro-cedures of SFM, our new framework provides an improvedanalysis procedure of the thermal capability of not only HBLED packages but also any electronic and optical devicepackages with an important thermal issue.

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PA.

Young-Bok Yoon received the B.S. and Ph.D.degrees in mechanical engineering from HanyangUniversity, Seoul, Korea, in 1995 and 2002, respec-tively.

Currently, he is a Senior Research and Develop-ment Engineer at the Computer-Aided EngineeringGroup, Corporate Research and Development In-stitute, Samsung Electro-Mechanics Company, Ltd.,Suwon, Korea. His research interests include sub-strate, packages, and board level reliability with afocus on modeling and predictive techniques.

Jin-Woo Park received the B.S. degree in metal-lurgical engineering from Yonsei University, Seoul,Korea, in 1996 and the Ph.D. degree in materi-als engineering from the Massachusetts Institute ofTechnology, Boston, in 2002.

Currently, she is an Assistant Professor at theDepartment of Materials Science and Engineering,Yonsei University, Seoul, Korea. She was a Post-doctoral Research Associate at Oak Ridge NationalLaboratories, Oak Ridge, TN. Her research interestsinclude controlling interfaces in joined dissimilar

materials systems.

the thermal resistance of solder joints in high brightness light emitting diode (hb led) packages

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