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Morphology changes in solder joints––experimental evidence and physical understanding
Microelectronics Reliability 44 (2004) 1901–1914 www.elsevier.com/locate/microrel
Morphology changes in solder joints––experimental evidence and physical understanding W.H. M€ uller
*
Institut f€ur Mechanik, LKM, Technische Universit€at Berlin, Einsteinufer 5, Berlin 10587, Germany Received 6 October 2003; received in revised form 14 January 2004 Available online 8 July 2004
Abstract The microstructures of solders in microelectronic components, lead containing as well as lead free, change over time. This is first of all due to comparatively high homologous temperatures which occur during reflow as well as during operation of the component. Moreover, because of the intrinsic thermal mismatch between the various materials that constitute the package substantial mechanical stresses and strains will arise and assist the process of microstructural change. In this paper we will, first, briefly provide experimental evidence for such microstructural change and how it relates to the solder bulk as well as to the various interfaces and passivation materials that are used when a solder joint is formed. Second, we will review state-of-the-art modeling techniques that allow to simulate such changes of microstructure provided certain material parameters are known. For this purpose we will set up all equations and then provide information on all the material parameters required for a numerical solution. We will present computer simulations based on this theoretical framework and study the influence of the material parameters on coarsening and aging and, in particular, examine the impact of mechanical stresses and strains. Finally we will address difficulties and challenges involved, experimental as well as modeling ones. 2004 Elsevier Ltd. All rights reserved.
1. Microstructural change in solders––experimental evidence 1.1. Typical SMT solder materials Tin is the element that eventually leads to the electromechanical connection with the copper pads used in surface mount technology (SMT) microelectronics technology. This is achieved by a chemical reaction during which the tin and the copper react by diffusion to form an intermetallic compound, Cu6 Sn5 ([1], p. 180). Unfortunately the melting point of tin is too high for microelectronic manufacturing (Tmelt ¼ 231:93 C) and, therefore, further elements are added to the tin so that a tin-based solder alloy with a lower melting point results.
*
Tel.: +49-30-314-27682; fax: +49-30-314-24499. E-mail address: [email protected] (W.H. M€ uller).
Originally this addend was lead, which is inexpensive and readily available. Typically binary eutectic tin–lead (SnPb38.1, 1 Tmelt ¼ 183 C) or slightly hyper- or hypoeutectic variants thereof were used. In general, the fact that an alloy is eutectic guarantees that it has a unique melting point whereas hyper- or hypoeutectic alloys show a melting range which, in microelectronics, is kept as narrow as possible for obvious processing reasons. Lead containing ternaries were also used, the most prominent example being hypereutecric Sn62Pb36Ag2. The silver is added to prevent dissolution from component terminations ([1], p. 221, [3]). Due to environmental restrictions lead is about to be completely banned from the microelectronic industry [4,5]. This requires alternative binary solders to be used, such as eutectic
1
Due to inevitable inaccuracies during calorimetric measurements eutectic tin–lead is often also referred to as Sn37.1Pb or (roughly) as Sn37Pb [2].
0026-2714/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.microrel.2004.04.020
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tin–silver and tin–copper, SnAg3.5 or SnCu0.7, showing melting points of 221 and 227 C, respectively. However, terneries (e.g., near eutectic SnAgCu) or even quartenary and higher systems (e.g., SnAgBiCu, SnInAgSb) are also considered the reason being an ongoing quest for finding readily available and affordable interconnection materials with a suitable melting point and electromechanical characteristics that are just as good or better than traditional tin–lead. Moreover, thermal mismatch between the various materials involved in microelectronic structures is almost inevitable even though serious attempts are made to keep it as small as possible. This mismatch in combination with comparatively high operating temperatures, i.e., high homologous temperatures may lead to a change of the solder micromorphology and hence joining capability. This issue will be discussed in the next two subsections. 1.2. The solder bulk As a first example of micromorphological change in solders consider Fig. 1 which shows a cross-section
Fig. 1. Cross-sectional cut through the solder joints of a ball grid array (BGA) [6].
through a BGA solder ball [6], made of eutectic tin–lead, before and after it has been subjected to several thousand thermal cycles during which it was exposed to homologous temperatures of 0.8 and more. The regions of different shades of gray and black indicate that after starting out as a fine mix between tin and lead ‘‘islands’’ of high Pb concentration keep growing in a ‘‘sea’’ of high Sn concentration. These two regions are known as a and b-phases, respectively. This micromorphological change is a result of a diffusion process of the elements, also known as spinodal decomposition, followed by coarsening through phase separation. It should be emphasized that phase separation can be accelerated considerably if the homologous temperatures are high and mechanical stresses are present. The first statement is supported by the experiments shown in Fig. 2 [7], and the latter one by the right micrograph in Fig. 1. Obviously coarsening is particularly high in the interface regions of the solder ball where, due to edge effects, the stresses are most pronounced. Clearly, once the microstructure, i.e., the local mechanical properties change over time the overall material properties of the ball will also change, which, eventually, can have a detrimental effect on its joining capability. It should be pointed out that changes in microstructure due to spinodal decomposition are by no means limited to tin–lead. Rather it has also been observed in lead free solders, e.g., in the brazing alloy AgCu [8]. The micrograph in Fig. 3 shows copper rich and silver rich phases regions. As in the case of tin–lead the corresponding equilibrium concentrations depend on temperature. In fact the phase diagrams of both alloys are very similar showing the characteristic V-shape depicted
Fig. 2. Coarsening in SnPb, 1st row 20 C (a) 2 h, (b) 17 d, (c) 63 d; 2nd row: 125 C (a) initially, (b) 3 h (c) 300 h [7].
W.H. M€uller / Microelectronics Reliability 44 (2004) 1901–1914
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‘‘inclusions’’ affect the structural properties of a material sometimes for the better and sometimes for the worse. Note that particle strengthening by intermetallic compound precipitation is a relatively new development in solders and has the potential to balance the difficulties associated with coarsening [10].
1.3. Experimental investigations on coarsening and intermetallic precipitation in bulk solder
Fig. 3. Coarsened AgCu microstructure and phase diagram [9].
in Fig. 3 (for AgCu). Note that the a and b-phases of different alloys normally have different crystal lattices. In fact Sn single crystals show hexagonal symmetry whereas Pb, Ag, and Cu are all of the cubic type. The same holds for the corresponding a and b-phases. This will be important during modeling of the coarsening effect since non-cubic lattices require embedded atom methods (EAM) to be used in order to obtain numerically reliable values for the so-called higher gradient coefficients (HGCs), which are surface energy related material characteristics. Moreover, in the bulk of certain solder materials intermetallic phases will form, which, depending upon aging, typically change their shape. Examples are silver or copper containing solders where in combination with tin, Ag3 Sn or Cu6 Sn5 precipitates arise. It is reported [4] that the intermetallic Ag3 Sn first forms as thin plates whereas Cu6 Sn5 precipitates as hollow rods. However, depending on aging and exposure to temperature the size and eventually the shape of these precipitates may change. From composite mechanics it is well known that
One of our first objectives [12] was to investigate the influence of cooling rate and type of specimen preparation on the resulting microstructure. These issues relate directly to microelectronics applications as indicated by the series of micrographs shown in Fig. 4. In a real microelectronic structure the exposure of the solder to temperature will not be uniform. Temperature gradients during reflow as well as during use will arise and lead to an inhomogeneous microstructural development, varying within a solder joint as well as within the whole array of joints belonging to a component. Note the different variations in crack length distributions observed for both types of solder, lead containing as well as lead free! Clearly, the speed and the impact of these processes on reliability will depend on the type of solder but, in general, they will always be present. During our experimental investigations solder paste was either processed in a crucible to obtain bulk-type specimens or directly applied to the surface of a copper block resulting in solder coatings of varying thickness. In the case of the latter type of preparation melting (and aging) was achieved either by means of a heating cartridge or directly in a muffle furnace. The resulting microstructures were investigated using optical microscopy immediately after solidification. Further experiments were carried out to study the temporal development of microstructures under welldefined aging conditions. For this purpose various layers of solder deposited on a copper block or bulk specimens of solder were subjected to accelerated aging by heating and keeping it at a relatively high temperature (>80% of the homologous temperature) for a certain time. The microstructures were then inspected using optical microscopy as well as atomic force microscopy and SEM. Fig. 5 shows the microstructure resulting from various cooling rates of bulk-type specimens made of eutectic tin–lead produced in the crucible. The findings can be summarized as follows: (a) Air cooling results in the formation of: • Pb-rich dendrites; • dark Pb-rich b-phase; • light tin-rich a-phase.
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00
Fig. 4. Ball microstructure resulting from accelerated aging tests TCT )40/+125, 300 /10 /300 ; flex CSP; 1000 cycles, outermost row for top: SnPb37; bottom: SnAg3.8Cu0.7 [11].
(b) Profile II (medium cooling rate) leads to: • formation of dendrites; • globular structures. (c) Profile I (low cooling rate) leads to: • fine globular structures.
Fig. 5. Microstructure of eutectic SnPb bulk specimens produced in the crucible, left: air-cooled, right: water-quenched.
(b) Quenching in water results in the formation of : • dark Pb-rich b-phase; • light tin-rich a-phase; • fine globular structures. Moreover, it should be noted that the textbook-type eutectic lamellae structure was not observed during these experiments. Fig. 6 shows the microstructures of various copper block SnPb solder coatings obtained using three different cooling profiles. In summary: (a) Profile I (high cooling rate) leads to: • globular structures.
As in the previous experiments lamellae formation was not observed. Finally, the first micrograph of Fig. 7 shows eutectic lamellae that resulted after extremely slow cooling (>24 h). This was achieved by switching off the heating of the muffle furnace containing a copper block to which an ample amount of solder paste had been added. After first solidification the specimen was aged at 170 C and examined at regular time intervals. This extremely high temperature was chosen to demonstrate microstructural change in a relatively short time. The resulting coarsening of the lamellae is illustrated by the other photos shown in Fig. 7. Moreover, an SEM analysis was performed in order to reveal the substructure of the lamellae (Fig. 8). Analogous experiments were then performed using eutectic SnAg. In Fig. 9 the influence of different ways of cooling on the microstructure of SnAg bulk specimens can be assessed. Our findings were as follows:
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Fig. 6. Microstructure of eutectic SnPb coatings obtained using different cooling rates.
Fig. 7. Optical micrographs showing aging of a eutectic SnPb lamella structure at 170 C.
(a) Air cooling results in the formation of: • Sn-rich dendrites; • light/gray tin–silver substructure. (b) Quenching in water results in: • light/gray tin–silver substructure. ‘‘Needles’’ and ‘‘spheres’’ consisting of intermetallic phase (Ag3 Sn) could not clearly be discerned during
Fig. 8. SEM scans of SnPb lamellae (top row) and lamellae substructures (bottom row) as a function of aging time.
these experiments. However, after coating the copper block with a thin layer of eutectic SnAg paste followed by melting and solidification needle-like structures were observed which are shown in the first SEM micrograph of Fig. 10.
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Fig. 9. Microstructure of eutectic SnAg bulk specimens produced in the crucible, left: air-cooled, right: water-quenched.
The specimen was then aged at 180 C for several hours during which the shape of the precipitates turned more and more spheroidal (see the last three micrographs in Fig. 10). In order to obtain a better resolution of the microstructure further optical scans of specimens were performed. These were prepared using a special etching technique ([13], Fig. 11). 1.4. Solder–interface interactions So far we have reported on microstructural changes in ‘‘bulk solders’’ exclusively, i.e., only the chemical species of the solder material itself were involved. However, in a real application the chemical elements within a solder ball will react with the chemicals of their immediate surroundings. Solder balls are typically placed on copper pads. Copper, however, oxidizes in air and, therefore, needs to be protected in order to guarantee that the chemical reaction leading to the mechanical bond, i.e., the formation of the intermetallic phases (e.g., Cu6 Sn5 or Cu3 Sn [14]), can still take place. For this purpose protective layers are added to cover the copper surface. A typical example are organic solderability preservatives (OSPs) [15], which vaporize during first reflow of the ball, so that Cu6 Sn5 , forms in a characteristic scallop-like shape and ripens to build relatively thick intermetallic layers (Fig. 12). Another option are electroless nickel/immersion gold (ENIG), Ni/ Au, finishes [15]. During first reflow the gold will dissolve in the tin containing solder ball. This allows the
Fig. 10. Aging of eutectic SnAg: Formation of intermetallic needles and spheres.
formation of an intermetallic layer made of Ni3 Sn4 . However, during second reflow the dissolved gold may
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2. Micromorphological change in solders––theory 2.1. Spinodal decomposition and coarsening in bulk solder
Fig. 11. Optical micrographs of eutectic SnAg, specially etched, before and after aging (180 C, 2 h).
In several recent papers (see [17–19] and the literature cited therein) an extended diffusion equation of the Cahn–Hilliard-type was presented and evaluated, which can be used for a quantitative description of spinodal decomposition and coarsening in binary alloys: q0
oc oJi þ ¼0 ot oXi
ð1Þ
containing an (extended) diffusion flux, Ji as follows: Ji ¼ q0 Mij T
Fig. 12. Scallop morphology of Cu–Sn intermetallics: (a) SnPb/ Cu at 200 C, 10 min; (b) SnBi/Cu at 160 C, 5 min; (c) SnAg/ Cu at 240 C, 5 min; (d) Sn/Cu at 250 C, 5 min [14].
promote the diffusion of copper from the adjacent pad toward this layer and substitute Ni to form compounds such as (Cu,Ni)6 Sn5 [16]. Such layers may affect the mechanical quality of a joint [15–17] in the following sense: intermetallic phases are relatively brittle but compared to the solder they are still very strong. However, because of the follow-up consequences of the reactions, such as stress increase, impurity accumulation, void formation and intermetallic spalling put the mechanical reliability severely at stake. In summary of this section we may say that it is imperative to quantify the microstructural change by means of suitable theories that combine diffusion, growth of precipitates, and locally acting stresses and strains. In turn, these models will require certain material parameters to be known. This will necessitate the development of suitable micromeasurement techniques. However, once a suitable alliance between theory and experiment has been formed allowing a quantitative assessment of the micro structural development for one type of solder through physically based understanding, a rationally based optimisation of this and other solders and of their macroscopic material properties can begin. In the next section we will report on the theoretical aspects of the modeling of micromorphological changes in solders.
oKc ; oXj
ð2Þ
where q0 is the (constant) total mass density of the alloy. c ¼ ~cðX ; tÞ denotes the mass concentration of one of the two species, e.g., of tin as a function of position, X , and of time, t. Mij is the mobility matrix, which can be expressed in terms of diffusion coefficients. Kc stands for a Lagrange multiplier which takes mass conservation into account: " 1 ow o ow c K ¼ T oc oXk oðoc=oXk Þ !# o2 ow : ð3Þ þ oXk oXs oðo2 c=oXk oXs Þ Moreover w is the Gibbs free energy density of the system. The last two equations can be combined to yield: owconf ðcÞ o2 c akl oc oXk oXl ! 1 o ekl ekl rkl ; þ 2 oc
Ji ¼ q0 Mij
o oXj
ð4Þ
where wconf ðcÞ is the configurational part of the Gibbs free energy and aij denotes the so-called higher gradient coefficients (HGCs), i.e., a matrix of quantities associated with surface tension, eij ; ekl and rij represent the total strains, the eigenstrains, and the Cauchy stress in the material. Eigenstrains comprise ‘‘non-elastic’’ strains. They are due to different thermal expansion of the two phases or differences in their lattice constants. Note that three driving forces of different nature contribute to the diffusion flux of Eq. (4) namely classical diffusion due to concentration gradients according to Fick, the effect of surface tensions according to Cahn– Hilliard (the underlined term) and the influence of local stresses and strains (the double-underlined term). It should be noted that the concentration in Eqs. (1) and (4) is sometimes referred to as a phase field. In phase field theories the quantity of interest varies continuously
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across an interface, which is in contrast to singular interface theories where physical quantities change abruptly at a material boundary. It should be pointed out that for describing the formation and morphological change of intermetallic phases, such as Ag3 Sn in the case of SnAg solder, the diffusion equation must be complemented by further relations. Intermetallic phases are ordered structures and modeling the process of the development of order requires an additional phase field, the so-called order parameter S. The temporal and spatial development of the order parameter is governed by an equation of the non-conserved or so-called Cahn–Allen-type: oS ¼ Ps ; ot
ð5Þ
with a production density, Ps , that is given by an equation similar to the one for the diffusion flux Eq. (4): Ps ¼ Ms
ow o2 S o 1 bkl ekl ekl rkl ; oS oXk oXl oS 2 ð6Þ
where Ms denotes a mobility parameter. Clearly, local changes of the concentrations and order parameters will also lead to local changes of the stresses and strains within a representative volume element (RVE) of the solder. Hence the question arises how this effect can be captured mathematically. The idea is that mechanical equilibrium is reached much faster than chemical equilibrium. Consequently, during the solution of Eqs. (1) and (4)–(6) by means of an appropriate Euler integration scheme it is sufficient to reevaluate the equations of elastostatics after each time step (cf. [18,32]). In this context the equations of equilibrium of forces, linear kinematic relations, and Hooke’s law are solved: orij 1 ouk oul þ ; rij ¼ Cijkl ekl ekl ; ¼ 0; ekl ¼ oXj 2 oXl oXk
Fig. 13. Square RVE (top) and its discretization (bottom) in 2D for N ¼ 8.
ð7Þ where ui denotes the displacements and Cijkl is the stiffness matrix which, for the time being, is assumed to be constant in space. For a suitable initial distribution of concentrations, to be prescribed within the RVE, the displacements uk can be computed in discrete points, based on a formalism suggested in [18]: We consider an array of N points, a, arranged equidistantly within a square shape RVE of dimension d and of side length 2pL (Fig. 13). Periodicity conditions are assumed to hold across the RVE and by mutual insertion of the equations shown in (7) and application of discrete Fourier transforms (DFT) the following formal solution is obtained in discrete Fourier space:
b ijkl ðsÞ^e ðsÞ þ ^e0 ðsÞ; ^eij ðsÞ ¼ A kl ij b ijkl ¼ A
0; 1 ðni Njs 2D
þ nj Nis ÞCsrkl nr ;
ð8Þ s¼0 s 6¼ 00
s being the discrete position vector. The symbols Njs and D are cumbersome but known functions of the stiffness, Cijkl , and of the Fourier transforms of difference quotients, ni , which were used for an approximate solution of the extended Lame–Navier system of PDEs that follows from Eqs. (7) (see [18] for details). Note that loading can be imposed from outside by prescribing suitable mean averages for the strains across
W.H. M€uller / Microelectronics Reliability 44 (2004) 1901–1914
the RVE, e0ij . These result and can be calculated from the global thermal mismatch of the microelectronic structure. Typically the various phases and intermetallic compounds have different stiffnesses. Consequently the stiffness varies in space as follows: Cijkl ðX ; tÞ ¼
a hðX ; tÞCijkl
þ ð1
b hðX ; tÞÞCijkl :
ð9Þ
b a In this equation Cijkl , and Cijkl , denote the constant elements of the stiffness matrix of the a and of the b-phase and hðX ; tÞ is the so-called shape function for which we can write: cb cðX ; tÞ 0 if X 2 b ; ð10Þ ) hðX ; tÞ ¼ hðx; tÞ ¼ 1 if X 2 a cb ca
ca and cb being the equilibrium concentrations of the a and of the b-phase, respectively, which, for different temperatures, can be read off from phase diagrams (see, e.g., Fig. 3). DFT techniques have also been used before to solve phase field Equation such as ((1),(4)–(6)). Particularly noteworthy is the work of the school headed by Khachaturyan (see, e.g., [20–22]) and the Japanese group of Miyazaki and co-workers (see, e.g., [23–25]). Their studies cover many alloy systems of technical importance, however, they do not address solders. As far as the stress–strain analysis of heterogeneous materials by means of DFT is concerned, the work of the French group of Suquet and coauthors is of great importance: [26–28]. More recently, a Dutch group [29] has used finite element techniques for solving extended diffusion equations that describe microstructural evolution in solders. They also used LSW-theory to describe the coarsening process [30], which, in an extended form, is also capable of describing the growth of intermetallic layers. In any case the modeling requires several material parameters to be quantitatively known. In what follows these will be discussed and examined for the special case of the SnPb system. 2.1.1. Gibbs free energy Following general practice, the Gibbs free energy densities of the two phases a=b of a binary system A=B are decomposed into three additive parts, first, a contribution accounting for the free energies of the pure components, gAa=b , gBa=b , second, a logarithmic part due to the entropy of mixture and, third, the heat of mixture term acknowledging the fact that the mixture is nonideal:
The choice of variables follows the convention employed by MTData [31], i.e., the Gibbs free energy shown in Eq. (11) is written in units of J/mol as a function of particle concentration, y. The coefficients gAa=b , gBa=b , and la=b A;B depend on absolute temperature, T :
i 2 fa; bg; j 2 fSn; Pbg;
¼
þ ð1 þ RT ½y lnðyÞ þ ð1 yÞ lnð1 yÞ þ yð1 yÞlaA;B :
The coefficients essentially stem from calorimetric experiments and, for SnPb, are compiled in [32]. Note that the diffusion equation (1/4) was originally derived in terms of mass concentrations, c, and not in particle concentrations, y. Therefore we rewrite the Gibbs free energy densities by using the following relation: y ¼ ~y ðcÞ ¼
M Sn
M Pb c : cðM Sn M Pb Þ
ð13Þ
Moreover, note that the free energy density of MTData is in J/mol. However, the one used in Eq. (11) is written in J/m3 instead. A conversion becomes possie ðcÞ, ble by using an average molecular weight, M ¼ M which changes as a function of concentration: e ðcÞ ¼ M¼M
M Sn
M Sn ¼ 118:69;
M Pb M Sn ; cðM Sn M Pb Þ
M Pb ¼ 207:19:
ð14Þ
By combination of these equations, an experimentally based specific free energy, w, is finally obtained, which, after multiplication by the macroscopic density of the eutectic alloy, was used for numerical evaluation of the extended diffusion equation shown in Eqs. (1) and (4) (see [31] for details). The result is shown in Fig. 14, for two different temperatures, 20 and 125 C, respectively. The figure also shows the common tangent construction (Maxwell lines) that defines the two equilibrium concentrations ca and cb mentioned before. It also contains the spinodal points that form the boundary of the non-convex unstable region of concentrations. 2.1.2. Diffusion constants In [18] it was assumed that the symmetry of a phase is determined by the symmetry of the dominant constituent. In other words, the a-phase was assumed as cubic (as in lead) and the b-phase as tetragonal (as in tin). We therefore write (provided the axes of the crystal and of the laboratory frame coincide):
Mija ¼ M a dij ; ð11Þ
liA;B
ð12Þ
0
yÞgBa=b
Fji ; T ¼ Ai þ Bi T ; i 2 fa; bg:
gji ¼ Aij þ Bij T þ Cji T lnðT Þ þ Dij T 2 þ Eji T 3 þ
ga=b ¼ g~a=b ðyÞ ygAa=b
1909
Mijb
M1b @ ¼ 0 0
0 M1b 0
1 0 0 A: M3b
ð15Þ
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W.H. M€uller / Microelectronics Reliability 44 (2004) 1901–1914
0
aakl ¼ aa dij ; a¼
aa ¼ 1:5 a;
2cDx ðcb
1 a 0 0 B C abkl ¼ @ 0 a 0 A; 0 0 14a
c a Þ2
;
c ¼ 1:5
J ; m2
Dx ¼ 25 nm: ð17Þ
More refined atomistic arguments were used in [38] to link these coefficients to the interatomic potentials between two element species A and B. For cubic materials it is sufficient to use potentials that only depend upon the radial distance Dab between two atoms a, b at positions Xib , Xia and not on their angular position: aukl ¼
1 X ab 2 ðD Þ uðDab ÞNk Nl ; 2 b
1 X ab 2 Dab ~ ðDab ÞNk Nl ; Ni ¼ iab ; ðD Þ u 2 b D 2 2 oy 1 o y u~ akl ¼ aukl þ ða 2yaukl Þ; oc 2 oc2 kl 1 b a ~ ðDab Þ ¼ ðuBB ðDab Þ uAA ðDab ÞÞ; Dab u i ¼ Xi Xi ; 2 1 ab ab uðD Þ ¼ uAB ðD Þ ðuAA ðDab Þ þ uBB ðDab ÞÞ: 2 ð18Þ aukl~ ¼
Fig. 14. Gibbs free energies at two temperatures. b In these equations M a and M1;3 denote the mobilities of tin atoms in a lead dominated lattice and of lead atoms in a tin dominated crystal, respectively:
The interatomic potentials, uAA=BB=AB ðDab Þ are typically assumed to be of the Lennard–Jones type: uAA=BB=AB ðDab Þ ¼
125C :
M a jca ¼ 2:42 1027
m5 ; Js
M1b jcb ¼ M3b jcb ¼ 4:52 1024 20C :
M a jca ¼ 1:27 1032
m5 ; Js
m5 ; Js
M1b jcb ¼ M3b jcb ¼ 1:11 1027
ð16Þ
m5 : Js
This data is based on diffusion coefficients for tin or lead being a tracer element in pure lead and tin, respectively [33]. Clearly, the diffusion coefficient for the a-phase is much smaller than the one for the b-phase and can be neglected in the quantitative simulations (see [31] for further details).
2.1.3. Higher gradient coefficients (HGCs) Following the original work of Cahn–Hilliard a simplified 2D study of the atomic potentials and lattice configurations revealed strong anisotropy [18]:
AAA=BB=AB ab 12
ðD Þ
BAA=BB=AB ðDab Þ6
:
ð19Þ
The constants AAA=BB=AB and BAA=BB=AB can be determined using the compressibilities of the pure substances, their sublimation energies, and characteristics of the mixture, e.g., Young’s modulus and Poisson’s ratio and the heat of mixing (see [38] for details). Tin, however, crystallizes in a tetragonal lattice and, consequently, SnPb requires a more complex approach, e.g., the use of EAM. The situation is even more cumbersome for the multicomponent lead free solders mentioned above. In order to describe their microstructural evolution multi-component phase field theories are required which lead to many more frequently unknown material parameters. Clearly, this will also require more complex numerical discretization schemes to be used, all of which presents challenging problems for the future. 2.1.4. Eigenstrains The eigenstrains in SnPb [32,33], which are incoherent in nature, are completely related to differences between the thermal expansion coefficients:
W.H. M€uller / Microelectronics Reliability 44 (2004) 1901–1914
ekl ¼ ~akl ðX ; tÞ DT ; DT ¼ ðT TR Þ; ~ ; tÞaa þ ð1 ~hðX ; tÞÞab ; akl ¼ hðX kl kl 0 b 1 a1 0 0 B C aaij ¼ aa dij ; abij ¼ @ 0 ab1 0 A; 0
ð22Þ
ð20Þ 3. Results
ab3
1
a
6
a ¼ 28:9 10
K ;
ab1
6
K1 ;
¼ 16:7 10
0
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Z cX2 Dc0 qAXmðtÞ 3 rðxÞ ¼ þ dt: 3NA LRT 4pmNp ðtÞ
1911
ab3 ¼ 36:4 106 K1 :
2.1.5. Stiffnesses Mechanical stiffnesses are readily and accurately available. We note that [18,32]: a ¼ 49:66 GPa; C11
a C12 ¼ 42:31 GPa;
a ¼ 14:98 GPa; C44
b C11 ¼ 75:29 GPa;
b C12 b C33 b C66
¼ 61:56 GPa;
b C13 ¼ 44:00 GPa;
¼ 95:52 GPa;
b C44 ¼ 21:93 GPa;
ð21Þ
¼ 23:36 GPa:
2.2. Growth of inter metallic phases The mathematical description of the growth of scallop shape intermetallic layers has been the focus of a series of papers by Tu and coworkers (e.g., [34,35]). The development of these layers is characterized by coupling two distinct processes, first, ripening growth between Cu6 Sn5 grains controlled by volume diffusion (‘‘survival of the fattest’’) and, second, interfacial reaction growth. Their equation for ripening is based on the Gibbs– Thomson effect and essentially an application of the so-called LSW-theory. However, in contrast to the traditional formalism the ripening between the Cu6 Sn5 grains does not occur at a constant volume. Rather there is a supply of grain material due to the interfacial reactions between the solder alloy and the copper. By balancing the interfacial reaction and adding the corresponding flux due to LSW-ripening Tu et al. finally arrive at the following equation for the growth of the mean radius of Cu6 Sn5 grains (c denotes the interfacial energy per unit area between the Cu6 Sn5 grains and the molten solder, X is the molar volume of Cu6 Sn5 , D is the diffusivity of Cu in the molten solder, c0 is the equilibrium concentration of Cu in the solder, NA is Avogadro’s constant, L is a dimensionless parameter indicating the fraction of the mean separation between grains and the mean grain radius, R is the gas constant, T is absolute temperature, q is the density of Cu, mðtÞ is the reaction rate, i.e., the rate at which the height of the copper substrate diminishes, m is the atomic mass of Cu, and Np ðtÞ stands for the total number of grains at the interface):
In the following simulations an inclination of 25 between the crystallographic and the laboratory system was assumed. The width and height of the RVE is 2pL ¼ 1 lm. Fig. 15 presents the microstructural development at a low and a high temperature (20 and 125 C) starting from a homogeneous mix of eutectic SnPb with a few slight fluctuations. It is important to note that the mobilities at these two temperatures are very different which explains that the time scales of both coarsening processes differ by an order of magnitude. This is in qualitative agreement with the experimental findings shown in Fig. 2. The lack of quantitative agreement can be explained by the fact that the mobilities stem from tracer experiments and, therefore, do not perfectly represent the actual situation. In the sequence of pictures of Fig. 16 the influence of tensile stress on microstructural development is investigated. From our simulations we may say that both uniaxial tensions in horizontal as well as in vertical direction clearly lead to enhanced coarsening behavior.
Fig. 15. Microstructural development of eutectic SnPb-low temperature (first two rows) vs. high temperature (last two rows).
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Fig. 16. High temperature development, external load of +5 MPa in horizontal direction.
Consequently, such a state of stress may be considered to contribute to the pronounced coarsening occurring in the interface regions of solder balls (cf., Fig. 1). Further studies [36] have revealed that equal tensile loads lead to hardly any coarsening at all. From these simulations it can be claimed that the effects of two tensile loads of equal size on the microstructure seem to annihilate each other although, during the development, some differences to the corresponding structures without external loads can be observed. Clearly, the state of stress in real solder balls is threedimensional in nature but it can be anticipated that the principal stresses are not all equal. Furthermore we may say that the microstructures resulting under compressive stress are essentially similar to their tensile counterparts, tensile stresses leading to slightly stronger coarsening. Finally, shear stresses that are sufficiently high, i.e., of the same magnitude (5 MPa) as the tensile and compressive counterparts, can have a dramatic influence on the resulting microstucture. Reducing the shear by more than 50% still leads to a noticeable effect during the development phase (see [36] for details). The sequence of Fig. 17 provides evidence that there is potential for ‘‘healing’’ of a coarsened microstructure.
Fig. 17. ‘‘Healing’’ of a microstructure initially coarsened by external stress by switching to low temperature 125 C fi 20 C.
Fig. 18. Mean grain radius of Cu6 Sn5 of grains as a function of re-scaled time, adapted from [34] (eutectic SnPb on Cu substrate for (a) L ¼ 0:15 and (b) c0 ¼ 0:3, see text for details).
In this simulation we used a stressed microstructure showing a particularly strong coarsening similar to the last picture of Fig. 16 as initial condition to further simulations of the microstructural development. More specifically we ‘‘switched’’ from high to low temperature and also ‘‘removed’’ the external stress. Clearly, it is an advantage of computer simulations that the impact of each driving force and material parameter can be studied separately and most conveniently by altering the input to the computer program. 2 Due to the fact that both equilibrium concentrations and phase volume fractions depend on temperature, diffusion sets in and this obviously has a soothing effect on the microstructure. Examples for simulations of microstructural change in alloys showing diffusion and transitions to a different state of order have been presented in [37] (e.g., rafting in NiAl superalloys and development of lenticular shaped tetragonal phase in PSZ ceramics). However, this strategy had not been applied to a study of the growth and coarsening of Ag3 Sn intermetallics in AgSn solder yet.
2 In this context it should also be mentioned that the computer simulations show that the thermal mismatch between the two phases does not have a significant impact on the coarsening behavior, at least in the case of the SnPb system.
W.H. M€uller / Microelectronics Reliability 44 (2004) 1901–1914
After providing an extreme wealth of materials data Kim and Tu successfully managed in [34] to predict the growth of the mean size of Cu6 Sn5 grains for eutectic SnPb on Cu substrates. They also compared their predictions with own measurements. Some of their results are shown in Fig. 18.
4. Conclusions We have shown that it is nowadays possible to simulate the microstructural development and change observed in microelectronic solders as well as the growth of intermetallic phases. The mathematical tools used for this purpose are phase field models and LSW-theory. A general outline of these theories was given together with references from which further details can be obtained. We conclude that these theories stand and fall with the various material parameters they require during their quantitative evaluation. Ideally these material parameters should stem from experiments that are independent of the theoretical model. For eutectic SnPb it was possible to obtain all the required parameters in this manner mainly because SnPb is a well characterized solder that has been in use and investigated for decades. Several numerical simulations of microstructural evolution were shown that can be compared to experimentally determined ones. These simulations allow to study which of the various material parameters involved have a particularly crucial influence on coarsening and aging. In particular the influence of mechanical stress could be assessed quantitatively for the first time. However, it is fair to say that even in the case of SnPb some material parameters proved to be very difficult to obtain and are still only inaccurately known. In particular this is the case for the so-called higher gradient coefficients. For that reason an atomistic interpretation was provided that allows to calculate these parameters from atomic pair potentials which, in turn, can be determined from the crystal lattice structure of the solder crystallites and some macroscopic material properties.
References [1] Scheel, W. Baugruppentechnologie der Elektronik, vol. 2. Berlin: 2. Auflage, Verlag Technik; 1999. [2] Frear D, Morgan H, Burchett S. The mechanics of solder alloy interconnects. New York: Van Nostrand Reinhold; 1993. [3] Darveaux R, Banerji K. Constitutive relations for tinbased solder joints. IEEE Trans Comp, Hybrids, Manuf Technol 1992;15(6):1013–24. [4] Abtew M, Selvaduray G. Lead-free solders in microelectronics. Mater Sci Eng 2000;27:95–141.
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[5] Lee N-C. Getting ready for lead-free solders. Solder Surf Mount Technol 1997;26:65–9. [6] Nylen, M, Hutchinson B, Gustavsson U. Microstructural degradation of solder. In: Proceedings of micro materials, Micro Mat ’97, Berlin. 1997. p. 890–5. [7] Harris PG, Chaggar KS, Whitmore MA. The effect of ageing on the microstructure of 60:40 tin–lead solders. Solder Surf Mount Technol 1991;7:20–3. [8] Tanaka Y, Udoh KI, Hisatsune K, Yasuda K. Spinodal ordering in the equiatomic AuCu alloy. Phil Mag A 1994;69(5):925–38. [9] http://www.metallurgy.nist.gov/phase/solder/agcu.html. [10] Yassin A, Reuben RL, Saad G, Beshai MHN, Habib SK. Effect of annealing and microstructure on the creep behaviour of an Sn–10 wt% Sb alloy. In: Proceedings of the institution of mechanical engineers, vol. 213 Part L. 1999. p. 59–68. [11] Albrecht H-J, Brodie DS, Gunn AJ, M€ uller WH, Reuben RL. A study of microstructural change of lead-containing and lead free solders. J SMT 2002;15(2):30–9. [12] Brodie DS. Experimental Investigation of Lamellae Formation and Coarsening in Eutecric Solders. Final Year Project B.E. Thesis. 2001. [13] Handing C. Mikromechanische Untersuchungen zur Zuverl€assigkeit elektronischer Bauteile und deren Materialien. Diploma Thesis. Universit€at Paderborn. 2001. [14] Kim HK, Tu KN. Kinetic analysis of the soldering reaction between eutectic SnPb alloy and Cu accompanied by ripening. Phys Rev B 1996;53(23):16027–34. [15] Winlow A., Surface Finishing, ppt-presentation. Available from: www.twi.co.uk/i32k/getFil/6febQ3 aw6.pdf. [16] Kang SK, Shih DY, Fogel K, Lauro P, Yim MJ, Advocate G, et al. Interfacial reaction studies on lead (Pb)-free solder alloys. In: Proceedings of the electronic components and technology conference (ECTC), 2001, IEEE 51th, Orlando. p. 448–54. [17] Lee KY, Li M, Olsen DR, Chen WT. Microstructure, joint strength and failure mechanism of Sn–Ag, Sn–Ag–Cu versus Sn–Pb–Ag solders in BGA packages. In: Proceedings of the electronic components and technology conference (ECTC) 2001, IEEE 51th, Orlando. p. 478–85. [18] Dreyer W, M€ uller WH. A study of the coarsening in tin/ lead solders. Int J Sol Struct 2000;37(28):3841–71. [19] Dreyer W, M€ uller WH. Modeling diffusional coarsening in microelectronic solders. In: Proceedings of fifth annual pan pacific microelectronics symposium, Kauai, 2001. p. 495– 504. [20] Khachaturyan AG, Semenovskaya S, Tsakalakos T. Elastic strain energy of in homogeneous solids. Phys Rev B 1995;52(22):15909–19. [21] Li DY, Chen LQ. Computer simulation of morphological evolution and rafting of particles in Ni-based superalloys under applied stress. Scr Mater 1997;37(9):1271–7. [22] McCormack M, Khachaturyan AG, Morris Jr JW. A two-dimensional analysis of the evolution of coherent precipitates in elastic media. Acta Metall Mater 1992;40(2): 325–36. [23] Miyazaki T, Koyama T. Theoretical analysis of phase decomposition in real alloy systems based on the nonlinear diffusion equation. Mater Trans JIM 1996;37(4): 684–90.
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[24] Miyazaki T, Takeuchi A, Koyama T, Kozakai T. Computer simulation of phase decomposition in the regular solid solution based upon the Chan–Hilliard’s non-linear diffusion equation. Mater Trans JIM 1991;32(10):915–20. [25] Koyama T, Miyazaki T, Doi M, Mebed AE-AM, Moriya T. Computer simulation of phase decomposition in Fe–Mo alloy based on discrete type diffusion equation. J Japan Inst Met 1996;60(6):560–8. [26] Suquet P. Une methode simplifiee pour le calcul de proprietes elastiques de materiaux heterogenes a structure periodique. CR Acad Sci Paris 1990;311(II):769–74. [27] Moulinec H, Suquet P. A fast numerical method for computing the linear and nonlinear mechanical properties of composites. C R Acad Sci Paris 1994;318(II):1417–23. [28] Moulinec H, Suquet P. A numerical method for computing the overall response of nonlinear composites with complex microstructure. Comput Meth Appl Mech Eng 1998; 157(1–2):69–94. [29] Ubachs RLJM, Schreurs PJG, Geers MGD. Microstucture evolution of tin–lead solder. Thermal and mechanical simulation of experiments in microelectronics and microsystems. In: Ernst LJ, Zhang GQ, Dudek R, de Saint Leger O, editors. Proceedings of the A SIME 2003. p. 103–9. [30] Matin MA, Vellinga WP, Geers MGD. Quantitative microscopy of microstructural evolution in eutectic solders subjected to static thermal load. Thermal and mechanical simulation of experiments in microelectronics and microsystems. In: Ernst LJ, Zhang GQ, Dudek R, de Saint Leger O, editors. Proceedings ASIME 2003. p. 111–6.
[31] MTData, NPL Databank for Materials Thermochemistry. National Physical Laboratory, Queens Road, Teddington, Middlesex, TW11 OLW. 1998. [32] Dreyer W, M€ uller WH. Modeling diffusional coarsening in eutectic tin/lead solders: a quantitative approach. Int J Sol Struct 2001;38(8):1433–58. [33] Ghosh G, Liu ZK. Modeling the atomic transport kinetics in high-lead solders. J Electr Mater 1998;27(12):1362–6. [34] Kirn HK, Liou HK, Tu KN. Three-dimensional morphology of a very rough interface formed in the soldering reaction between eutectic SnPb and Cu. Appl Phys Lett 1995;66(18):2337–9. [35] Tu KN, Zeng K. Tin–lead (SnPb) solder reaction in flip chip technology. Mater Sci Eng 2001;R34:1–58. [36] Brodie DS, Gunn AJ, M€ uller WH, Reuben RL. Toward a better understanding of morphology changes in solders using phase field theories: quantitative modeling and experimental verification. In: Proceedings of the 4th electronics packaging technology conference (EPTC2002), Singapore, 2002. p. 404–9. [37] Dreyer W, M€ uller WH. Computer modeling of micromorphological change by phase field models: applications to metals and ceramics. J Aust Ceram Soc 2000;36(1):83– 94. [38] Dreyer W, M€ uller WH. Toward quantitative modeling of morphology changes in solids with phase field models: atomistic arguments for the determination of higher gradient coefficients. Key Eng Mater 2003;240–242:901– 14.
Morphology changes in solder joints––experimental evidence and physical understanding W.H. M€ uller
*
Institut f€ur Mechanik, LKM, Technische Universit€at Berlin, Einsteinufer 5, Berlin 10587, Germany Received 6 October 2003; received in revised form 14 January 2004 Available online 8 July 2004
Abstract The microstructures of solders in microelectronic components, lead containing as well as lead free, change over time. This is first of all due to comparatively high homologous temperatures which occur during reflow as well as during operation of the component. Moreover, because of the intrinsic thermal mismatch between the various materials that constitute the package substantial mechanical stresses and strains will arise and assist the process of microstructural change. In this paper we will, first, briefly provide experimental evidence for such microstructural change and how it relates to the solder bulk as well as to the various interfaces and passivation materials that are used when a solder joint is formed. Second, we will review state-of-the-art modeling techniques that allow to simulate such changes of microstructure provided certain material parameters are known. For this purpose we will set up all equations and then provide information on all the material parameters required for a numerical solution. We will present computer simulations based on this theoretical framework and study the influence of the material parameters on coarsening and aging and, in particular, examine the impact of mechanical stresses and strains. Finally we will address difficulties and challenges involved, experimental as well as modeling ones. 2004 Elsevier Ltd. All rights reserved.
1. Microstructural change in solders––experimental evidence 1.1. Typical SMT solder materials Tin is the element that eventually leads to the electromechanical connection with the copper pads used in surface mount technology (SMT) microelectronics technology. This is achieved by a chemical reaction during which the tin and the copper react by diffusion to form an intermetallic compound, Cu6 Sn5 ([1], p. 180). Unfortunately the melting point of tin is too high for microelectronic manufacturing (Tmelt ¼ 231:93 C) and, therefore, further elements are added to the tin so that a tin-based solder alloy with a lower melting point results.
*
Tel.: +49-30-314-27682; fax: +49-30-314-24499. E-mail address: [email protected] (W.H. M€ uller).
Originally this addend was lead, which is inexpensive and readily available. Typically binary eutectic tin–lead (SnPb38.1, 1 Tmelt ¼ 183 C) or slightly hyper- or hypoeutectic variants thereof were used. In general, the fact that an alloy is eutectic guarantees that it has a unique melting point whereas hyper- or hypoeutectic alloys show a melting range which, in microelectronics, is kept as narrow as possible for obvious processing reasons. Lead containing ternaries were also used, the most prominent example being hypereutecric Sn62Pb36Ag2. The silver is added to prevent dissolution from component terminations ([1], p. 221, [3]). Due to environmental restrictions lead is about to be completely banned from the microelectronic industry [4,5]. This requires alternative binary solders to be used, such as eutectic
1
Due to inevitable inaccuracies during calorimetric measurements eutectic tin–lead is often also referred to as Sn37.1Pb or (roughly) as Sn37Pb [2].
0026-2714/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.microrel.2004.04.020
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tin–silver and tin–copper, SnAg3.5 or SnCu0.7, showing melting points of 221 and 227 C, respectively. However, terneries (e.g., near eutectic SnAgCu) or even quartenary and higher systems (e.g., SnAgBiCu, SnInAgSb) are also considered the reason being an ongoing quest for finding readily available and affordable interconnection materials with a suitable melting point and electromechanical characteristics that are just as good or better than traditional tin–lead. Moreover, thermal mismatch between the various materials involved in microelectronic structures is almost inevitable even though serious attempts are made to keep it as small as possible. This mismatch in combination with comparatively high operating temperatures, i.e., high homologous temperatures may lead to a change of the solder micromorphology and hence joining capability. This issue will be discussed in the next two subsections. 1.2. The solder bulk As a first example of micromorphological change in solders consider Fig. 1 which shows a cross-section
Fig. 1. Cross-sectional cut through the solder joints of a ball grid array (BGA) [6].
through a BGA solder ball [6], made of eutectic tin–lead, before and after it has been subjected to several thousand thermal cycles during which it was exposed to homologous temperatures of 0.8 and more. The regions of different shades of gray and black indicate that after starting out as a fine mix between tin and lead ‘‘islands’’ of high Pb concentration keep growing in a ‘‘sea’’ of high Sn concentration. These two regions are known as a and b-phases, respectively. This micromorphological change is a result of a diffusion process of the elements, also known as spinodal decomposition, followed by coarsening through phase separation. It should be emphasized that phase separation can be accelerated considerably if the homologous temperatures are high and mechanical stresses are present. The first statement is supported by the experiments shown in Fig. 2 [7], and the latter one by the right micrograph in Fig. 1. Obviously coarsening is particularly high in the interface regions of the solder ball where, due to edge effects, the stresses are most pronounced. Clearly, once the microstructure, i.e., the local mechanical properties change over time the overall material properties of the ball will also change, which, eventually, can have a detrimental effect on its joining capability. It should be pointed out that changes in microstructure due to spinodal decomposition are by no means limited to tin–lead. Rather it has also been observed in lead free solders, e.g., in the brazing alloy AgCu [8]. The micrograph in Fig. 3 shows copper rich and silver rich phases regions. As in the case of tin–lead the corresponding equilibrium concentrations depend on temperature. In fact the phase diagrams of both alloys are very similar showing the characteristic V-shape depicted
Fig. 2. Coarsening in SnPb, 1st row 20 C (a) 2 h, (b) 17 d, (c) 63 d; 2nd row: 125 C (a) initially, (b) 3 h (c) 300 h [7].
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‘‘inclusions’’ affect the structural properties of a material sometimes for the better and sometimes for the worse. Note that particle strengthening by intermetallic compound precipitation is a relatively new development in solders and has the potential to balance the difficulties associated with coarsening [10].
1.3. Experimental investigations on coarsening and intermetallic precipitation in bulk solder
Fig. 3. Coarsened AgCu microstructure and phase diagram [9].
in Fig. 3 (for AgCu). Note that the a and b-phases of different alloys normally have different crystal lattices. In fact Sn single crystals show hexagonal symmetry whereas Pb, Ag, and Cu are all of the cubic type. The same holds for the corresponding a and b-phases. This will be important during modeling of the coarsening effect since non-cubic lattices require embedded atom methods (EAM) to be used in order to obtain numerically reliable values for the so-called higher gradient coefficients (HGCs), which are surface energy related material characteristics. Moreover, in the bulk of certain solder materials intermetallic phases will form, which, depending upon aging, typically change their shape. Examples are silver or copper containing solders where in combination with tin, Ag3 Sn or Cu6 Sn5 precipitates arise. It is reported [4] that the intermetallic Ag3 Sn first forms as thin plates whereas Cu6 Sn5 precipitates as hollow rods. However, depending on aging and exposure to temperature the size and eventually the shape of these precipitates may change. From composite mechanics it is well known that
One of our first objectives [12] was to investigate the influence of cooling rate and type of specimen preparation on the resulting microstructure. These issues relate directly to microelectronics applications as indicated by the series of micrographs shown in Fig. 4. In a real microelectronic structure the exposure of the solder to temperature will not be uniform. Temperature gradients during reflow as well as during use will arise and lead to an inhomogeneous microstructural development, varying within a solder joint as well as within the whole array of joints belonging to a component. Note the different variations in crack length distributions observed for both types of solder, lead containing as well as lead free! Clearly, the speed and the impact of these processes on reliability will depend on the type of solder but, in general, they will always be present. During our experimental investigations solder paste was either processed in a crucible to obtain bulk-type specimens or directly applied to the surface of a copper block resulting in solder coatings of varying thickness. In the case of the latter type of preparation melting (and aging) was achieved either by means of a heating cartridge or directly in a muffle furnace. The resulting microstructures were investigated using optical microscopy immediately after solidification. Further experiments were carried out to study the temporal development of microstructures under welldefined aging conditions. For this purpose various layers of solder deposited on a copper block or bulk specimens of solder were subjected to accelerated aging by heating and keeping it at a relatively high temperature (>80% of the homologous temperature) for a certain time. The microstructures were then inspected using optical microscopy as well as atomic force microscopy and SEM. Fig. 5 shows the microstructure resulting from various cooling rates of bulk-type specimens made of eutectic tin–lead produced in the crucible. The findings can be summarized as follows: (a) Air cooling results in the formation of: • Pb-rich dendrites; • dark Pb-rich b-phase; • light tin-rich a-phase.
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00
Fig. 4. Ball microstructure resulting from accelerated aging tests TCT )40/+125, 300 /10 /300 ; flex CSP; 1000 cycles, outermost row for top: SnPb37; bottom: SnAg3.8Cu0.7 [11].
(b) Profile II (medium cooling rate) leads to: • formation of dendrites; • globular structures. (c) Profile I (low cooling rate) leads to: • fine globular structures.
Fig. 5. Microstructure of eutectic SnPb bulk specimens produced in the crucible, left: air-cooled, right: water-quenched.
(b) Quenching in water results in the formation of : • dark Pb-rich b-phase; • light tin-rich a-phase; • fine globular structures. Moreover, it should be noted that the textbook-type eutectic lamellae structure was not observed during these experiments. Fig. 6 shows the microstructures of various copper block SnPb solder coatings obtained using three different cooling profiles. In summary: (a) Profile I (high cooling rate) leads to: • globular structures.
As in the previous experiments lamellae formation was not observed. Finally, the first micrograph of Fig. 7 shows eutectic lamellae that resulted after extremely slow cooling (>24 h). This was achieved by switching off the heating of the muffle furnace containing a copper block to which an ample amount of solder paste had been added. After first solidification the specimen was aged at 170 C and examined at regular time intervals. This extremely high temperature was chosen to demonstrate microstructural change in a relatively short time. The resulting coarsening of the lamellae is illustrated by the other photos shown in Fig. 7. Moreover, an SEM analysis was performed in order to reveal the substructure of the lamellae (Fig. 8). Analogous experiments were then performed using eutectic SnAg. In Fig. 9 the influence of different ways of cooling on the microstructure of SnAg bulk specimens can be assessed. Our findings were as follows:
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Fig. 6. Microstructure of eutectic SnPb coatings obtained using different cooling rates.
Fig. 7. Optical micrographs showing aging of a eutectic SnPb lamella structure at 170 C.
(a) Air cooling results in the formation of: • Sn-rich dendrites; • light/gray tin–silver substructure. (b) Quenching in water results in: • light/gray tin–silver substructure. ‘‘Needles’’ and ‘‘spheres’’ consisting of intermetallic phase (Ag3 Sn) could not clearly be discerned during
Fig. 8. SEM scans of SnPb lamellae (top row) and lamellae substructures (bottom row) as a function of aging time.
these experiments. However, after coating the copper block with a thin layer of eutectic SnAg paste followed by melting and solidification needle-like structures were observed which are shown in the first SEM micrograph of Fig. 10.
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Fig. 9. Microstructure of eutectic SnAg bulk specimens produced in the crucible, left: air-cooled, right: water-quenched.
The specimen was then aged at 180 C for several hours during which the shape of the precipitates turned more and more spheroidal (see the last three micrographs in Fig. 10). In order to obtain a better resolution of the microstructure further optical scans of specimens were performed. These were prepared using a special etching technique ([13], Fig. 11). 1.4. Solder–interface interactions So far we have reported on microstructural changes in ‘‘bulk solders’’ exclusively, i.e., only the chemical species of the solder material itself were involved. However, in a real application the chemical elements within a solder ball will react with the chemicals of their immediate surroundings. Solder balls are typically placed on copper pads. Copper, however, oxidizes in air and, therefore, needs to be protected in order to guarantee that the chemical reaction leading to the mechanical bond, i.e., the formation of the intermetallic phases (e.g., Cu6 Sn5 or Cu3 Sn [14]), can still take place. For this purpose protective layers are added to cover the copper surface. A typical example are organic solderability preservatives (OSPs) [15], which vaporize during first reflow of the ball, so that Cu6 Sn5 , forms in a characteristic scallop-like shape and ripens to build relatively thick intermetallic layers (Fig. 12). Another option are electroless nickel/immersion gold (ENIG), Ni/ Au, finishes [15]. During first reflow the gold will dissolve in the tin containing solder ball. This allows the
Fig. 10. Aging of eutectic SnAg: Formation of intermetallic needles and spheres.
formation of an intermetallic layer made of Ni3 Sn4 . However, during second reflow the dissolved gold may
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2. Micromorphological change in solders––theory 2.1. Spinodal decomposition and coarsening in bulk solder
Fig. 11. Optical micrographs of eutectic SnAg, specially etched, before and after aging (180 C, 2 h).
In several recent papers (see [17–19] and the literature cited therein) an extended diffusion equation of the Cahn–Hilliard-type was presented and evaluated, which can be used for a quantitative description of spinodal decomposition and coarsening in binary alloys: q0
oc oJi þ ¼0 ot oXi
ð1Þ
containing an (extended) diffusion flux, Ji as follows: Ji ¼ q0 Mij T
Fig. 12. Scallop morphology of Cu–Sn intermetallics: (a) SnPb/ Cu at 200 C, 10 min; (b) SnBi/Cu at 160 C, 5 min; (c) SnAg/ Cu at 240 C, 5 min; (d) Sn/Cu at 250 C, 5 min [14].
promote the diffusion of copper from the adjacent pad toward this layer and substitute Ni to form compounds such as (Cu,Ni)6 Sn5 [16]. Such layers may affect the mechanical quality of a joint [15–17] in the following sense: intermetallic phases are relatively brittle but compared to the solder they are still very strong. However, because of the follow-up consequences of the reactions, such as stress increase, impurity accumulation, void formation and intermetallic spalling put the mechanical reliability severely at stake. In summary of this section we may say that it is imperative to quantify the microstructural change by means of suitable theories that combine diffusion, growth of precipitates, and locally acting stresses and strains. In turn, these models will require certain material parameters to be known. This will necessitate the development of suitable micromeasurement techniques. However, once a suitable alliance between theory and experiment has been formed allowing a quantitative assessment of the micro structural development for one type of solder through physically based understanding, a rationally based optimisation of this and other solders and of their macroscopic material properties can begin. In the next section we will report on the theoretical aspects of the modeling of micromorphological changes in solders.
oKc ; oXj
ð2Þ
where q0 is the (constant) total mass density of the alloy. c ¼ ~cðX ; tÞ denotes the mass concentration of one of the two species, e.g., of tin as a function of position, X , and of time, t. Mij is the mobility matrix, which can be expressed in terms of diffusion coefficients. Kc stands for a Lagrange multiplier which takes mass conservation into account: " 1 ow o ow c K ¼ T oc oXk oðoc=oXk Þ !# o2 ow : ð3Þ þ oXk oXs oðo2 c=oXk oXs Þ Moreover w is the Gibbs free energy density of the system. The last two equations can be combined to yield: owconf ðcÞ o2 c akl oc oXk oXl ! 1 o ekl ekl rkl ; þ 2 oc
Ji ¼ q0 Mij
o oXj
ð4Þ
where wconf ðcÞ is the configurational part of the Gibbs free energy and aij denotes the so-called higher gradient coefficients (HGCs), i.e., a matrix of quantities associated with surface tension, eij ; ekl and rij represent the total strains, the eigenstrains, and the Cauchy stress in the material. Eigenstrains comprise ‘‘non-elastic’’ strains. They are due to different thermal expansion of the two phases or differences in their lattice constants. Note that three driving forces of different nature contribute to the diffusion flux of Eq. (4) namely classical diffusion due to concentration gradients according to Fick, the effect of surface tensions according to Cahn– Hilliard (the underlined term) and the influence of local stresses and strains (the double-underlined term). It should be noted that the concentration in Eqs. (1) and (4) is sometimes referred to as a phase field. In phase field theories the quantity of interest varies continuously
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across an interface, which is in contrast to singular interface theories where physical quantities change abruptly at a material boundary. It should be pointed out that for describing the formation and morphological change of intermetallic phases, such as Ag3 Sn in the case of SnAg solder, the diffusion equation must be complemented by further relations. Intermetallic phases are ordered structures and modeling the process of the development of order requires an additional phase field, the so-called order parameter S. The temporal and spatial development of the order parameter is governed by an equation of the non-conserved or so-called Cahn–Allen-type: oS ¼ Ps ; ot
ð5Þ
with a production density, Ps , that is given by an equation similar to the one for the diffusion flux Eq. (4): Ps ¼ Ms
ow o2 S o 1 bkl ekl ekl rkl ; oS oXk oXl oS 2 ð6Þ
where Ms denotes a mobility parameter. Clearly, local changes of the concentrations and order parameters will also lead to local changes of the stresses and strains within a representative volume element (RVE) of the solder. Hence the question arises how this effect can be captured mathematically. The idea is that mechanical equilibrium is reached much faster than chemical equilibrium. Consequently, during the solution of Eqs. (1) and (4)–(6) by means of an appropriate Euler integration scheme it is sufficient to reevaluate the equations of elastostatics after each time step (cf. [18,32]). In this context the equations of equilibrium of forces, linear kinematic relations, and Hooke’s law are solved: orij 1 ouk oul þ ; rij ¼ Cijkl ekl ekl ; ¼ 0; ekl ¼ oXj 2 oXl oXk
Fig. 13. Square RVE (top) and its discretization (bottom) in 2D for N ¼ 8.
ð7Þ where ui denotes the displacements and Cijkl is the stiffness matrix which, for the time being, is assumed to be constant in space. For a suitable initial distribution of concentrations, to be prescribed within the RVE, the displacements uk can be computed in discrete points, based on a formalism suggested in [18]: We consider an array of N points, a, arranged equidistantly within a square shape RVE of dimension d and of side length 2pL (Fig. 13). Periodicity conditions are assumed to hold across the RVE and by mutual insertion of the equations shown in (7) and application of discrete Fourier transforms (DFT) the following formal solution is obtained in discrete Fourier space:
b ijkl ðsÞ^e ðsÞ þ ^e0 ðsÞ; ^eij ðsÞ ¼ A kl ij b ijkl ¼ A
0; 1 ðni Njs 2D
þ nj Nis ÞCsrkl nr ;
ð8Þ s¼0 s 6¼ 00
s being the discrete position vector. The symbols Njs and D are cumbersome but known functions of the stiffness, Cijkl , and of the Fourier transforms of difference quotients, ni , which were used for an approximate solution of the extended Lame–Navier system of PDEs that follows from Eqs. (7) (see [18] for details). Note that loading can be imposed from outside by prescribing suitable mean averages for the strains across
W.H. M€uller / Microelectronics Reliability 44 (2004) 1901–1914
the RVE, e0ij . These result and can be calculated from the global thermal mismatch of the microelectronic structure. Typically the various phases and intermetallic compounds have different stiffnesses. Consequently the stiffness varies in space as follows: Cijkl ðX ; tÞ ¼
a hðX ; tÞCijkl
þ ð1
b hðX ; tÞÞCijkl :
ð9Þ
b a In this equation Cijkl , and Cijkl , denote the constant elements of the stiffness matrix of the a and of the b-phase and hðX ; tÞ is the so-called shape function for which we can write: cb cðX ; tÞ 0 if X 2 b ; ð10Þ ) hðX ; tÞ ¼ hðx; tÞ ¼ 1 if X 2 a cb ca
ca and cb being the equilibrium concentrations of the a and of the b-phase, respectively, which, for different temperatures, can be read off from phase diagrams (see, e.g., Fig. 3). DFT techniques have also been used before to solve phase field Equation such as ((1),(4)–(6)). Particularly noteworthy is the work of the school headed by Khachaturyan (see, e.g., [20–22]) and the Japanese group of Miyazaki and co-workers (see, e.g., [23–25]). Their studies cover many alloy systems of technical importance, however, they do not address solders. As far as the stress–strain analysis of heterogeneous materials by means of DFT is concerned, the work of the French group of Suquet and coauthors is of great importance: [26–28]. More recently, a Dutch group [29] has used finite element techniques for solving extended diffusion equations that describe microstructural evolution in solders. They also used LSW-theory to describe the coarsening process [30], which, in an extended form, is also capable of describing the growth of intermetallic layers. In any case the modeling requires several material parameters to be quantitatively known. In what follows these will be discussed and examined for the special case of the SnPb system. 2.1.1. Gibbs free energy Following general practice, the Gibbs free energy densities of the two phases a=b of a binary system A=B are decomposed into three additive parts, first, a contribution accounting for the free energies of the pure components, gAa=b , gBa=b , second, a logarithmic part due to the entropy of mixture and, third, the heat of mixture term acknowledging the fact that the mixture is nonideal:
The choice of variables follows the convention employed by MTData [31], i.e., the Gibbs free energy shown in Eq. (11) is written in units of J/mol as a function of particle concentration, y. The coefficients gAa=b , gBa=b , and la=b A;B depend on absolute temperature, T :
i 2 fa; bg; j 2 fSn; Pbg;
¼
þ ð1 þ RT ½y lnðyÞ þ ð1 yÞ lnð1 yÞ þ yð1 yÞlaA;B :
The coefficients essentially stem from calorimetric experiments and, for SnPb, are compiled in [32]. Note that the diffusion equation (1/4) was originally derived in terms of mass concentrations, c, and not in particle concentrations, y. Therefore we rewrite the Gibbs free energy densities by using the following relation: y ¼ ~y ðcÞ ¼
M Sn
M Pb c : cðM Sn M Pb Þ
ð13Þ
Moreover, note that the free energy density of MTData is in J/mol. However, the one used in Eq. (11) is written in J/m3 instead. A conversion becomes possie ðcÞ, ble by using an average molecular weight, M ¼ M which changes as a function of concentration: e ðcÞ ¼ M¼M
M Sn
M Sn ¼ 118:69;
M Pb M Sn ; cðM Sn M Pb Þ
M Pb ¼ 207:19:
ð14Þ
By combination of these equations, an experimentally based specific free energy, w, is finally obtained, which, after multiplication by the macroscopic density of the eutectic alloy, was used for numerical evaluation of the extended diffusion equation shown in Eqs. (1) and (4) (see [31] for details). The result is shown in Fig. 14, for two different temperatures, 20 and 125 C, respectively. The figure also shows the common tangent construction (Maxwell lines) that defines the two equilibrium concentrations ca and cb mentioned before. It also contains the spinodal points that form the boundary of the non-convex unstable region of concentrations. 2.1.2. Diffusion constants In [18] it was assumed that the symmetry of a phase is determined by the symmetry of the dominant constituent. In other words, the a-phase was assumed as cubic (as in lead) and the b-phase as tetragonal (as in tin). We therefore write (provided the axes of the crystal and of the laboratory frame coincide):
Mija ¼ M a dij ; ð11Þ
liA;B
ð12Þ
0
yÞgBa=b
Fji ; T ¼ Ai þ Bi T ; i 2 fa; bg:
gji ¼ Aij þ Bij T þ Cji T lnðT Þ þ Dij T 2 þ Eji T 3 þ
ga=b ¼ g~a=b ðyÞ ygAa=b
1909
Mijb
M1b @ ¼ 0 0
0 M1b 0
1 0 0 A: M3b
ð15Þ
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W.H. M€uller / Microelectronics Reliability 44 (2004) 1901–1914
0
aakl ¼ aa dij ; a¼
aa ¼ 1:5 a;
2cDx ðcb
1 a 0 0 B C abkl ¼ @ 0 a 0 A; 0 0 14a
c a Þ2
;
c ¼ 1:5
J ; m2
Dx ¼ 25 nm: ð17Þ
More refined atomistic arguments were used in [38] to link these coefficients to the interatomic potentials between two element species A and B. For cubic materials it is sufficient to use potentials that only depend upon the radial distance Dab between two atoms a, b at positions Xib , Xia and not on their angular position: aukl ¼
1 X ab 2 ðD Þ uðDab ÞNk Nl ; 2 b
1 X ab 2 Dab ~ ðDab ÞNk Nl ; Ni ¼ iab ; ðD Þ u 2 b D 2 2 oy 1 o y u~ akl ¼ aukl þ ða 2yaukl Þ; oc 2 oc2 kl 1 b a ~ ðDab Þ ¼ ðuBB ðDab Þ uAA ðDab ÞÞ; Dab u i ¼ Xi Xi ; 2 1 ab ab uðD Þ ¼ uAB ðD Þ ðuAA ðDab Þ þ uBB ðDab ÞÞ: 2 ð18Þ aukl~ ¼
Fig. 14. Gibbs free energies at two temperatures. b In these equations M a and M1;3 denote the mobilities of tin atoms in a lead dominated lattice and of lead atoms in a tin dominated crystal, respectively:
The interatomic potentials, uAA=BB=AB ðDab Þ are typically assumed to be of the Lennard–Jones type: uAA=BB=AB ðDab Þ ¼
125C :
M a jca ¼ 2:42 1027
m5 ; Js
M1b jcb ¼ M3b jcb ¼ 4:52 1024 20C :
M a jca ¼ 1:27 1032
m5 ; Js
m5 ; Js
M1b jcb ¼ M3b jcb ¼ 1:11 1027
ð16Þ
m5 : Js
This data is based on diffusion coefficients for tin or lead being a tracer element in pure lead and tin, respectively [33]. Clearly, the diffusion coefficient for the a-phase is much smaller than the one for the b-phase and can be neglected in the quantitative simulations (see [31] for further details).
2.1.3. Higher gradient coefficients (HGCs) Following the original work of Cahn–Hilliard a simplified 2D study of the atomic potentials and lattice configurations revealed strong anisotropy [18]:
AAA=BB=AB ab 12
ðD Þ
BAA=BB=AB ðDab Þ6
:
ð19Þ
The constants AAA=BB=AB and BAA=BB=AB can be determined using the compressibilities of the pure substances, their sublimation energies, and characteristics of the mixture, e.g., Young’s modulus and Poisson’s ratio and the heat of mixing (see [38] for details). Tin, however, crystallizes in a tetragonal lattice and, consequently, SnPb requires a more complex approach, e.g., the use of EAM. The situation is even more cumbersome for the multicomponent lead free solders mentioned above. In order to describe their microstructural evolution multi-component phase field theories are required which lead to many more frequently unknown material parameters. Clearly, this will also require more complex numerical discretization schemes to be used, all of which presents challenging problems for the future. 2.1.4. Eigenstrains The eigenstrains in SnPb [32,33], which are incoherent in nature, are completely related to differences between the thermal expansion coefficients:
W.H. M€uller / Microelectronics Reliability 44 (2004) 1901–1914
ekl ¼ ~akl ðX ; tÞ DT ; DT ¼ ðT TR Þ; ~ ; tÞaa þ ð1 ~hðX ; tÞÞab ; akl ¼ hðX kl kl 0 b 1 a1 0 0 B C aaij ¼ aa dij ; abij ¼ @ 0 ab1 0 A; 0
ð22Þ
ð20Þ 3. Results
ab3
1
a
6
a ¼ 28:9 10
K ;
ab1
6
K1 ;
¼ 16:7 10
0
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Z cX2 Dc0 qAXmðtÞ 3 rðxÞ ¼ þ dt: 3NA LRT 4pmNp ðtÞ
1911
ab3 ¼ 36:4 106 K1 :
2.1.5. Stiffnesses Mechanical stiffnesses are readily and accurately available. We note that [18,32]: a ¼ 49:66 GPa; C11
a C12 ¼ 42:31 GPa;
a ¼ 14:98 GPa; C44
b C11 ¼ 75:29 GPa;
b C12 b C33 b C66
¼ 61:56 GPa;
b C13 ¼ 44:00 GPa;
¼ 95:52 GPa;
b C44 ¼ 21:93 GPa;
ð21Þ
¼ 23:36 GPa:
2.2. Growth of inter metallic phases The mathematical description of the growth of scallop shape intermetallic layers has been the focus of a series of papers by Tu and coworkers (e.g., [34,35]). The development of these layers is characterized by coupling two distinct processes, first, ripening growth between Cu6 Sn5 grains controlled by volume diffusion (‘‘survival of the fattest’’) and, second, interfacial reaction growth. Their equation for ripening is based on the Gibbs– Thomson effect and essentially an application of the so-called LSW-theory. However, in contrast to the traditional formalism the ripening between the Cu6 Sn5 grains does not occur at a constant volume. Rather there is a supply of grain material due to the interfacial reactions between the solder alloy and the copper. By balancing the interfacial reaction and adding the corresponding flux due to LSW-ripening Tu et al. finally arrive at the following equation for the growth of the mean radius of Cu6 Sn5 grains (c denotes the interfacial energy per unit area between the Cu6 Sn5 grains and the molten solder, X is the molar volume of Cu6 Sn5 , D is the diffusivity of Cu in the molten solder, c0 is the equilibrium concentration of Cu in the solder, NA is Avogadro’s constant, L is a dimensionless parameter indicating the fraction of the mean separation between grains and the mean grain radius, R is the gas constant, T is absolute temperature, q is the density of Cu, mðtÞ is the reaction rate, i.e., the rate at which the height of the copper substrate diminishes, m is the atomic mass of Cu, and Np ðtÞ stands for the total number of grains at the interface):
In the following simulations an inclination of 25 between the crystallographic and the laboratory system was assumed. The width and height of the RVE is 2pL ¼ 1 lm. Fig. 15 presents the microstructural development at a low and a high temperature (20 and 125 C) starting from a homogeneous mix of eutectic SnPb with a few slight fluctuations. It is important to note that the mobilities at these two temperatures are very different which explains that the time scales of both coarsening processes differ by an order of magnitude. This is in qualitative agreement with the experimental findings shown in Fig. 2. The lack of quantitative agreement can be explained by the fact that the mobilities stem from tracer experiments and, therefore, do not perfectly represent the actual situation. In the sequence of pictures of Fig. 16 the influence of tensile stress on microstructural development is investigated. From our simulations we may say that both uniaxial tensions in horizontal as well as in vertical direction clearly lead to enhanced coarsening behavior.
Fig. 15. Microstructural development of eutectic SnPb-low temperature (first two rows) vs. high temperature (last two rows).
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W.H. M€uller / Microelectronics Reliability 44 (2004) 1901–1914
Fig. 16. High temperature development, external load of +5 MPa in horizontal direction.
Consequently, such a state of stress may be considered to contribute to the pronounced coarsening occurring in the interface regions of solder balls (cf., Fig. 1). Further studies [36] have revealed that equal tensile loads lead to hardly any coarsening at all. From these simulations it can be claimed that the effects of two tensile loads of equal size on the microstructure seem to annihilate each other although, during the development, some differences to the corresponding structures without external loads can be observed. Clearly, the state of stress in real solder balls is threedimensional in nature but it can be anticipated that the principal stresses are not all equal. Furthermore we may say that the microstructures resulting under compressive stress are essentially similar to their tensile counterparts, tensile stresses leading to slightly stronger coarsening. Finally, shear stresses that are sufficiently high, i.e., of the same magnitude (5 MPa) as the tensile and compressive counterparts, can have a dramatic influence on the resulting microstucture. Reducing the shear by more than 50% still leads to a noticeable effect during the development phase (see [36] for details). The sequence of Fig. 17 provides evidence that there is potential for ‘‘healing’’ of a coarsened microstructure.
Fig. 17. ‘‘Healing’’ of a microstructure initially coarsened by external stress by switching to low temperature 125 C fi 20 C.
Fig. 18. Mean grain radius of Cu6 Sn5 of grains as a function of re-scaled time, adapted from [34] (eutectic SnPb on Cu substrate for (a) L ¼ 0:15 and (b) c0 ¼ 0:3, see text for details).
In this simulation we used a stressed microstructure showing a particularly strong coarsening similar to the last picture of Fig. 16 as initial condition to further simulations of the microstructural development. More specifically we ‘‘switched’’ from high to low temperature and also ‘‘removed’’ the external stress. Clearly, it is an advantage of computer simulations that the impact of each driving force and material parameter can be studied separately and most conveniently by altering the input to the computer program. 2 Due to the fact that both equilibrium concentrations and phase volume fractions depend on temperature, diffusion sets in and this obviously has a soothing effect on the microstructure. Examples for simulations of microstructural change in alloys showing diffusion and transitions to a different state of order have been presented in [37] (e.g., rafting in NiAl superalloys and development of lenticular shaped tetragonal phase in PSZ ceramics). However, this strategy had not been applied to a study of the growth and coarsening of Ag3 Sn intermetallics in AgSn solder yet.
2 In this context it should also be mentioned that the computer simulations show that the thermal mismatch between the two phases does not have a significant impact on the coarsening behavior, at least in the case of the SnPb system.
W.H. M€uller / Microelectronics Reliability 44 (2004) 1901–1914
After providing an extreme wealth of materials data Kim and Tu successfully managed in [34] to predict the growth of the mean size of Cu6 Sn5 grains for eutectic SnPb on Cu substrates. They also compared their predictions with own measurements. Some of their results are shown in Fig. 18.
4. Conclusions We have shown that it is nowadays possible to simulate the microstructural development and change observed in microelectronic solders as well as the growth of intermetallic phases. The mathematical tools used for this purpose are phase field models and LSW-theory. A general outline of these theories was given together with references from which further details can be obtained. We conclude that these theories stand and fall with the various material parameters they require during their quantitative evaluation. Ideally these material parameters should stem from experiments that are independent of the theoretical model. For eutectic SnPb it was possible to obtain all the required parameters in this manner mainly because SnPb is a well characterized solder that has been in use and investigated for decades. Several numerical simulations of microstructural evolution were shown that can be compared to experimentally determined ones. These simulations allow to study which of the various material parameters involved have a particularly crucial influence on coarsening and aging. In particular the influence of mechanical stress could be assessed quantitatively for the first time. However, it is fair to say that even in the case of SnPb some material parameters proved to be very difficult to obtain and are still only inaccurately known. In particular this is the case for the so-called higher gradient coefficients. For that reason an atomistic interpretation was provided that allows to calculate these parameters from atomic pair potentials which, in turn, can be determined from the crystal lattice structure of the solder crystallites and some macroscopic material properties.
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