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Cu interface during multiple reflows
Intermetallics 96 (2018) 1–12
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Intermetallics journal homepage: www.elsevier.com/locate/intermet
Evolution behavior and growth kinetics of intermetallic compounds at Sn/ Cu interface during multiple reflows
T
H.R. Maa, A. Kunwarb, S.Y. Shanga, C.R. Jianga, Y.P. Wanga, H.T. Maa,∗, N. Zhaoa,∗∗ a b
Dalian University of Technology, School of Materials Science and Engineering, Dalian, 116024, China Dalian University of Technology, School of Mechanical Engineering, Dalian, 116024, China
A R T I C L E I N F O
A B S T R A C T
Keywords: A Intermetallics B In situ C Joining D Interfaces E Finite-element modeling
Evolution behavior and growth kinetics of Sn/Cu interfacial intermetallic compound (IMC) during multiple reflows were investigated. Scanning electron microscope (SEM) and shanghai synchrotron radiation facility (SSRF) images have shown that, scallop Cu6Sn5, formed at interface during the heating stage of a reflow, converted to facet type during subsequent cooling, and transformed back to the scalloped grains with larger size during the next re-heating stage. Furthermore, the value of IMC growth time exponent n during soldering gradually changed from 0.405 to 0.485 while nearly kept 1 during cooling and heating with reflow times. In addition, n was 0.613 for the overall multiple reflow process.
1. Introduction Multilayer structure interconnection achieved by 3D chip stacking technology using Through-Silicon Via (TSV) or Flip-chip bonding has advantages of high performance, small shape factor, easy heterogeneous formation, lightweight, low power consumption, lower cost, etc [1–3]. In the current generation of 3D electronic packaging characterized by the miniaturization of electronic products, multiple reflows are generally required during soldering. For example, in the Double-POSSUMTM 3D IC packaging developed by Amkor [4], three daughter dies are flip-chip first attached to a larger mother die which is then attached to the largest grandma die. The grandma die is again flip chip solder bumped on a package substrate, and this whole substrate is then attached on to a PCB (printed circuit board). In general, multiple reflows are inevitably required as flip chip technology is applied to this 3D structure for many times. Interfacial intermetallic compound (IMC), occurring at the interface of solder/substrate, is a crucial factor for the reliability of solder joints [5–7]. Researchers have found that the thickness of IMC will continually increase with reflow times and too much thicker IMC is described to be detrimental for the resultant joint strength and reliability [8–11]. In recent studies concerning multiple reflows, some researchers [12–14] believe the IMC growth is controlled by grain boundary diffusion and the value of time exponent (n) is equal to1/3, but the others [15,16] consider volume diffusion dominates the IMC growth and the value of time exponent n matches1/2. In effect, the conflict between
∗
these two conclusions can be ascribed to the impractical hypothesis that equating multiple reflow process to a long time soldering reaction. This assumption may result in design flaws for solder joints undergoing several reflows. In reality, a solder joint undergoing several cycles of heating and cooling may have its IMC growth influenced by precipitation (magnified during cooling duration) apart from the usual diffusion induced mechanism. The isolation of IMC growth mechanism during a single-reflow cooling [17], that has been mostly avoided by many researchers till now, in fact can be utilized in the rectification of errors during growth kinetics study for multi-reflow soldering. Owing to the practical application of multiple reflow process in 3D electronic packaging, the accuracy in the prediction or determination of associated growth kinetics exponent n has a huge impact in the concurrent materials design in microelectronics industries. In soldering process, synchrotron radiation is a powerful analytical tool that provides information on the interfacial IMC growth in real time. In traditional study, the analysis of IMC growth is always based on the observation for size and morphology after soldering using some exsitu experimental techniques, in other words, most of the IMC thickness data was obtained through rapid cooling and then the dynamic reaction mechanism between liquid solder and substrate under high temperature can be predicted by combing the IMC size and morphology features after cooling. Obviously, this method is unable to observe the IMC growth continuously and lacks accuracy in measurement for IMC size due to the two-dimensional measuring section view. Of course, the analysis of grain growth behavior during soldering is also unscientific.
Corresponding author. Corresponding author. E-mail addresses: [email protected] (H.T. Ma), [email protected] (N. Zhao).
∗∗
https://doi.org/10.1016/j.intermet.2018.01.022 Received 8 November 2017; Received in revised form 26 January 2018; Accepted 31 January 2018 0966-9795/ © 2018 Elsevier Ltd. All rights reserved.
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setup implies keeping the furnace windows open. The parameters, namely resolution ratio and exposure time of the charge coupled device (CCD) camera were designated as 0.325μm/pix and 4s, respectively. The high intensity beam radiation from x-ray source was made to pass through the solder-substrate system and the image presented on the screen by the transmitted beam was recorded by CCD camera. When the X-ray was interfered by the sample, the portion of the incident radiation beam was absorbed by the material and the remaining part is transmitted through the solder system, resulting in the less intensity of the beam after transmission. Actually, the intensity of the beam after transmission would reduce with the increase of density, absorptivity and thickness of the medium. In our liquid Sn/solid Cu interface, the phase absorptivity ranking should be: Cu > IMC > solder. Finally, based on the SSRF image contrast, we measured the IMC thickness. Same materials were used in the ex situ characterization based 60s reflow for 3 times experiment at 250 °C for IMC morphology and size evolution. After each soldering cycle, the specimens were followed by air cooling (AC). Specially, parts of the first 60s-reflow specimens were cooled by other methods: high pressure air blowing (HP, no cooling), furnace cooling (FC) and water cooling (WC). The overview of the procedure for different cooling condition is sketched in Fig. 2, wherein the length of cubical Sn is about 1 mm and Cu substrate is of size 5 mm × 5 mm × 100 m. Then the microstructure of multiple reflow solder joints was analyzed via scanning electron microscope (SEM). For top-view observation of IMC by SEM, the samples were etched by 10% HNO3 solution (in volume) in order to remove the solder away; and for cross-sectional morphology of IMC by SEM, 5% HNO3 +2%HCl+93% C2H5OH (in volume) solution was utilized to surface treat the samples. Scanning electron microscope [Zeiss Supra 55(VP)] was used for obtaining the images of the samples.
Recently, the application of synchrotron radiation on interfacial reaction in electronic packaging becomes increasingly popular and has its unique advantages. For instance, in situ observation on dynamic interfacial grain growth behavior as well as the substrate consumption [18], which is an important scientific issue in linking reliability; connection problem induced by defect evolution including voids and cracks inside solder joints [19]; three-dimensional microstructure variation or deformation in solders [20]; effect of addition elements and particles on size and morphology of interfacial primary crystal [21]; failure locus inside complex part structural solders [22]; can be holistically investigated and used to finally enhance the reliability in electronic devices. This paper investigates the IMC growth behavior during multiple reflows by utilizing the cutting edge experimental technique based on real-time imaging technology of Shanghai Synchrotron Radiation Facility (SSRF). A finite element method (FEM) based numerical model is developed to assess the relative proportion of precipitation and diffusion induced IMC sizes during a single reflow cooling in air, water and furnace media. The FEM model for single reflow and the experimental results for multiple reflow are blinded together to develop the growth kinetics model for multi-reflow soldering. These experimental results can highly help to establish the IMC growth model during multiple reflow process and thereafter achieve an effective tool to improve the overall quality as well as the reliability of the resultant solder joints. 2. Experimental methods and numerical formulation 2.1. Material and experimental procedure Pure Sn (99.95%) solder and pure Cu (99.95%) were used as the materials for SSRF experiment. The experimental setup for observation of interfacial microstructure of liquid Sn/Cu joints by BL13W1 of the Shanghai SSRF is sketched in Fig. 1. The Cu substrate of height 5 mm and thickness 100 μm was butt joined to the solder of 100 μm × 100 μm. This SSRF experiment of four-time reflows was carried out at 300 °C, in which the holding time for the first isothermal reflow was kept for 1 h whereas the later 3 ones had the isothermal reflow keeping time of 20min and the cooling between two consecutive reflows was carried out in air medium. Air cooling for the experimental
2.2. Numerical formulation for copper precipitation in single reflow cooling The most difficult portion for the understanding of the growth kinetics of IMC during cooling is the accounting of mixed mode contribution to the IMC size with diffusion and precipitation effects. Assuming that significant amount of the IMC growth takes place in the liquid-solid interfacial reaction and neglecting the solid state interfacial reaction, the mathematical formulation of compound evolution can be simplified solely to the liquid stage of Sn solder. Furthermore, for the formation of Cu6Sn5 compound with interfacial reaction of Cu substrate with pure liquid Sn; the Cu flux, being the dominant diffusing species, can be considered as the limiting agent [23] and thus the mathematical analysis of mass transfer can be focused only on the transport of Cu species in the medium. As the total size ytotal of Cu6Sn5can be obtained from the in-situ cooling experiments, the determination of precipitation induced compound size can lead to the separation of relative contribution of diffusion and precipitation effects in accordance to the following formula:
ytotal = ydiffusion + yprecipitation
(1)
For a cooling procedure with a given cooling rate, the mass transport equation for Cu species in the liquid Sn medium is given by the following expression [24]:
kprcpt×A L dCCu L [CS,0 − C(T)LS,t] = DCu ∇2 CCu + V dt
(2)
with In partial differential equation (PDE) 2, CCu is the concentration variable with unit mol/cm3 and the term in the left hand side (LHS) is a transient term whereas the first term in the right hand side (RHS) corresponds to a diffusion term. The second term in the RHS is an implicit source term representing precipitation of Cu in the physical domain provided that the time (t) and temperature (T) dependent solubility of Cu in liquid solder C(T)LS,t can be numerically alienated from the solution variable. The material properties kprcpt and CLS,0 are precipitation rate of Cu and saturated solubility of Cu in liquid Sn at the
Fig. 1. In the picture, figure (A) represents the experimental setup for real time imaging of multiple reflow experiments using synchrotron radiation. Figure (B) elaborates the vertical portion of the solder-substrate sample that is irradiated by X-ray.
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Fig. 2. For the ex situ characterization experiments for multiple reflow soldering, figure (a) represents the schematic sketch of the samples undergoing cooling via water, air and furnace at the end of each reflow. The practical approach of multiple reflow with zero cooling rate can be modeled as shown in figure (b) by the use of high pressure air jet to remove the liquid solder at the stage of heat removal for each reflow.
includes the stump and prism types as well. Furthermore, SSRF results also illustrate that for 4-time multiple reflow samples, the number or width of IMC grains at Sn/Cu interface nearly reaches its limitation and almost remains unchanged in the later process after I hour's reflow at 300 °C. Clearly, the transformation of IMC grains between scallop and facet is a kind of reversible behavior in case of invertible temperature variation. However, the facet cannot transform totally back to the scallop and still some left, which can be seen from the area between the yellow and white curves in Fig. 4.
isothermal holding temperature. The symbols A and V represent the cross-section of the interface and volume of the liquid solder respectively. The corresponding growth of Cu6Sn5 or η phase due to precipitation is related to liquid phase rate as following:
vη h×kpart
η η [C(T)S,t ]= − Cconst
kprcpt×A V
[CLS,0 − C(T)LS,t]
(3)
wherein, vη is the interface growth velocity and kpart is the partition coefficient. On the other hand, the evolution of temperature variable (T) in the solder system during cooling is given by the following equation [25]:
∂T + V ∇T⎞ = kth, Sn∇2 T ρSn Cp ⎛ ⎝ ∂t ⎠
3.2. Annexation behavior and growth kinetics of IMC during isothermal welding
(4)
where, the temperature dependence of density ρSn, specific heat capacity Cp and thermal conductivity kth,Sn of solder is duly considered for the cooling procedure. The Biot number of the physical system is less than 0.1 and thus the convection heat transfer in Eq. (4) is neglected, that is ⱱ = 0. The solution of coupled sets of Eqs. (2) and (4) can help in the determination of amount of copper precipitated during the cooling process. Finite element analysis (FEA) is performed in Multiphysics Object Oriented Simulation Environment (MOOSE) Framework [26,27] in order to determine the solution variables CCu and T for these systems of PDEs. The temperature dependent material properties used in the FEA, namely density, thermal conductivity as well as specific heat capacity of Sn and solubility, diffusivity and precipitation rate constant of Cu in liquid Sn are presented in Fig. 3. For transient simulation, the initial conditions for concentration and temperature are provided as 1.59 × 10−3 mol/cm3 and 523.15 K respectively. Zero flux boundary conditions (BCs) are imposed at the boundaries for CCu variable as the solution is always at the saturation limit. For T variable, in context of solder-substrate interface, robin BCs is applied with interfacial heat transfer coefficient, hinterfacial = 11500 × t−0.03 and in other boundaries function Dirichlet BCs are applied in accordance to the given cooling rate.
Fig. 6 plots the average width of IMC grains following the soldering temperature profile. For 3-time reflows, the heat preservation stage characters the IMC annexation phenomenon and greatly increases the grain width. On the contrary, the cooling-heating procedure nearly has no effect on grain numbers causing the stable IMC width throughout this period. Hence, we can infer that only in isothermal welding of multiple reflows that the annexation behavior of IMC at solder/copper interface takes place, cooling and heating simply change the morphology and average thickness of IMC and have no effect on the total number. Kinetically, the thickness increase of a reaction layer in the diffusion couples can be generally expressed by a simple power-law equation [12,13]:
Δ y= ktn
(5)
where Δy is the thickness increase of IMC, k is the growth-rate constant, n is the time exponent and t is the reaction time. Especially, the time exponent n was obtained from the slope of the plot of ln(Δy) versus lnt. Normally, IMC growth based on grain boundary diffusion follows a t1/3 dependence on time t [17]. However, when the growth kinetics of a layer are controlled by volume diffusion through the planar IMC layer, the time exponent should be 1/2, and when controlled by chemical reaction at the interface, the exponent should be 1 [32]. With the current scenario of no any existing experimental works on in-situ study on every cycle of multiple reflows, the IMC growth kinetics for each of the heat preservation stages are demonstrated in Fig. 7. The results exhibit that the values of time exponent n increase from 0.405 to 0.485 with four-time reflow cycles, implying that the control mechanism for IMC growth has gradually changed from grain boundary diffusion to volume diffusion during heat preservation in multiple reflow process. Two factors can contribute to this phenomenon: one is the reduction of grain boundaries due to the annexation behavior of grains in isothermal soldering part; the other is the blocking of grain boundaries owing to un-dissolved cooling (shown in chapter 3.6) IMC in
3. Results and discussion 3.1. IMC morphology evolution during multiple reflows SSRF images for IMC evolution during 4-time multiple reflows at 300°C and SEM top-view pictures for IMC growth during 3-time reflow cycles at 250 °C are shown in Figs. 4 and 5 Clearly, we can observe the IMC rapidly grows from scallop grains in keeping stage (the yellow profile in Fig. 4 and d-f in Fig. 5) to facet type in cooling stage (the red profile in Fig. 4 and g-i in Fig. 5) and transforms back to the scallop (the white profile in Fig. 4 and a-c in Fig. 5) with a larger size during the next re-heating stage. Here, the facet means grains with facets and 3
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Fig. 3. Among the temperature dependent thermophysical properties for the solder-substrate system presented in the figure, density, thermal conductivity, diffusivity, solubility and precipitation rate constant are obtained from Refs. [28–30] whereas specific heat capacity is computed using opencalphad software [31].
nearly has no change since the cooling rate is so high (727 K/s) that the Cu atoms have no time to diffuse. The travel of Cu atoms in liquid is very quick but it still needs time. For AC, the CCu content declines in accordance with the temperature profile inside 60s, but the cooling rate is still too fast for Cu atoms to travel fully. For FC, the solder takes 900s to freeze to solid state and Cu atoms have more time to migrate to the interface area. Of course, FC is the one closest to the equilibrium deposition condition and the final value of CCu in solder is the lowest. Cooling rate is the driven force for IMC growth, but enough reaction time is also an objective condition in deposition. Therefore, the cooling rate should be controlled reasonably in the assessment of IMC growth.
heating stage and the plate-like Cu3Sn under Cu6Sn5 layer, specially the thickness of Cu3Sn layer increases linearly with reflow numbers [33]. Clearly, an increase in reflow cycles will accelerate the transformation of IMC growth control mechanism from grain boundary to volume diffusion.
3.3. Modeling analysis for Cu deposition behavior in cooling The IMC increase in cooling is mainly caused by the decrease of Cu concentration in liquid. For different cooling rate, the deposition of Cu atoms has different characteristic and thus the IMC increase differs as well. When the cooling rate is very small and the deposition behavior can be viewed as a perfect balanced reaction, the Cu content in solder declines along the liquid line in Sn-Cu binary phase diagram. However, most cooling behavior in real experiments belongs to non-equilibrium condition, and is affected by cooling rate. Regardless of the substrate dissolution in cooling, the IMC thickness increase is proportional to the Cu concentration decrease. Fig. 8 visually presents the temperature and Cu concentration variation for WC, AC and FC in the form of colorized graphs. Besides, the detail data can be read from Fig. 9 as well. For WC, the solidification of liquid solder finishes inside 0.06s and the Cu concentration in solder
3.4. IMC growth behavior and kinetics in cooling The cooling condition in SSRF experiment is similar with the FC in modeling analysis in the last chapter. Thus the kinetics calculation in this part is mainly related to the Cu deposition behavior. During cooling, all the values of time exponent n in Fig. 10 agree well with 1. In our previous work [25], actually, we have found IMC growth shows linear dependence with time during cooling stage under a given cooling rate and so n = 1 in the equation (5). Meanwhile, the thickness increase of IMC is related to the instantaneous concentration of Cu in liquid and
Fig. 4. SSRF images for IMC evolution during multiple reflows:(a) (d) (e): after isothermal welding; (b) (e) (h): after cooling; (c) (f) (i): after heating.
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Fig. 5. SEM images for IMC evolution during multiple reflows: (a)–(c): after heating; (d)–(f): after isothermal welding; (g)–(i): after cooling.
the constant k of the precipitation reaction during cooling. For a single short reflow, we can equal the instantaneous CCu in liquid to the composition of utilized solder, so the constant k is only determined by cooling rate and the IMC deposition is under the control of k and t. In fact, t is also related to cooling rate since its increase creates the larger k and smaller t at the same time. As summed up in Fig. 11, four different cooling methods are given by showing the topview morphology and cross-section size of IMC. From HP to FC, the effective reaction time rises from 0 to 20 min approximately while the cooling rate gradually declines, which consequently results in a much larger size of IMC after FC. Moreover, the type of IMC varies from scallop to prism as well. However, the instantaneous CCu cannot be regarded as a constant value due to the prolonged diffusion of Cu from substrate to liquid when it comes to multiple reflows. Results in Fig. 12 indicate that IMC deposition is continually enhanced with reflow cycles for 60s-3-time Sn/Cu samples at 250 °C. Obviously, smaller cooling rates and more reflow cycles can probably lead to massive growth of IMC during multiple reflow process and a suitable cooling rate is important for modern electronic packages.
Fig. 6. Average width of IMC grains VS soldering temperature profile.
3.5. IMC dissolution behavior and kinetics in heating The combination of temperature profile and IMC growth in Fig. 13 provides a direct sight for the size variation in every stage of multiple reflows. Clearly, IMC thickness keeps growing during isothermal soldering and cooling parts until the dissolution phenomenon appears in heating periods. To better understand the essence of IMC dissolving behavior, the following transformation reaction throughout the entire multiple reflow process should be clearly presented:
L⇌η where L means the melt solder and η stands for Cu6Sn5 phase. This reaction controls the thickness variation of IMC during the whole process. From the Sn-Cu binary phase diagram we can know that the copper concentration in η formed under a certain temperature is smaller than that under a higher temperature. Fig. 14 illustrates the relationship between Gibbs free energy and Cu concentration in different reaction materials, revealing that a smaller Cu concentration in η can
Fig. 7. IMC growth kinetics for keeping stage during multiple reflows.
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Fig. 8. Modeling graph results for variation of temperature and Cu concentration in the solder bulk: (A1-A4) and (a1-a4) for WC; (B1-B4) and (b1-b4) for AC; (C1-C4) and (c1-c4) for FC.
In addition, by measuring the IMC thickness in Fig. 18 we find that the size of IMC dissolution in heating is not exactly equal to the size of IMC growth in cooling, and still some IMC generated in cooling left after heating. Comparing the IMC after HP with that after AC in Fig. 19, we can find that the Cu deposits on the surface of the Cu6Sn5 in cooling stage and forms new IMC, which will dissolve in next heating stage. However, the new IMC in the boundary area between two grains is not easy to dissolve as it forms at the beginning of cooling, so that it has similar Cu concentration with the initial IMC. Furthermore, because of the large Cu concentration gradient inside the new IMC of boundary area (Cu/new IMC), diffusion of Cu from substrate to IMC during cooling can raise the Cu concentration in IMC, consequently resulting in the left-IMC. This blocks the grain boundaries and accelerates the changing for n s from 1/3 to 1/2, finally heighten the n for the whole multiple process. Of course, new IMC outside the boundary area may also be kept in heating, but being ignored here because it is very small and has no big effect on the changing of IMC growth control mechanism. Obviously, a large cooling rate and less reflow cycles can greatly reduce the thickness of left IMC and make the Δyc ≈ Δyh as there is no enough time for Cu diffusion.
raise the Gibbs free energy of η under a given temperature according to the Cη-left region. According to the above analysis, expression for the IMC dissolving behavior can be described as the following: Cu concentration in η gradually becomes less with temperature lower during cooling giving rise to a higher Gibbs free energy for η, which can greatly boost the transformation from η to L in the next re-heating stage. That is why the dissolution phenomenon of IMC happens in heating stages of multiple reflow process. In other words, IMC formed at a lower temperature will begin to dissolve when the temperature gets higher. To support our theory, we have added another experiment in which samples were immediately cooled in furnace after melting at 300 °C, so that most of the IMCs were formed under temperatures below 300 °C. Then the average thickness of IMC in the next re-heating respectively under 275 °C, 300 °C and 325 °C was plotted in Fig. 15. It can be found that the size of IMC linearly-decreases rapidly under 325 °C but much slowly under 275 °C in the dissolution stage. This gives a strong evidence for our analysis. According to equation (5), we also get similar n values around 1 for heating stage shown in Fig. 16. This can be explained by the reversible reaction between solidification of L in cooling and dissolution of η in heating, and dissolving in heating is exactly the inverted procedure of growing in cooling. Therefore the n also equals to 1 for heating.
3.7. IMC growth model for multiple reflows At present, there are four models valued in analysis of interfacial IMC growth during a single reflow. Firstly, the ripening or flux-driven ripening (FDR) model developed by K.N. Tu [17,34,35]. In this model, the authors thought the IMC growth was controlled by Cu diffusion through the liquid channel between two adjacent grains and ripening mechanism based on Gibbs-Thomson equation. It can describe the scallop-like Cu6Sn5 growth well, but has some disadvantages simultaneously in the explanations of prims-like Cu6Sn5 growth, influence of cooling process on IMC evolution and size effect on IMC morphology due to its neglect of Cu diffusion from substrate to solder bulk. Secondly, scholar M. Schaefer [36] built a model in which the grain boundary (channels in ripening model) was viewed as the main factor for IMC growth. The surface of Cu6Sn5 grain was regarded as parabolic cap-like in contact with liquid and hexagonal base-like towards Cu substrate. This is an improvement, but this model still ignored the Cu migration from substrate to liquid solder. Thirdly, professor Dybkov [37] raises that the grain growth was dominated by IMC growing and dissolving. In the model, he considered the Cu dissolving from substrate to liquid, but has not valued the contribution of liquid grain boundary to IMC growth. Besides, this model cannot account for the IMC growth in small solders because of the thickness setup of 100 μm for a diffusion barrier layer. Fourthly, Huang [38] established a concentration gradient controlled (CGC) interfacial reaction theoretical model, where the
3.6. IMC growth kinetics throughout the multiple reflow process Generally, most of the research works hither to, simply have been regarding the multiple reflow process as a long time soldering reaction consequently resulting in deduction of some inaccurate or impractical mechanisms for IMC growth. By our above individual analysis for every stage in multiple reflows, the total IMC increase should be:
Δ Y= Δys + Δyc − Δyh where Δys and Δyc mean the increase of IMC in soldering and cooling parts, and Δyh means the decrease of IMC in heating stage. In other forms, the IMC increase can be written as:
ktn = k st sns + k ct c − khth in the equation, k s , k c and kh stand for the growing or dissolving rate of IMC in isothermal welding, cooling and heating; t s , t c and th represent the reacting time in every stage; n s is the time exponent for IMC growth in heat preservation, changing from 1/3 to 1/2 with reflow cycles; k, n are the fitting parameters for the whole process and t is the total keeping time over the solder melting temperature. So n should be a value between 1/3 and 1, which has expressed the result n = 0.613 in Fig. 17. 6
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Fig. 10. IMC growth kinetics for cooling stage during multiple reflows.
boundary diffusion, contribution of volume diffusion through IMC grains and Cu dissolving into liquid bulk should all be considered into the establishment of IMC growth model in multiple reflows. For a single soldering, we propose a model for interfacial IMC growth as sketched in Fig. 20 (a). In this model, we make some hypotheses: (1) grains at Sn/Cu interface are hemispheric during soldering and the average thickness of IMC equals to the grain radius [39]; (2) Cu is the predominant element for IMC growth and Cu3Sn is ignored; (3) the length between two grains is defined as the distance between the two inscribed hexagons and δ = 0.05 μm [34]; (4) the distribution of Cu in L outside the IMC area is uniform. Table 1 gives the nomenclature of parameters applied in the following equations. For the single reflow model, area proportion of grain boundaries per m2 at Sn/Cu interface can be expressed as:
Sb =
3Lδ 3Lδ +
3 3 L2 2
1
=
1+
3L 2δ
(6)
Adding δ = 0.05 μm in,
Sb ≈
10−7 3L
(7)
Sa + Sb = 1 The two fluxes of Cu from substrate to IMC region through bulk and boundary diffusion are:
Jin −a = Dη Sa ρη Fig. 9. Modeling data results for variation of temperature and Cu concentration in the solder bulk: (a) for WC; (b) for AC; (c) for FC.
1 − Cη
Jin −b = DL Sb ρL
(8)
L Cb − Ce L
(9)
The average Cu concentration in L outside the IMC region can be defined as [37]:
Cu concentration gradient was revealed to be the root cause of the size effect. This model has taken the grain boundary diffusion and the Cu dissolving into solder bulk into consideration, but still has no cooling stage. Above all, the last CGC model for IMC growth analysis is the most suitable one for a single reflow. In the generation of 3D electronic packaging characterized by the miniaturization of electronic products, multiple reflows are generally required during soldering. Indeed, grain boundary diffusion and Cu dissolving into liquid plays an important role in soldering; but for multiple reflow, the Cu volume diffusion through solid IMC grains and cooling effect cannot be ignored anymore; besides, the contribution of grain boundary diffusion should recalculated owing to the increasing blocking of solid phase following reflow cycle in the liquid channel between two adjacent grains. In a word, reassessment of grain
dC =
Kd (Cs − C)dt L0 − L
(10)
Besides,
dC =
Jout −L dt (L 0 − L)ρL
(11)
Combining equations (10) and (11), the flux of Cu from IMC area to liquid Sn through liquid can be written as:
K Jout −L = K d ρL Cs exp ⎛− d ⎞ t ⎝ L 0−L ⎠ ⎜
⎟
The flux of Cu in total for the growth of IMC should be: 7
(12)
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Fig. 11. IMC growth for samples after 60s-reflow at 250 °C under different cooling condition: (a) SEM images for morphology; (b) data for thickness.
Jg = Jin −a + Jin −b − Jout −L
(13)
IMC growth rate should be,
(14)
ρL ⎡ DL (Cb − Ce) E− 7 ⎤ dL = ⎥ ⎢ dt C η ρη ⎣ 3 L2 ⎦
As Jin −b ≫ Jin −a , we can get the IMC growth flux:
Jg = Jin −b − Jout −L
(17)
So,
As
Jg dL = dt C η ρη
1 dL 1 ∝ 2 , L∝ t 3 dt L
(15)
Hence, for a single reflow we hold a conclusion that the IMC growth 1 kinetic is exactly coincided with t 3 and controlled by grain boundary diffusion when L is saturated, but exists a deviation when L is unsaturated. Model for multiple reflows (MMR) is sketched in Fig. 20 (b). Specially, we view the L as saturated in the soldering parts, Jout −L = 0 . Then
The final expression comes as the following:
ρL ⎡ DL (Cb − Ce) E− 7 dL K = − K d Cs exp ⎛− d t⎞ ⎤ 2 ⎥ dt C η ρη ⎢ L 3 L 0−L ⎠ ⎦ ⎝ ⎣ ⎜
⎟
(16)
When the Cu concentration in L has met its limit Cs, Jout −L = 0, the 8
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Fig. 15. IMC dissolution during re-heating stage.
Fig. 12. IMC thickness for HP and AC samples after 60s-reflow at 250 °C.
Fig. 13. Temperature profile and IMC growth during multiple reflows. Fig. 16. IMC dissolving kinetics for heating stage during multiple reflows.
Fig. 17. IMC growth kinetics during the whole multiple reflow process.
Fig. 14. Gibbs free energy VS Cu concentration. The Cu quasi equilibrium concentration in the melt in the vicinity of the substrate (Cb), in the η phase (Cη), and in the melt for stable equilibrium with η phase (Ce) [34].
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But gradually, ω→ 1 with the increase of reflow cycles,
Dŋ (1 − Cŋ)Sa dL = dt CŋL
10−7 3 ωL
≪ Sa , (23)
1 dL 1 ∝ , L∝ t 2 dt L
Clearly, these deductions from the models show highly consistence with the experiment results. 4. Conclusions The abstract of highlight points about evolution and growth kinetics of IMC during multiple reflows include the following: 1 In multiple reflow process, the IMC grows rapidly from scallop grains in isothermal welding to facet type in cooling and transforms back to the scallop of larger size in the next heating stage. Furthermore, only in heat preservation periods of multiple reflows that the annexation behavior of IMC at solder/copper interface takes place, cooling and re-heating simply change the morphology and average thickness of IMC. 2 For every cooling stage in multiple reflows, IMC growth shows linear dependence with time under a given cooling rate. Besides, smaller cooling rates and more reflow cycles can probably lead to massive growth of IMC during multiple reflow process and a suitable cooling rate is important for modern packages. 3 In heating parts of multiple reflows, the dissolution phenomenon of IMC happens as the Cu concentration in η gradually becomes less with temperature lower during cooling, consequently giving rise to a higher Gibbs free energy for η. In other words, IMC formed at a lower temperature will begin to dissolve when the temperature gets higher. 4 The control mechanism for IMC growth during heat preservation has gradually changed from grain boundary to volume diffusion with reflow cycles. During multiple reflows, the total IMC increase can be written as:
Fig. 18. IMC thickness for growth in cooling and dissolution in heating.
these formulas for IMC growth kinetic can be expressed as,
Jin −a = Dŋ Sa ρŋ Jin −b = Dŋ Sb ρŋ
1 − Cŋ (18)
L 1 − Cŋ
(19)
Lb
Here, we define a ω to mark the
Lb ,
Lb
= ωL (0 < ω < 1) , then
Dŋ (1 − Cŋ) dL J S + Jin −b ⎛Sa + b ⎞ = in −a = dt Cŋρŋ CŋL ω⎠ ⎝
(20)
Finally, −7 Dŋ (1 − Cŋ) dL ⎛Sa + 10 ⎞ = dt CŋL 3 ωL ⎠ ⎝ ⎜
When ω→ 0 ,
10−7 3 ωL
⎟
(21)
≫ Sa ,
Dŋ (1 − Cŋ) E− 7 dL = dt 3 ωCŋL2
ktn = k st sns + k ct c − khth
(22)
Fig. 19. SEM images showing cross section of samples after HP and AC.
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Fig. 20. Schematic sketch for IMC growth during multiple reflows: (a): model for a single reflow; (b): model for multiple reflows.
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Table 1 Nomenclature of parameters applied in the equations. Parameter
Nomenclature
C Cŋ Ce Cb C b- C e T Sa Sb Cs Δ DL Dŋ Jin-a Jin-b Jout-l Jg ρL ρŋ MCu MSn Kd
mass fraction of the Cu in liquid content of Cu in IMC layer in mass fraction equilibrium mass fraction of Cu in Sn/IMC interface region equilibrium mass fraction of Cu in Sn/Cu interface region concentration difference in Sn/Cu interface region absolute temperature area ratio of grains per m2 area proportion of grain boundaries per m2 solubility limit of Cu in liquid in mass fraction the length between two grains diffusion coefficient of Cu in liquid Sn diffusion coefficient of Cu in solid IMC flux of Cu from substrate to IMC region through bulk diffusion flux of Cu from solid Cu to IMC region through boundaries flux of Cu from IMC area to liquid Sn through liquid flux of Cu in total for the growth of IMC density of liquid tin density of solid IMC relative atomic mass of Cu relative atomic mass of Sn dissolution rate constant
In the equation, n s varies from 1/3 to 1/2 and n is between 1/3 and 1. These results have provided experimental evidence for our Model for multiple reflows (MMR). Acknowledgements This work was supported by the National Natural Science Foundation of China (Grant Nos. 51571049 and 51675080), China Postdoctoral Science Foundation (Grant Nos. 2017M611215) and National Natural Science Foundation of China through the Research Fund for International Young Scientists (Grant Nos. 51750110504). The synchrotron radiation experiments were performed at the BL13W1 beam line of Shanghai Synchrotron Radiation Facility (SSRF), China. References [1] F. Le, S.W.R. Lee, Q. Zhang, 3D chip stacking with through-silicon-vias (TSVs) for vertical interconnect and underfill dispensing, J. Micromech. Microeng. 27 (2017) 045012. [2] J.H. Lau, Overview and outlook of 3D IC packaging, 3D Si integration, and 3D IC integration, J. Electron. Packag. 136 (2014). [3] Z. Wang, 3-D integration and through-silicon vias in MEMS and microsensors, J. Microelectromech. Syst. 24 (2015) 1211–1244. [4] J.H. Lau, Recent advances and new trends In flip chip technology, J. Electron. Packag. 138 (2016) 030802.
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H.R. Ma et al. [27] M.R. Tonks, D. Gaston, P.C. Millett, D. Andrs, P. Talbot, An object-oriented finite element framework for multiphysics phase field simulations, Comput. Mater. Sci. 51 (2012) 20–29. [28] T. Gancarz, W. Gasior, H. Henein, Physicochemical properties of Sb, Sn, Zn, and SbSn system, Int. J. Thermophys. 34 (2013) 250–266. [29] F. Meydaneri, M. Gündüz, M. Özdemir, B. Saatçi, Determination of thermal conductivities of solid and liquid phases for rich-Sn compositions of Sn-Mg alloy, Met. Mater. Int. 18 (2012) 77–85. [30] A. Kunwar, H. Ma, H. Ma, B. Guo, Z. Meng, N. Zhao, M. Huang, On the thickness of Cu6Sn5 compound at the anode of Cu/liquid Sn/Cu joints undergoing electromigration, J. Mater. Sci. Mater. Electron. 27 (2016) 7699–7706. [31] B. Sundman, U.R. Kattner, M. Palumbo, S.G. Fries, OpenCalphad – a free thermodynamic software, Integr. Mater. Manuf. Innov. 4 (2015) 1. [32] J.M. Koo, Y.H. Lee, S.K. Kim, Mechanical and electrical properties of Sn-3.5Ag Solder/Cu BGA packages during multiple reflows, J. Key Eng. Mater. 297 (2005) 801–806.
[33] Sang-Su Ha, J.-K. Jang, Effect of multiple reflows on interfacial reaction and shear strength of Sn–Ag electroplated solder bumps for flip chip package, Microelectro. Eng. 87 (2010) 517–521. [34] A.M. Gusak, K.N.Tu. Kinetic theory of flux-driven ripening, Phys. Rev. B 66 (2002) 115403. [35] K.N. Tu, Solder Joint Technology, Springer, New York, 2007. [36] M. Schaefer, R.A. Fournelle, J. Liang, Theory for intermetallic phase growth between Cu and liquid Sn-Pb solder based on grain boundary diffusion control, J. Electron. Mater. 27 (1998) 1167–1176. [37] V.I. Dybkov, Growth Kinetics of Chemical Compound Layers, Cambridge Int Science Publishing, 1998. [38] M.L. Huang, F. Yang, Size effect model on kinetics of interfacial reaction between Sn-xAg-yCu solders and Cu substrate, Sci. Rep. 4 (2014) 7117. [39] J.F. Li, S.H. Mannan, M.P. Clode, D.C. Whalley, D.A. Hutt, Interfacial reactions between molten Sn-Bi-X solders and Cu substrates for liquid solder interconnects, Acta Mater. 54 (2006) 2907–2922.
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Intermetallics journal homepage: www.elsevier.com/locate/intermet
Evolution behavior and growth kinetics of intermetallic compounds at Sn/ Cu interface during multiple reflows
T
H.R. Maa, A. Kunwarb, S.Y. Shanga, C.R. Jianga, Y.P. Wanga, H.T. Maa,∗, N. Zhaoa,∗∗ a b
Dalian University of Technology, School of Materials Science and Engineering, Dalian, 116024, China Dalian University of Technology, School of Mechanical Engineering, Dalian, 116024, China
A R T I C L E I N F O
A B S T R A C T
Keywords: A Intermetallics B In situ C Joining D Interfaces E Finite-element modeling
Evolution behavior and growth kinetics of Sn/Cu interfacial intermetallic compound (IMC) during multiple reflows were investigated. Scanning electron microscope (SEM) and shanghai synchrotron radiation facility (SSRF) images have shown that, scallop Cu6Sn5, formed at interface during the heating stage of a reflow, converted to facet type during subsequent cooling, and transformed back to the scalloped grains with larger size during the next re-heating stage. Furthermore, the value of IMC growth time exponent n during soldering gradually changed from 0.405 to 0.485 while nearly kept 1 during cooling and heating with reflow times. In addition, n was 0.613 for the overall multiple reflow process.
1. Introduction Multilayer structure interconnection achieved by 3D chip stacking technology using Through-Silicon Via (TSV) or Flip-chip bonding has advantages of high performance, small shape factor, easy heterogeneous formation, lightweight, low power consumption, lower cost, etc [1–3]. In the current generation of 3D electronic packaging characterized by the miniaturization of electronic products, multiple reflows are generally required during soldering. For example, in the Double-POSSUMTM 3D IC packaging developed by Amkor [4], three daughter dies are flip-chip first attached to a larger mother die which is then attached to the largest grandma die. The grandma die is again flip chip solder bumped on a package substrate, and this whole substrate is then attached on to a PCB (printed circuit board). In general, multiple reflows are inevitably required as flip chip technology is applied to this 3D structure for many times. Interfacial intermetallic compound (IMC), occurring at the interface of solder/substrate, is a crucial factor for the reliability of solder joints [5–7]. Researchers have found that the thickness of IMC will continually increase with reflow times and too much thicker IMC is described to be detrimental for the resultant joint strength and reliability [8–11]. In recent studies concerning multiple reflows, some researchers [12–14] believe the IMC growth is controlled by grain boundary diffusion and the value of time exponent (n) is equal to1/3, but the others [15,16] consider volume diffusion dominates the IMC growth and the value of time exponent n matches1/2. In effect, the conflict between
∗
these two conclusions can be ascribed to the impractical hypothesis that equating multiple reflow process to a long time soldering reaction. This assumption may result in design flaws for solder joints undergoing several reflows. In reality, a solder joint undergoing several cycles of heating and cooling may have its IMC growth influenced by precipitation (magnified during cooling duration) apart from the usual diffusion induced mechanism. The isolation of IMC growth mechanism during a single-reflow cooling [17], that has been mostly avoided by many researchers till now, in fact can be utilized in the rectification of errors during growth kinetics study for multi-reflow soldering. Owing to the practical application of multiple reflow process in 3D electronic packaging, the accuracy in the prediction or determination of associated growth kinetics exponent n has a huge impact in the concurrent materials design in microelectronics industries. In soldering process, synchrotron radiation is a powerful analytical tool that provides information on the interfacial IMC growth in real time. In traditional study, the analysis of IMC growth is always based on the observation for size and morphology after soldering using some exsitu experimental techniques, in other words, most of the IMC thickness data was obtained through rapid cooling and then the dynamic reaction mechanism between liquid solder and substrate under high temperature can be predicted by combing the IMC size and morphology features after cooling. Obviously, this method is unable to observe the IMC growth continuously and lacks accuracy in measurement for IMC size due to the two-dimensional measuring section view. Of course, the analysis of grain growth behavior during soldering is also unscientific.
Corresponding author. Corresponding author. E-mail addresses: [email protected] (H.T. Ma), [email protected] (N. Zhao).
∗∗
https://doi.org/10.1016/j.intermet.2018.01.022 Received 8 November 2017; Received in revised form 26 January 2018; Accepted 31 January 2018 0966-9795/ © 2018 Elsevier Ltd. All rights reserved.
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setup implies keeping the furnace windows open. The parameters, namely resolution ratio and exposure time of the charge coupled device (CCD) camera were designated as 0.325μm/pix and 4s, respectively. The high intensity beam radiation from x-ray source was made to pass through the solder-substrate system and the image presented on the screen by the transmitted beam was recorded by CCD camera. When the X-ray was interfered by the sample, the portion of the incident radiation beam was absorbed by the material and the remaining part is transmitted through the solder system, resulting in the less intensity of the beam after transmission. Actually, the intensity of the beam after transmission would reduce with the increase of density, absorptivity and thickness of the medium. In our liquid Sn/solid Cu interface, the phase absorptivity ranking should be: Cu > IMC > solder. Finally, based on the SSRF image contrast, we measured the IMC thickness. Same materials were used in the ex situ characterization based 60s reflow for 3 times experiment at 250 °C for IMC morphology and size evolution. After each soldering cycle, the specimens were followed by air cooling (AC). Specially, parts of the first 60s-reflow specimens were cooled by other methods: high pressure air blowing (HP, no cooling), furnace cooling (FC) and water cooling (WC). The overview of the procedure for different cooling condition is sketched in Fig. 2, wherein the length of cubical Sn is about 1 mm and Cu substrate is of size 5 mm × 5 mm × 100 m. Then the microstructure of multiple reflow solder joints was analyzed via scanning electron microscope (SEM). For top-view observation of IMC by SEM, the samples were etched by 10% HNO3 solution (in volume) in order to remove the solder away; and for cross-sectional morphology of IMC by SEM, 5% HNO3 +2%HCl+93% C2H5OH (in volume) solution was utilized to surface treat the samples. Scanning electron microscope [Zeiss Supra 55(VP)] was used for obtaining the images of the samples.
Recently, the application of synchrotron radiation on interfacial reaction in electronic packaging becomes increasingly popular and has its unique advantages. For instance, in situ observation on dynamic interfacial grain growth behavior as well as the substrate consumption [18], which is an important scientific issue in linking reliability; connection problem induced by defect evolution including voids and cracks inside solder joints [19]; three-dimensional microstructure variation or deformation in solders [20]; effect of addition elements and particles on size and morphology of interfacial primary crystal [21]; failure locus inside complex part structural solders [22]; can be holistically investigated and used to finally enhance the reliability in electronic devices. This paper investigates the IMC growth behavior during multiple reflows by utilizing the cutting edge experimental technique based on real-time imaging technology of Shanghai Synchrotron Radiation Facility (SSRF). A finite element method (FEM) based numerical model is developed to assess the relative proportion of precipitation and diffusion induced IMC sizes during a single reflow cooling in air, water and furnace media. The FEM model for single reflow and the experimental results for multiple reflow are blinded together to develop the growth kinetics model for multi-reflow soldering. These experimental results can highly help to establish the IMC growth model during multiple reflow process and thereafter achieve an effective tool to improve the overall quality as well as the reliability of the resultant solder joints. 2. Experimental methods and numerical formulation 2.1. Material and experimental procedure Pure Sn (99.95%) solder and pure Cu (99.95%) were used as the materials for SSRF experiment. The experimental setup for observation of interfacial microstructure of liquid Sn/Cu joints by BL13W1 of the Shanghai SSRF is sketched in Fig. 1. The Cu substrate of height 5 mm and thickness 100 μm was butt joined to the solder of 100 μm × 100 μm. This SSRF experiment of four-time reflows was carried out at 300 °C, in which the holding time for the first isothermal reflow was kept for 1 h whereas the later 3 ones had the isothermal reflow keeping time of 20min and the cooling between two consecutive reflows was carried out in air medium. Air cooling for the experimental
2.2. Numerical formulation for copper precipitation in single reflow cooling The most difficult portion for the understanding of the growth kinetics of IMC during cooling is the accounting of mixed mode contribution to the IMC size with diffusion and precipitation effects. Assuming that significant amount of the IMC growth takes place in the liquid-solid interfacial reaction and neglecting the solid state interfacial reaction, the mathematical formulation of compound evolution can be simplified solely to the liquid stage of Sn solder. Furthermore, for the formation of Cu6Sn5 compound with interfacial reaction of Cu substrate with pure liquid Sn; the Cu flux, being the dominant diffusing species, can be considered as the limiting agent [23] and thus the mathematical analysis of mass transfer can be focused only on the transport of Cu species in the medium. As the total size ytotal of Cu6Sn5can be obtained from the in-situ cooling experiments, the determination of precipitation induced compound size can lead to the separation of relative contribution of diffusion and precipitation effects in accordance to the following formula:
ytotal = ydiffusion + yprecipitation
(1)
For a cooling procedure with a given cooling rate, the mass transport equation for Cu species in the liquid Sn medium is given by the following expression [24]:
kprcpt×A L dCCu L [CS,0 − C(T)LS,t] = DCu ∇2 CCu + V dt
(2)
with In partial differential equation (PDE) 2, CCu is the concentration variable with unit mol/cm3 and the term in the left hand side (LHS) is a transient term whereas the first term in the right hand side (RHS) corresponds to a diffusion term. The second term in the RHS is an implicit source term representing precipitation of Cu in the physical domain provided that the time (t) and temperature (T) dependent solubility of Cu in liquid solder C(T)LS,t can be numerically alienated from the solution variable. The material properties kprcpt and CLS,0 are precipitation rate of Cu and saturated solubility of Cu in liquid Sn at the
Fig. 1. In the picture, figure (A) represents the experimental setup for real time imaging of multiple reflow experiments using synchrotron radiation. Figure (B) elaborates the vertical portion of the solder-substrate sample that is irradiated by X-ray.
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Fig. 2. For the ex situ characterization experiments for multiple reflow soldering, figure (a) represents the schematic sketch of the samples undergoing cooling via water, air and furnace at the end of each reflow. The practical approach of multiple reflow with zero cooling rate can be modeled as shown in figure (b) by the use of high pressure air jet to remove the liquid solder at the stage of heat removal for each reflow.
includes the stump and prism types as well. Furthermore, SSRF results also illustrate that for 4-time multiple reflow samples, the number or width of IMC grains at Sn/Cu interface nearly reaches its limitation and almost remains unchanged in the later process after I hour's reflow at 300 °C. Clearly, the transformation of IMC grains between scallop and facet is a kind of reversible behavior in case of invertible temperature variation. However, the facet cannot transform totally back to the scallop and still some left, which can be seen from the area between the yellow and white curves in Fig. 4.
isothermal holding temperature. The symbols A and V represent the cross-section of the interface and volume of the liquid solder respectively. The corresponding growth of Cu6Sn5 or η phase due to precipitation is related to liquid phase rate as following:
vη h×kpart
η η [C(T)S,t ]= − Cconst
kprcpt×A V
[CLS,0 − C(T)LS,t]
(3)
wherein, vη is the interface growth velocity and kpart is the partition coefficient. On the other hand, the evolution of temperature variable (T) in the solder system during cooling is given by the following equation [25]:
∂T + V ∇T⎞ = kth, Sn∇2 T ρSn Cp ⎛ ⎝ ∂t ⎠
3.2. Annexation behavior and growth kinetics of IMC during isothermal welding
(4)
where, the temperature dependence of density ρSn, specific heat capacity Cp and thermal conductivity kth,Sn of solder is duly considered for the cooling procedure. The Biot number of the physical system is less than 0.1 and thus the convection heat transfer in Eq. (4) is neglected, that is ⱱ = 0. The solution of coupled sets of Eqs. (2) and (4) can help in the determination of amount of copper precipitated during the cooling process. Finite element analysis (FEA) is performed in Multiphysics Object Oriented Simulation Environment (MOOSE) Framework [26,27] in order to determine the solution variables CCu and T for these systems of PDEs. The temperature dependent material properties used in the FEA, namely density, thermal conductivity as well as specific heat capacity of Sn and solubility, diffusivity and precipitation rate constant of Cu in liquid Sn are presented in Fig. 3. For transient simulation, the initial conditions for concentration and temperature are provided as 1.59 × 10−3 mol/cm3 and 523.15 K respectively. Zero flux boundary conditions (BCs) are imposed at the boundaries for CCu variable as the solution is always at the saturation limit. For T variable, in context of solder-substrate interface, robin BCs is applied with interfacial heat transfer coefficient, hinterfacial = 11500 × t−0.03 and in other boundaries function Dirichlet BCs are applied in accordance to the given cooling rate.
Fig. 6 plots the average width of IMC grains following the soldering temperature profile. For 3-time reflows, the heat preservation stage characters the IMC annexation phenomenon and greatly increases the grain width. On the contrary, the cooling-heating procedure nearly has no effect on grain numbers causing the stable IMC width throughout this period. Hence, we can infer that only in isothermal welding of multiple reflows that the annexation behavior of IMC at solder/copper interface takes place, cooling and heating simply change the morphology and average thickness of IMC and have no effect on the total number. Kinetically, the thickness increase of a reaction layer in the diffusion couples can be generally expressed by a simple power-law equation [12,13]:
Δ y= ktn
(5)
where Δy is the thickness increase of IMC, k is the growth-rate constant, n is the time exponent and t is the reaction time. Especially, the time exponent n was obtained from the slope of the plot of ln(Δy) versus lnt. Normally, IMC growth based on grain boundary diffusion follows a t1/3 dependence on time t [17]. However, when the growth kinetics of a layer are controlled by volume diffusion through the planar IMC layer, the time exponent should be 1/2, and when controlled by chemical reaction at the interface, the exponent should be 1 [32]. With the current scenario of no any existing experimental works on in-situ study on every cycle of multiple reflows, the IMC growth kinetics for each of the heat preservation stages are demonstrated in Fig. 7. The results exhibit that the values of time exponent n increase from 0.405 to 0.485 with four-time reflow cycles, implying that the control mechanism for IMC growth has gradually changed from grain boundary diffusion to volume diffusion during heat preservation in multiple reflow process. Two factors can contribute to this phenomenon: one is the reduction of grain boundaries due to the annexation behavior of grains in isothermal soldering part; the other is the blocking of grain boundaries owing to un-dissolved cooling (shown in chapter 3.6) IMC in
3. Results and discussion 3.1. IMC morphology evolution during multiple reflows SSRF images for IMC evolution during 4-time multiple reflows at 300°C and SEM top-view pictures for IMC growth during 3-time reflow cycles at 250 °C are shown in Figs. 4 and 5 Clearly, we can observe the IMC rapidly grows from scallop grains in keeping stage (the yellow profile in Fig. 4 and d-f in Fig. 5) to facet type in cooling stage (the red profile in Fig. 4 and g-i in Fig. 5) and transforms back to the scallop (the white profile in Fig. 4 and a-c in Fig. 5) with a larger size during the next re-heating stage. Here, the facet means grains with facets and 3
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Fig. 3. Among the temperature dependent thermophysical properties for the solder-substrate system presented in the figure, density, thermal conductivity, diffusivity, solubility and precipitation rate constant are obtained from Refs. [28–30] whereas specific heat capacity is computed using opencalphad software [31].
nearly has no change since the cooling rate is so high (727 K/s) that the Cu atoms have no time to diffuse. The travel of Cu atoms in liquid is very quick but it still needs time. For AC, the CCu content declines in accordance with the temperature profile inside 60s, but the cooling rate is still too fast for Cu atoms to travel fully. For FC, the solder takes 900s to freeze to solid state and Cu atoms have more time to migrate to the interface area. Of course, FC is the one closest to the equilibrium deposition condition and the final value of CCu in solder is the lowest. Cooling rate is the driven force for IMC growth, but enough reaction time is also an objective condition in deposition. Therefore, the cooling rate should be controlled reasonably in the assessment of IMC growth.
heating stage and the plate-like Cu3Sn under Cu6Sn5 layer, specially the thickness of Cu3Sn layer increases linearly with reflow numbers [33]. Clearly, an increase in reflow cycles will accelerate the transformation of IMC growth control mechanism from grain boundary to volume diffusion.
3.3. Modeling analysis for Cu deposition behavior in cooling The IMC increase in cooling is mainly caused by the decrease of Cu concentration in liquid. For different cooling rate, the deposition of Cu atoms has different characteristic and thus the IMC increase differs as well. When the cooling rate is very small and the deposition behavior can be viewed as a perfect balanced reaction, the Cu content in solder declines along the liquid line in Sn-Cu binary phase diagram. However, most cooling behavior in real experiments belongs to non-equilibrium condition, and is affected by cooling rate. Regardless of the substrate dissolution in cooling, the IMC thickness increase is proportional to the Cu concentration decrease. Fig. 8 visually presents the temperature and Cu concentration variation for WC, AC and FC in the form of colorized graphs. Besides, the detail data can be read from Fig. 9 as well. For WC, the solidification of liquid solder finishes inside 0.06s and the Cu concentration in solder
3.4. IMC growth behavior and kinetics in cooling The cooling condition in SSRF experiment is similar with the FC in modeling analysis in the last chapter. Thus the kinetics calculation in this part is mainly related to the Cu deposition behavior. During cooling, all the values of time exponent n in Fig. 10 agree well with 1. In our previous work [25], actually, we have found IMC growth shows linear dependence with time during cooling stage under a given cooling rate and so n = 1 in the equation (5). Meanwhile, the thickness increase of IMC is related to the instantaneous concentration of Cu in liquid and
Fig. 4. SSRF images for IMC evolution during multiple reflows:(a) (d) (e): after isothermal welding; (b) (e) (h): after cooling; (c) (f) (i): after heating.
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Fig. 5. SEM images for IMC evolution during multiple reflows: (a)–(c): after heating; (d)–(f): after isothermal welding; (g)–(i): after cooling.
the constant k of the precipitation reaction during cooling. For a single short reflow, we can equal the instantaneous CCu in liquid to the composition of utilized solder, so the constant k is only determined by cooling rate and the IMC deposition is under the control of k and t. In fact, t is also related to cooling rate since its increase creates the larger k and smaller t at the same time. As summed up in Fig. 11, four different cooling methods are given by showing the topview morphology and cross-section size of IMC. From HP to FC, the effective reaction time rises from 0 to 20 min approximately while the cooling rate gradually declines, which consequently results in a much larger size of IMC after FC. Moreover, the type of IMC varies from scallop to prism as well. However, the instantaneous CCu cannot be regarded as a constant value due to the prolonged diffusion of Cu from substrate to liquid when it comes to multiple reflows. Results in Fig. 12 indicate that IMC deposition is continually enhanced with reflow cycles for 60s-3-time Sn/Cu samples at 250 °C. Obviously, smaller cooling rates and more reflow cycles can probably lead to massive growth of IMC during multiple reflow process and a suitable cooling rate is important for modern electronic packages.
Fig. 6. Average width of IMC grains VS soldering temperature profile.
3.5. IMC dissolution behavior and kinetics in heating The combination of temperature profile and IMC growth in Fig. 13 provides a direct sight for the size variation in every stage of multiple reflows. Clearly, IMC thickness keeps growing during isothermal soldering and cooling parts until the dissolution phenomenon appears in heating periods. To better understand the essence of IMC dissolving behavior, the following transformation reaction throughout the entire multiple reflow process should be clearly presented:
L⇌η where L means the melt solder and η stands for Cu6Sn5 phase. This reaction controls the thickness variation of IMC during the whole process. From the Sn-Cu binary phase diagram we can know that the copper concentration in η formed under a certain temperature is smaller than that under a higher temperature. Fig. 14 illustrates the relationship between Gibbs free energy and Cu concentration in different reaction materials, revealing that a smaller Cu concentration in η can
Fig. 7. IMC growth kinetics for keeping stage during multiple reflows.
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Fig. 8. Modeling graph results for variation of temperature and Cu concentration in the solder bulk: (A1-A4) and (a1-a4) for WC; (B1-B4) and (b1-b4) for AC; (C1-C4) and (c1-c4) for FC.
In addition, by measuring the IMC thickness in Fig. 18 we find that the size of IMC dissolution in heating is not exactly equal to the size of IMC growth in cooling, and still some IMC generated in cooling left after heating. Comparing the IMC after HP with that after AC in Fig. 19, we can find that the Cu deposits on the surface of the Cu6Sn5 in cooling stage and forms new IMC, which will dissolve in next heating stage. However, the new IMC in the boundary area between two grains is not easy to dissolve as it forms at the beginning of cooling, so that it has similar Cu concentration with the initial IMC. Furthermore, because of the large Cu concentration gradient inside the new IMC of boundary area (Cu/new IMC), diffusion of Cu from substrate to IMC during cooling can raise the Cu concentration in IMC, consequently resulting in the left-IMC. This blocks the grain boundaries and accelerates the changing for n s from 1/3 to 1/2, finally heighten the n for the whole multiple process. Of course, new IMC outside the boundary area may also be kept in heating, but being ignored here because it is very small and has no big effect on the changing of IMC growth control mechanism. Obviously, a large cooling rate and less reflow cycles can greatly reduce the thickness of left IMC and make the Δyc ≈ Δyh as there is no enough time for Cu diffusion.
raise the Gibbs free energy of η under a given temperature according to the Cη-left region. According to the above analysis, expression for the IMC dissolving behavior can be described as the following: Cu concentration in η gradually becomes less with temperature lower during cooling giving rise to a higher Gibbs free energy for η, which can greatly boost the transformation from η to L in the next re-heating stage. That is why the dissolution phenomenon of IMC happens in heating stages of multiple reflow process. In other words, IMC formed at a lower temperature will begin to dissolve when the temperature gets higher. To support our theory, we have added another experiment in which samples were immediately cooled in furnace after melting at 300 °C, so that most of the IMCs were formed under temperatures below 300 °C. Then the average thickness of IMC in the next re-heating respectively under 275 °C, 300 °C and 325 °C was plotted in Fig. 15. It can be found that the size of IMC linearly-decreases rapidly under 325 °C but much slowly under 275 °C in the dissolution stage. This gives a strong evidence for our analysis. According to equation (5), we also get similar n values around 1 for heating stage shown in Fig. 16. This can be explained by the reversible reaction between solidification of L in cooling and dissolution of η in heating, and dissolving in heating is exactly the inverted procedure of growing in cooling. Therefore the n also equals to 1 for heating.
3.7. IMC growth model for multiple reflows At present, there are four models valued in analysis of interfacial IMC growth during a single reflow. Firstly, the ripening or flux-driven ripening (FDR) model developed by K.N. Tu [17,34,35]. In this model, the authors thought the IMC growth was controlled by Cu diffusion through the liquid channel between two adjacent grains and ripening mechanism based on Gibbs-Thomson equation. It can describe the scallop-like Cu6Sn5 growth well, but has some disadvantages simultaneously in the explanations of prims-like Cu6Sn5 growth, influence of cooling process on IMC evolution and size effect on IMC morphology due to its neglect of Cu diffusion from substrate to solder bulk. Secondly, scholar M. Schaefer [36] built a model in which the grain boundary (channels in ripening model) was viewed as the main factor for IMC growth. The surface of Cu6Sn5 grain was regarded as parabolic cap-like in contact with liquid and hexagonal base-like towards Cu substrate. This is an improvement, but this model still ignored the Cu migration from substrate to liquid solder. Thirdly, professor Dybkov [37] raises that the grain growth was dominated by IMC growing and dissolving. In the model, he considered the Cu dissolving from substrate to liquid, but has not valued the contribution of liquid grain boundary to IMC growth. Besides, this model cannot account for the IMC growth in small solders because of the thickness setup of 100 μm for a diffusion barrier layer. Fourthly, Huang [38] established a concentration gradient controlled (CGC) interfacial reaction theoretical model, where the
3.6. IMC growth kinetics throughout the multiple reflow process Generally, most of the research works hither to, simply have been regarding the multiple reflow process as a long time soldering reaction consequently resulting in deduction of some inaccurate or impractical mechanisms for IMC growth. By our above individual analysis for every stage in multiple reflows, the total IMC increase should be:
Δ Y= Δys + Δyc − Δyh where Δys and Δyc mean the increase of IMC in soldering and cooling parts, and Δyh means the decrease of IMC in heating stage. In other forms, the IMC increase can be written as:
ktn = k st sns + k ct c − khth in the equation, k s , k c and kh stand for the growing or dissolving rate of IMC in isothermal welding, cooling and heating; t s , t c and th represent the reacting time in every stage; n s is the time exponent for IMC growth in heat preservation, changing from 1/3 to 1/2 with reflow cycles; k, n are the fitting parameters for the whole process and t is the total keeping time over the solder melting temperature. So n should be a value between 1/3 and 1, which has expressed the result n = 0.613 in Fig. 17. 6
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Fig. 10. IMC growth kinetics for cooling stage during multiple reflows.
boundary diffusion, contribution of volume diffusion through IMC grains and Cu dissolving into liquid bulk should all be considered into the establishment of IMC growth model in multiple reflows. For a single soldering, we propose a model for interfacial IMC growth as sketched in Fig. 20 (a). In this model, we make some hypotheses: (1) grains at Sn/Cu interface are hemispheric during soldering and the average thickness of IMC equals to the grain radius [39]; (2) Cu is the predominant element for IMC growth and Cu3Sn is ignored; (3) the length between two grains is defined as the distance between the two inscribed hexagons and δ = 0.05 μm [34]; (4) the distribution of Cu in L outside the IMC area is uniform. Table 1 gives the nomenclature of parameters applied in the following equations. For the single reflow model, area proportion of grain boundaries per m2 at Sn/Cu interface can be expressed as:
Sb =
3Lδ 3Lδ +
3 3 L2 2
1
=
1+
3L 2δ
(6)
Adding δ = 0.05 μm in,
Sb ≈
10−7 3L
(7)
Sa + Sb = 1 The two fluxes of Cu from substrate to IMC region through bulk and boundary diffusion are:
Jin −a = Dη Sa ρη Fig. 9. Modeling data results for variation of temperature and Cu concentration in the solder bulk: (a) for WC; (b) for AC; (c) for FC.
1 − Cη
Jin −b = DL Sb ρL
(8)
L Cb − Ce L
(9)
The average Cu concentration in L outside the IMC region can be defined as [37]:
Cu concentration gradient was revealed to be the root cause of the size effect. This model has taken the grain boundary diffusion and the Cu dissolving into solder bulk into consideration, but still has no cooling stage. Above all, the last CGC model for IMC growth analysis is the most suitable one for a single reflow. In the generation of 3D electronic packaging characterized by the miniaturization of electronic products, multiple reflows are generally required during soldering. Indeed, grain boundary diffusion and Cu dissolving into liquid plays an important role in soldering; but for multiple reflow, the Cu volume diffusion through solid IMC grains and cooling effect cannot be ignored anymore; besides, the contribution of grain boundary diffusion should recalculated owing to the increasing blocking of solid phase following reflow cycle in the liquid channel between two adjacent grains. In a word, reassessment of grain
dC =
Kd (Cs − C)dt L0 − L
(10)
Besides,
dC =
Jout −L dt (L 0 − L)ρL
(11)
Combining equations (10) and (11), the flux of Cu from IMC area to liquid Sn through liquid can be written as:
K Jout −L = K d ρL Cs exp ⎛− d ⎞ t ⎝ L 0−L ⎠ ⎜
⎟
The flux of Cu in total for the growth of IMC should be: 7
(12)
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Fig. 11. IMC growth for samples after 60s-reflow at 250 °C under different cooling condition: (a) SEM images for morphology; (b) data for thickness.
Jg = Jin −a + Jin −b − Jout −L
(13)
IMC growth rate should be,
(14)
ρL ⎡ DL (Cb − Ce) E− 7 ⎤ dL = ⎥ ⎢ dt C η ρη ⎣ 3 L2 ⎦
As Jin −b ≫ Jin −a , we can get the IMC growth flux:
Jg = Jin −b − Jout −L
(17)
So,
As
Jg dL = dt C η ρη
1 dL 1 ∝ 2 , L∝ t 3 dt L
(15)
Hence, for a single reflow we hold a conclusion that the IMC growth 1 kinetic is exactly coincided with t 3 and controlled by grain boundary diffusion when L is saturated, but exists a deviation when L is unsaturated. Model for multiple reflows (MMR) is sketched in Fig. 20 (b). Specially, we view the L as saturated in the soldering parts, Jout −L = 0 . Then
The final expression comes as the following:
ρL ⎡ DL (Cb − Ce) E− 7 dL K = − K d Cs exp ⎛− d t⎞ ⎤ 2 ⎥ dt C η ρη ⎢ L 3 L 0−L ⎠ ⎦ ⎝ ⎣ ⎜
⎟
(16)
When the Cu concentration in L has met its limit Cs, Jout −L = 0, the 8
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Fig. 15. IMC dissolution during re-heating stage.
Fig. 12. IMC thickness for HP and AC samples after 60s-reflow at 250 °C.
Fig. 13. Temperature profile and IMC growth during multiple reflows. Fig. 16. IMC dissolving kinetics for heating stage during multiple reflows.
Fig. 17. IMC growth kinetics during the whole multiple reflow process.
Fig. 14. Gibbs free energy VS Cu concentration. The Cu quasi equilibrium concentration in the melt in the vicinity of the substrate (Cb), in the η phase (Cη), and in the melt for stable equilibrium with η phase (Ce) [34].
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But gradually, ω→ 1 with the increase of reflow cycles,
Dŋ (1 − Cŋ)Sa dL = dt CŋL
10−7 3 ωL
≪ Sa , (23)
1 dL 1 ∝ , L∝ t 2 dt L
Clearly, these deductions from the models show highly consistence with the experiment results. 4. Conclusions The abstract of highlight points about evolution and growth kinetics of IMC during multiple reflows include the following: 1 In multiple reflow process, the IMC grows rapidly from scallop grains in isothermal welding to facet type in cooling and transforms back to the scallop of larger size in the next heating stage. Furthermore, only in heat preservation periods of multiple reflows that the annexation behavior of IMC at solder/copper interface takes place, cooling and re-heating simply change the morphology and average thickness of IMC. 2 For every cooling stage in multiple reflows, IMC growth shows linear dependence with time under a given cooling rate. Besides, smaller cooling rates and more reflow cycles can probably lead to massive growth of IMC during multiple reflow process and a suitable cooling rate is important for modern packages. 3 In heating parts of multiple reflows, the dissolution phenomenon of IMC happens as the Cu concentration in η gradually becomes less with temperature lower during cooling, consequently giving rise to a higher Gibbs free energy for η. In other words, IMC formed at a lower temperature will begin to dissolve when the temperature gets higher. 4 The control mechanism for IMC growth during heat preservation has gradually changed from grain boundary to volume diffusion with reflow cycles. During multiple reflows, the total IMC increase can be written as:
Fig. 18. IMC thickness for growth in cooling and dissolution in heating.
these formulas for IMC growth kinetic can be expressed as,
Jin −a = Dŋ Sa ρŋ Jin −b = Dŋ Sb ρŋ
1 − Cŋ (18)
L 1 − Cŋ
(19)
Lb
Here, we define a ω to mark the
Lb ,
Lb
= ωL (0 < ω < 1) , then
Dŋ (1 − Cŋ) dL J S + Jin −b ⎛Sa + b ⎞ = in −a = dt Cŋρŋ CŋL ω⎠ ⎝
(20)
Finally, −7 Dŋ (1 − Cŋ) dL ⎛Sa + 10 ⎞ = dt CŋL 3 ωL ⎠ ⎝ ⎜
When ω→ 0 ,
10−7 3 ωL
⎟
(21)
≫ Sa ,
Dŋ (1 − Cŋ) E− 7 dL = dt 3 ωCŋL2
ktn = k st sns + k ct c − khth
(22)
Fig. 19. SEM images showing cross section of samples after HP and AC.
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Fig. 20. Schematic sketch for IMC growth during multiple reflows: (a): model for a single reflow; (b): model for multiple reflows.
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Table 1 Nomenclature of parameters applied in the equations. Parameter
Nomenclature
C Cŋ Ce Cb C b- C e T Sa Sb Cs Δ DL Dŋ Jin-a Jin-b Jout-l Jg ρL ρŋ MCu MSn Kd
mass fraction of the Cu in liquid content of Cu in IMC layer in mass fraction equilibrium mass fraction of Cu in Sn/IMC interface region equilibrium mass fraction of Cu in Sn/Cu interface region concentration difference in Sn/Cu interface region absolute temperature area ratio of grains per m2 area proportion of grain boundaries per m2 solubility limit of Cu in liquid in mass fraction the length between two grains diffusion coefficient of Cu in liquid Sn diffusion coefficient of Cu in solid IMC flux of Cu from substrate to IMC region through bulk diffusion flux of Cu from solid Cu to IMC region through boundaries flux of Cu from IMC area to liquid Sn through liquid flux of Cu in total for the growth of IMC density of liquid tin density of solid IMC relative atomic mass of Cu relative atomic mass of Sn dissolution rate constant
In the equation, n s varies from 1/3 to 1/2 and n is between 1/3 and 1. These results have provided experimental evidence for our Model for multiple reflows (MMR). Acknowledgements This work was supported by the National Natural Science Foundation of China (Grant Nos. 51571049 and 51675080), China Postdoctoral Science Foundation (Grant Nos. 2017M611215) and National Natural Science Foundation of China through the Research Fund for International Young Scientists (Grant Nos. 51750110504). The synchrotron radiation experiments were performed at the BL13W1 beam line of Shanghai Synchrotron Radiation Facility (SSRF), China. References [1] F. Le, S.W.R. Lee, Q. Zhang, 3D chip stacking with through-silicon-vias (TSVs) for vertical interconnect and underfill dispensing, J. Micromech. Microeng. 27 (2017) 045012. [2] J.H. Lau, Overview and outlook of 3D IC packaging, 3D Si integration, and 3D IC integration, J. Electron. Packag. 136 (2014). [3] Z. Wang, 3-D integration and through-silicon vias in MEMS and microsensors, J. Microelectromech. Syst. 24 (2015) 1211–1244. [4] J.H. Lau, Recent advances and new trends In flip chip technology, J. Electron. Packag. 138 (2016) 030802.
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