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1.
We have done experimental research on the dissolution rate and intermetallic growth on Cu, Ni, and CuNi-alloy substrates as a function of time and Cu/Ni ratio of the substrate. Reactions that occur when CuNi metallizations are soldered with lead-free solders were investigated. The experiments were performed using Sn-3.5Ag and Sn-3.8Ag-0.7Cu solders and different CuNi alloys. To determine the rate of dissolution of the substrate material into the solder, CuNi foils of different concentrations were immersed in Sn-3.5Ag and Sn-3.8Ag-0.7Cu solder baths for soldering times ranging from 15 sec to 5 min at 250°C. In addition, reflows of solder balls were made on top of bulk substrates to study the reaction when there is a practically infinite amount of CuNi available compared to the amount of solder. Thin film experiments were also done, where Ni containing under bump metallizations (UBMs) were fabricated and reflowed with eutectic SnAg solder balls. The nickel slows down the dissolution of the UBM into the solder and the formation of intermetallics during reflow compared to Cu metallizations. The solder/UBM interfaces were analyzed with SEM to find out how Ni concentration affects the reaction, and how much Ni is needed to obtain a sufficiently slow reaction rate.  相似文献   

2.
The interfacial reactions between two Sn-Cu (Sn-0.7Cu and Sn-3Cu, wt.%) ball-grid-array (BGA) solders and the Au/Ni/Cu substrate by solid-state isothermal aging were examined at temperatures between 70°C and 170°C for 0 to 100 days. For the Sn-0.7Cu solder, a (Cu,Ni)6Sn5 layer was observed in the samples aged at 70–150°C. After isothermal aging at 170°C for 50 days, the solder/Ni interface exhibited a duplex structure of (Cu,Ni)6Sn5 and (Ni,Cu)3Sn4. For the Sn-3Cu solder, only the (Cu,Ni)6Sn5 layer was formed in all aged samples. Compared to these two Sn-Cu solders, the Cu content in the (Cu,Ni)6Sn5 layer formed at the interface increased with the Cu concentration in the Sn-xCu solders. And, the shear strength was measured to evaluate the effect of the interfacial reactions on the mechanical reliability as a function of aging conditions. The shear strength significantly decreased after aging for 1 day and then remained nearly unchanged by further prolonged aging. In all the samples, the fracture always occurred in the bulk solder. Also, we studied the electrical property of Cu/Sn-3Cu/Cu BGA packages with the number of reflows. The electrical resistivity increased with the number of reflows because of an increase of intermetallic compound (IMC) thickness.  相似文献   

3.
Bi-Sn alloys with high Bi concentration are potential candidates to replace high-Pb alloys as high-temperature Pb-free solders. Interfacial reactions between high-Bi alloys (Sn concentration 2 wt.%, 5 wt.%, and 10 wt.%) and various substrates have been investigated to understand the intermetallic compound formation and interfacial morphological evolution at the joint interface. The substrates investigated include Ni, Au/Ni, Cu, and Ag/Cu layers deposited on Si chips. The interfacial reactions were carried out at 300°C and 120°C to simulate the liquid/solid and solid/solid reactions, respectively, at such solder joints. Experimental results reveal that the intermetallic compound formation and interfacial morphological evolution vary with the substrate and the Sn concentration of the Bi-Sn alloy.  相似文献   

4.
The formation and growth of intermetallics in composite solder   总被引:5,自引:0,他引:5  
The formation and growth of intermetallics at the solder/substrate interface are factors affecting the solderability and reliability of electronic solder joints. This study was performed to better understand the diffusion behavior and microstructural evolution of Cu−Sn intermetallics at the composite solder/copper substrate interface for eutectic solder and solder alloys containing particle additions of Cu, Cu3Sn, Cu6Sn5, Ag, Au, and Ni. Annealing temperatures of 110 to 160°C were used with aging times of 0 to 64 days. The copper-containing composite solders generally formed thinner Cu6Sn5 layers, but thicker Cu3Sn layers than were formed by the eutectic solder alone. These copper-containing additions, therefore, resulted in increased activation energies for Cu6Sn5 formation and decreased activation energies for Cu3Sn formation as compared to the eutectic solder. The activation energy for Cu3Sn formation decreased relative to eutectic solder for silver and gold composite solders even though less Cu3Sn was formed at the substrate interface. Nickel and palladium drastically reduced the Cu3Sn thickness and increased the Cu6Sn5 thickness. However, the Cu6Sn5 contained a substantial volume fraction of voids close to the copper substrate. We propose two mechanisms to explain the effects of the copper-containing and silver particles on the kinetics of intermetallic formation. First, the particles act as tin-sinks which remove tin from the solder and decrease the amount of tin available for reaction at the solder/substrate interface. Second, the particles reduce the cross-sectional area available for tin diffusion, which also reduces the amount of tin available at the interface for reaction.  相似文献   

5.
The interfacial reaction in soldering is a crucial subject for the solder-joint integrity and reliability in electronic packaging technology. However, electronic industries are moving toward lead-free alloys because of environmental concerns. This drive has highlighted the fact that the industry has not yet arrived at a decision for lead-free solders. Among the lead-free alloys, Sn-3.5Ag and Sn-3.5Ag-0.5Cu are the two potential candidates. Here, detailed microstructural studies were carried out to compare the interfacial reaction of Sn-3.5Ag and Sn-3.5Ag-0.5Cu solder with a ball grid array (BGA) Cu substrate for different reflow times. The Cu dissolution from the substrate was observed for different soldering temperatures ranging from 230°C to 250°C, and the dissolution was found to increase with time and temperature. Dissolution of Cu in the Sn-3.5Ag solder is so fast that, at 240°C, 12 μm of the Cu substrate is fully consumed within 5 min. Much less dissolution is observed for the Sn-3.5Ag-0.5Cu solder. In respect to such high dissolution, there is no significant difference observed in the intermetallic compound (IMC) thickness at the interface for both solder alloys. A simplistic theoretical approach is carried out to find out the amount of Cu6Sn5 IMCs in the bulk of the solder by the measurement of the Cu consumption from the substrate and the thickness of the IMCs that form on the interface.  相似文献   

6.
A comparative study of the kinetics of interfacial reaction between the eutectic solders (Sn-3.5Ag, Sn-57Bi, and Sn-38Pb) and electroplated Ni/Pd on Cu substrate (Cu/Ni/NiPd/Ni/Pd) was performed. The interfacial microstructure was characterized by imaging and energy dispersive x-ray analysis in scanning electron microscope (SEM). For a Pd-layer thickness of less than 75 nm, the presence or the absence of Pd-bearing intermetallic was found to be dependent on the reaction temperature. In the case of Sn-3.5Ag solder, we did not observe any Pd-bearing intermetallic after reaction even at 230°C. In the case of Sn-57Bi solder the PdSn4 intermetallic was observed after reaction at 150°C and 180°C, while in the case of Sn-38Pb solder the PdSn4 intermetallic was observed after reaction only at 200°C. The PdSn4 grains were always dispersed in the bulk solder within about 10 μm from the solder/substrate interface. At higher reaction temperatures, there was no Pd-bearing intermetallic due to increased solubility in the liquid solder. The presence or absence of Pd-bearing intermetallic was correlated with the diffusion path in the calculated Pd-Sn-X (X=Ag, Bi, Pb) isothermal sections. In the presence of unconsumed Ni, only Ni3Sn4 intermetallic was observed at the solder-substrate interface by SEM. The presence of Ni3Sn4 intermetallic was consistent with the expected diffusion path based on the calculated Ni-Sn-X (X=Ag, Bi, Pb) isothermal sections. Selective etching of solders revealed that Ni3Sn4 had a faceted scallop morphology. Both the radial growth and the thickening kinetics of Ni3Sn4 intermetallic were studied. In the thickness regime of 0.14 μm to 1.2 μm, the growth kinetics always yielded a time exponent n >3 for liquid-state reaction. The temporal law for coarsening also yielded time exponent m >3. The apparent activation energies for thickening were: 16936J/mol for the Sn-3.5Ag solder, 17804 J/mol for the Sn-57Bi solder, and 25749 J/mol for the Sn-38Pb solder during liquid-state reaction. The corresponding activation energies for coarsening were very similar. However, an apparent activation energy of 37599 J/mol was obtained for the growth of Ni3Sn4 intermetallic layer during solid-state aging of the Sn-57Bi/substrate diffusion couples. The kinetic parameters associated with thickening and radial growth were discussed in terms of current theories.  相似文献   

7.
Soldering with the lead-free tin-base alloys requires substantially higher temperatures (∼235–250°C) than those (213–223°C) required for the current tin-lead solders, and the rates for intermetallic compound (IMC) growth and substrate dissolution are known to be significantly greater for these alloys. In this study, the IMC growth kinetics for Sn-3.7Ag, Sn-0.7Cu, and Sn-3.8Ag-0.7Cu solders on Cu substrates and for Sn-3.8Ag-0.7Cu solder with three different substrates (Cu, Ni, and Fe-42Ni) are investigated. For all three solders on Cu, a thick scalloped layer of η phase (Cu6Sn5) and a thin layer of ε phase (Cu3Sn) were observed to form, with the growth of the layers being fastest for the Sn-3.8Ag-0.7Cu alloy and slowest for the Sn-3.7Ag alloy. For the Sn-3.8Ag-0.7Cu solder on Ni, only a relatively uniform thick layer of η phase (Cu,Ni)6Sn5 growing faster than that on the Cu substrate was found to form. IMC growth in both cases appears to be controlled by grain-boundary diffusion through the IMC layer. For the Fe-42Ni substrate with the Sn-3.8Ag-0.7Cu, only a very thin layer of (Fe,Ni)Sn2 was observed to develop.  相似文献   

8.
Au-Ge-based alloys are interesting as novel high-temperature lead-free solders because of their low melting point, good thermal and electrical conductivity, and high corrosion resistance. In the present work, the wetting and soldering behavior of the eutectic Au-28Ge (at.%) alloy on Cu and Ni substrates have been investigated. Good wetting on both substrates with final contact angles of 13° to 14° was observed. In addition, solder joints with bond shear strength of 30 MPa to 35 MPa could be produced under controlled conditions. Cu substrates exhibit pronounced dissolution into the Au-Ge filler metal. On Ni substrates, the NiGe intermetallic compound was formed at the filler/substrate interface, which prevents dissolution of Ni into the solder. Using thin filler metal foils (25 μm), complete consumption of Ge in the reaction at the Ni interface was observed, leading to the formation of an almost pure Au layer in the soldering zone.  相似文献   

9.
A Pb-free composite solder is prepared with a Pb-free solder substrate and a plated-indium layer. The indium layer melts during the soldering process, wets the substrates, and forms a sound solder joint. Since the melting temperature of indium is 156.6°C, lower than that of the eutectic Sn-Pb, which is at 183°C, the soldering process can be carried out at a temperature lower than that of the conventional soldering process. Composite solder joints with three different Pb-free solders, Sn, Sn-3.5 wt.% Ag, and Sn-3.5 wt.% Ag-0.5 wt.% Cu, and two substrates, Ni and Cu, are prepared. The interfaces between the indium layer, Pb-free solder, and Ni and Cu substrate are examined. A good solder joint is formed after a 2-min reflow at 170°C. A very thick reaction zone at the indium/Pb-free solder interface and a thin reaction layer at the indium/substrate interface are observed.  相似文献   

10.
The effect of aging on the evolution of interfacial microstructure and mechanical properties of Pb-rich PbSnAg solder joints with different Sn content was investigated. Tensile samples were prepared by soldering two pieces of Ni or Cu strips resulting in joints with gap sizes of about 250 μm. Multi-layered structures composed of Ni coated Si-chips soldered onto Ni/Cu metallized ceramic substrates were used for fatigue testing. All samples were subjected to thermal aging at 250 °C up to 500 h. Microstructural investigations revealed that independent from the substrate material, increased Sn content of the solder alloy results in improvement of the tensile and fatigue properties of the joints and a higher growth rate of the interfacial intermetallic compound (IMC) layers. It was found that the thickness of the wettable substrate especially in the case of low-Sn alloys, also affects the interfacial properties of high temperature PbSnAg solder joints. In this case, a reduced Sn content in solder joints results in weakening of the interface during the reflow process and subsequent thermal aging. The dominant failure mode of the solder joints subjected to cyclic loading was delamination of the interfacial IMC layer from the substrate. Finite element simulations were conducted by using a strain rate and pressure dependent material model for PbSnAg solder in order to analyse the states of stress and strain during static and cyclic loading.  相似文献   

11.
The near-eutectic Sn-3.5 wt.% Ag-0.7 wt.% Cu (Sn-3.5Ag-0.7Cu) alloy was doped with rare earth (RE) elements of primarily Ce and La of 0.05–0.25 wt.% to form Sn-3.5Ag-0.7Cu-xRE solder alloys. The aim of this research was to investigate the effect of the addition of RE elements on the microstructure and solderability of this alloy. Sn-3.5Ag-0.7Cu-xRE solders were soldered on copper coupons. The thickness of the intermetallic layer (IML) formed between the solder and Cu substrate just after soldering, as well as after thermal aging at 170°C up to 1000 h, was investigated. It was found that, due to the addition of the RE elements, the size of the Sn grains was reduced. In particular, the addition of 0.1wt.%RE to the Sn-3.5Ag-0.7Cu solder improved the wetting behavior. Besides, the IML growth during thermal aging was inhibited.  相似文献   

12.
The interfacial reaction between two prototype multicomponent lead-free solders, Sn-3.4Ag-1Bi-0.7Cu-4In and Sn-3.4Ag-3Bi-0.7Cu-4In (mass%), and Ag, Cu, Ni, and Pd substrates are studied at 250°C and 150°C. The microstructural characterization of the solder bumps is carried out by scanning electron microscopy (SEM) coupled with energy dispersive x-ray analysis. Ambient temperature, isotropic elastic properties (bulk, shear, and Young’s moduli and Poisson’s ratio) of these solders along with eutectic Sn-Ag, Sn-Bi, and Sn-Zn solders are measured. The isotropic elastic moduli of multicomponent solders are very similar to the eutectic Sn-Ag solder. The measured solubility of the base metal in liquid solders at 250°C agrees very well with the solubility limits reported in assessed Sn-X (X=Ag, Cu, Ni, Pd) phase diagrams. The measured contact angles were generally less than 15° on Cu and Pd substrates, while they were between 25° and 30° on Ag and Ni substrates. The observed intermediate phases in Ag/solder couples were Ag3Sn after reflow at 250°C and Ag3Sn and ζ (Ag-Sn) after solid-state aging at 150°C. In Cu/solder and Ni/solder couples, the interfacial phases were Cu6Sn5 and (Cu,Ni)6Sn5, respectively. In Pd/solder couples, only PdSn4 after 60-sec reflow, while both PdSn4 and PdSn3 after 300-sec reflow, were observed.  相似文献   

13.
The growth behavior of interfacial intermetallic compounds (IMCs) of SnAgCu/Cu soldered joints was investigated during the reflow process, isothermal aging, and thermal cycling with a focus on the influence of these parameters on growth kinetics. The SnAgCu/Cu soldered joints were isothermally aged at 125°C, 150°C, and 175°C while the thermal cycling was performed within the temperature ranges from −25°C to 125°C and −40°C to 125°C. It was observed that a Cu6Sn5 layer formed, followed by rapid coarsening at the solder/Cu interface during reflowing. The grain size of the interfacial Cu6Sn5 was found to increase with aging time, and the morphology evolved from scallop-like to needle-like to rod-like and finally to particles. The rod-like Ag3Sn phase was formed on the solder side in front of the previously formed Cu6Sn5 layer. However, when subject to an increase of the aging time, the Cu3Sn phase was formed at the interface of the Cu6Sn5 layer and Cu substrate. The IMC growth rate increased with aging temperature for isothermally aged joints. During thermal cycling, the thickness of the IMC layer was found to increase with the number of thermal cycles, although the growth rate was slower than that for isothermal aging. The dwell time at the high-temperature end of the thermal cycles was found to significantly influence the growth rate of the IMCs. The growth of the IMCs, for both isothermal aging and thermal cycling, was found to be Arrhenius with aging temperature, and the corresponding diffusion factor and activation energy were obtained by data fitting. The tensile strength of the soldered joints decreased with increasing aging time. Consequently, the fracture site of the soldered joints migrated from the solder matrix to the interfacial Cu6Sn5 layer. Finally, the shear strength of the joints was found to decrease with both an increase in the number of thermal cycles and a decrease in the dwell temperature at the low end of the thermal cycle.  相似文献   

14.
高温高铅焊料无铅化的研究进展   总被引:2,自引:0,他引:2  
微电子封装工业中应用于高温领域的高铅焊料的无铅化是一个国际化难题。对目前高温无铅焊料的研究进展进行了综述,包括80Au-20Sn、Bi基合金、Sn-Sb基合金和Zn-Al基合金。从各种焊料的熔化行为、力学性能、导电导热性能、润湿性、界面反应和可靠性等方面,总结了这些高温无铅焊料的特性以及在应用中各自存在的问题。通过比较,认为Sn-Sb基合金在高温领域取代高铅焊料将有很大的应用前景。  相似文献   

15.
Since both Ag and In are important melting point depressants in Sn–Zn based solders, a series Sn–Zn based solders with various amounts of Ag and In additions was studied in the experiment. The melting behavior of solder alloys, wetting characteristics, coefficients of thermal expansion, microstructural evolution and long-term reliability of the selected Sn–Zn based solder on Au/Ni–P metallized copper substrate were examined. Based on the experimental result, there is little change in the melting range of Sn–Zn based solder alloys by minor addition of Ag. On the contrary, the melting point of Sn–Zn based alloys can be effectively decreased by In additions. However, the difference between solidus and liquidus temperature is broadened as the increment of In into Sn–Zn based solders. 76Sn–9Zn–15In has the lowest liquidus temperature among all alloys, and it can effectively bond the Au/Ni–P metallized copper substrate. The microstructure of 76Sn–9Zn–15In alloy soldered at 200 °C for 20 min is primarily comprised of Sn–In γ phase and needle-like ZnO2. Since there is no flux usage during soldering, zinc oxide cannot be avoided even the process performed under 2×10−2 mbar vacuum environment. It is also noted that there is no interfacial reaction layer between 76Sn–9Zn–15In and Au/Ni–P metallized copper substrate after soldering. However, there is a reaction layer between 76Sn–9Zn–15In and substrate as the soldered specimen aged at 90 °C for 168 h. Its chemical composition is close to Zn-rich γ phase (NiZn3) alloyed with minor Sn, In, Cu and P. For the specimen further aged at 90 °C for 336 h, there are cracks along the interface between solder alloy and electroless Ni–P layer. The oxidation of the interfacial Zn-rich γ phase plays an important role in deterioration of the bonding between 76Sn–9Zn–15In and Au/Ni–P metallized copper substrate.  相似文献   

16.
The Cu/SnAg double-bump structure is a promising candidate for fine-pitch flip-chip applications. In this study, the interfacial reactions of Cu (60 μm)/SnAg (20 μm) double-bump flip chip assemblies with a 100 μm pitch were investigated. Two types of thermal treatments, multiple reflows and thermal aging, were performed to evaluate the thermal reliability of Cu/SnAg flip-chip assemblies on organic printed circuit boards (PCBs). After these thermal treatments, the resulting intermetallic compounds (IMCs) were identified with scanning electron microscopy (SEM), and the contact resistance was measured using a daisy-chain and a four-point Kelvin structure. Several types of intermetallic compounds form at the Cu column/SnAg solder interface and the SnAg solder/Ni pad interface. In the case of flip-chip samples reflowed at 250°C and 280°C, Cu6Sn5 and (Cu, Ni)6Sn5 IMCs were found at the Cu/SnAg and SnAg/Ni interfaces, respectively. In addition, an abnormal Ag3Sn phase was detected inside the SnAg solder. However, no changes were found in the electrical contact resistance in spite of severe IMC formation in the SnAg solder after five reflows. In thermally aged flip-chip samples, Cu6Sn5 and Cu3Sn IMCs were found at the Cu/SnAg interface, and (Cu, Ni)6Sn5 IMCs were found at the SnAg/Ni interface. However, Ag3Sn IMCs were not observed, even for longer aging times and higher temperatures. The growth of Cu3Sn IMCs at the Cu/SnAg interface was found to lead to the formation of Kirkendall voids inside the Cu3Sn IMCs and linked voids within the Cu3Sn/Cu column interfaces. These voids became more evident when the aging time and temperature increased. The contact resistance was found to be nearly unchanged after 2000 h at 125°C, but increases slightly at 150°C, and a number of Cu/SnAg joints failed after 2000 h. This failure was caused by a reduction in the contact area due to the formation of Kirkendall and linked voids at the Cu column/Cu3Sn IMC interface.  相似文献   

17.
Au over Ni on Cu is a widely used printed circuit board (PCB) surface finish, under bump metallization (UBM), and component lead metallization. It is generally accepted that less than 3 wt.% Au in Sn-Pb solder joints inhibits formation of detrimental intermetallic compounds (IMC). However, the critical limit for Au content in Pb-free solder joints is not well established. Three surface-mount package platforms, one with a matte Sn surface finish and the others with Ni/Au finish, were soldered to Ni/Au-finished PCB using Sn-3.0Ag-0.5Cu (SAC305) solder, in a realistic manufacturing setting. The assembled boards were divided into three groups: one without any thermal treatment, one subjected to isothermal aging at 125°C for 30 days, and the third group aged at 125°C for 56 days. Representative solder joints were cross-sectioned and analyzed using scanning electron microscopy (SEM) and energy-dispersive x-ray spectroscopy (EDX) to investigate the evolution of the solder joint morphology as a function of Au content and isothermal aging. It was found that, if Cu is available to dissolve in the solder joint, the migration of AuSn4 from the bulk to the interface as a result of thermal aging is mitigated.  相似文献   

18.
SnAgCu is one of the most promising candidates for lead-free solders to replace conventional eutectic SnPb solders. The effects of solder volume on interfacial reactions and microstructure evolution in Ni/Au-SnAgCu-Ni(P) solder joints have been investigated under soldering and thermal aging conditions. The results show that solder volume has a strong effect on the formation of Au-containing intermetallic compounds (IMCs) and their redeposition at the interfaces. The size and volume fraction of Au-containing IMCs dispersed in the solder bulk increased with decreasing solder joint dimensions. For the small solder joint with 300-μm solder ball, the (Au,Ni)Sn4 IMCs redeposited to the interfaces after thermal aging at 150°C for 9 days, but this was not observed for the other two solder joints with large solder volume. These results also indicate that the redeposition of (Au,Ni)Sn4 is closely associated with the migration of Cu toward the interfaces.  相似文献   

19.
Nano-sized, nonreacting, noncoarsening oxide dispersoids have been incorporated into solder alloys to create a new, improved solder structure with an ultrafine grain size of ∼200–500 nm. The new solders exhibit significantly enhanced creep resistance combined with increased strength. The well-known thermal instability problem with ultrafine-grained structure appears to have been overcome in these solder alloys and the microstructure was seen to be quite stable upon high temperature exposure (e.g. 120°C). This is attributed to the presence of very fine dispersoid particles which impede grain boundary sliding and dislocation movement. The dispersions are seen to have a profound effect on the mechanical deformation characteristics of the solders with respect to creep. As much as three orders of magnitude reduction in the steady state creep rate has been achieved. The new solders also exhibit improved ductility under high strain rate deformation and improved strength (4–5 times higher tensile strength) at low strain rates. It is demonstrated that with a dispersion of TiO2 particles, the Pb-Sn eutectic solder with a melting point of 183°C can be made more creep-resistant than the 80Au-20Sn eutectic solder with a much higher melting point of 278°C. The new creep-resistant solders can be useful for optical and optoelectronic packaging in which dimensional stability of the assembled structure is essential.  相似文献   

20.
The adhesion strength of A lead-free solder hot-dipped on copper substrate   总被引:1,自引:0,他引:1  
Eutectic Sn-Zn-Al solder alloy was used [composition: 91Sn-9(5Al-Zn)] to investigate the effects of dipping parameters such as the temperature, rate and time dipping on the adhesion strength between solder and substrate using dimethylammonium chloride (DMAHCl) flux. The optimum conditions for the highest adhesion strength (about 8 MPa) were determined as dipping at 350°C, and a rate of 10.8∼11.8 mm/s for 5∼7.5 min. A poor solder coating was obtained as dipped at 250°C. Some defects by non-wetting were found as dipped at a slow rate (slower than 8.2 mm/s). Quite different from the most tin-based solders for copper substrate, γ-Cu5Zn8 intermetallic compound particles were found by x-ray diffraction (XRD) analysis at the interface of solder and substrate as dipped at 300°C after pull-off test by etching out the unreacted solder layer. The morphology of the intermetallic compound formed was observed by scanning electron microscopy (SEM). The elements of Al (near Cu), Zn (near Sn) are enriched at the interface of solder and copper substrate as determined by the line scanning and mapping analysis.  相似文献   

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