Research on Reliability of Nano Silver Tin Pulp in Flip Chip Solder Joint


 The authors have requested that this preprint be withdrawn due to erroneous posting.


Introduction
At present, high-temperature power device chip bonding often uses nano silver paste sintering method, and the joint formed by sintering of nano silver paste has good electrical and thermal conductivity [1] , but there are also the following problems: (1) The sintering temperature of the nano silver paste is in the range of 300 ° C to 400 ° C. This high heating temperature is not compatible with other packaging materials [2] .
(2) The intermetallic compound is not formed after the nano silver paste is sintered, and the joint shear strength is low. Therefore, it is imperative to improve the sintering performance of nano silver paste. There are two general methods. One method is to use a short-chain organic surfactant as a dispersing agent in the preparation of the nano-silver. Generally, such organic matter has a relatively low thermal decomposition temperature and can lower the sintering temperature. However, this makes the dispersibility of the nanosilver worse, increasing the risk of agglomeration of the nanoparticles; the other method is to reduce the particle size of the nano-silver particles, and the melting point of the nanoparticles decreases with the decrease of the particle size, thereby lowering the sintering temperature. However, this makes the production process complicated and costly [3] , which is not conducive to large-scale industrial applications. Adding low-melting alloy elements is a good way to improve the sintering performance of nano-silver solder paste. Among the doped metals, the melting points of tin, indium and gallium are relatively low, but the cost of indium and gallium is relatively high, so we choose nano tin as the Dopant.
The sintering process of tin-doped nano-silver is divided into four stages of dissolution, diffusion, solidi cation and reaction. As the sintering temperature increases, nano-tin diffuses into the nano-silver.
When the Sn melts, the diffusion speed will increase. The liquid phase Sn will contact the solid phase Ag, and the liquid will rise or penetrate along the gap, thereby rapidly diffusing uniformly in the matrix, resulting in matrix lattice changes; after the solidi cation process, the reaction forms an intermetallic compound IMC phase. Finally, an Ag-based replacement solid solution and a uniformly distributed Ag 3 Sn are obtained. The Ag-based replacement solid solution acts as a solid solution strengthening, and Ag 3 Sn acts as a second phase strengthening, thereby increasing the shear strength of the joint [4,5] .
Through my previous experiments, it was determined that the sintering performance of the slurry was the best when the tin content was 5%. According to this ratio, the volume of the Ag 3 Sn particles was about 20% of the volume of the Ag matrix. In this silver tin solder paste, the reinforcing phase Ag 3 Sn particles are very hard, and the plastic deformation of the solder joint is mainly caused by the Ag matrix. Therefore, this paper will regard Ag 3 Sn particles as elastic materials and matrix Ag as viscoplastic materials, which are described by Anand uni ed viscoplastic constitutive model [6] . The uniaxial shear and thermal cycle loading processes were simulated by the nite element method, and the fatigue life of the ip chip solder joints was predicted.
In this study, a series of uniaxial shear tests were performed on ip chip solder joints of silver tin paste.
The reason why shear is introduced into the solder instead of the stretching mode is that the plastic instability caused by necking during stretching can be avoided, and a large strain can be obtained when shearing [7] .

Experimental process
The ip chip used in this article is customized by Wuxi Huajin Semiconductor Co., Ltd., which is a silicon chip containing 54 diameters of 100um solder joints, as shown in Fig. 1.

a)Flip chip (Upper chip) (b Substrate (Lower chip)
The bottom plate is a silicon substrate, and the sample in which the chip and the substrate are welded together by silver tin paste is used for stress strain measurement. The experiment was carried out on a shear tester Dage 4000, the new material was tested for uniaxial shear at three different shear strain rates, high, medium and low, and at various temperatures ranging from room temperature to high temperature.

Experimental results
The shear stress-strain curve of the sample is given in Fig. 2. From Fig. 2, the relationship between the temperature and the stress of the silver tin solder joint can be obtained. In the case of the same strain, the shear strength is inversely proportional to the temperature, and when the temperature is increased to a Page 4/18 certain extent, the shear strength is signi cantly reduced. The relationship between the strain rate and the stress of the silver tin solder joint can also be seen by comparing the three graphs a, b, and c. At the same temperature, the shear strength is proportional to the strain rate,that is, the shear strength increases as the strain rate increases. At the same time, from Figure. 2, it can be seen that the simulation curves of the nite element agree well with the experimental data.

Anand constitutive equation and parameter tting
The Anand model is a viscoplastic model of metal thermal work proposed by Anand and Brown [8] .
Suitable for describing large viscoplastic and small elastic deformations. The characteristics of the uni ed viscoplastic Anand constitutive model are as follows: (1) There is no clear yielding phenomenon during the stress loading process, so the load formula is not required as the standard in the plastic ow process, and the inelastic strain is generated under any size of loading.
(2) The unique internal variable is used to express the macroscopic impedance of the internal state of the object to the inelastic ow. Internal variable (deformation impedances) are marked with s [9] .
The relationship between the saturation stress and the strain rate of the viscoplastic Anand model is as follows: According to the formula derivation and calculation, the parameters of the constitutive equation model of the nano-silver matrix are shown in Table 1 [10] .

ANSYS nite element model
The simpli ed model consists of two parts. The upper and lower symmetrical part is a silicon chip, and the middle is a copper pillar and a silver tin paste sintered layer solder joint. The dimensions of each component are shown in Table 2. According to the previous experiment, the Ag 3 Sn particle diameter was 0.4 µm. According to the volume content of 20%, there were about 32 Ag 3 Sn spherical particles in one solder joint, which were evenly distributed in the silver matrix. In the nite element analysis software ANSYS, since the chip has a completely symmetrical structure, a 1/4 model is selected for research, and a simpli ed 2D FEM model is used for modeling and meshing, as shown in Fig. 3 and Fig. 4. The material of each component is shown in Table 3 and Table 4 [11] . Since the Anand model is used for the research of s 0 nano-Ag matrix in solder joints, the choice of unit type is viscoplastic unit VISCO107, Ag 3 Sn particles and other components in solder joints are regarded as elastomers, so entity unit SOLID45 is selected. [12] .

Loading loads and boundary conditions
The thermal cycle loading is determined according to various conditions that may be encountered during the service process. The temperature range is − 50 °C 150 °C, the lifting temperature rate is 25 °C/min, the temperature is raised to the highest temperature for 10 min, and the lowest temperature is kept for 10 min, and the cycle time is 36 min. It has been studied that the stress and strain of the solder joints show periodic changes during the thermal cycle. Generally, after loading several cycles, and the results will tend to be stable. This model calculates 5 cycles [13] , as shown in Fig. 5.
The substrate is mounted on the xture, and the bottom surface of the lower chip can be applied with zero displacement constraints in each direction, and the two symmetrical planes of the ip chip are applied with one-direction zero displacement constraints.

Calculation Results And Discussion
Alternating changes in displacement and strain occur within the ip chip interconnect material after several thermal cycling conditions have been applied. Figure 6 shows the displacement and strain cloud diagram of the ip chip and solder joint after several thermal cycling conditions. In Fig. 6a, it can be seen that the maximum displacement of the solder joint appears at the center solder joint of the chip. The reason for the analysis may be that the heat dissipation effect at the center is poor and it is a dangerous area. As shown in Fig. 6b, after the end of the thermal cycle loading, there is a large displacement at both ends of the dangerous solder joint, and the displacement at the center of the solder joint is not large. Figure 6c shows that the strain at the contact between the solder and the copper column is large. The main reason is that the thermal expansion coe cients of nano-silver and copper are different, misalignment occurs, and no intermetallic compound is formed between silver and copper, and the interface bonding force is not strong.
Due to the different thermal expansion coe cients of different joint materials, the thermal cycle load is further affected, resulting in different degrees of expansion and deformation at the interface of different materials, resulting in displacement deformation. It can be seen from Fig. 7 that the interface between the copper pillar and the silicon chips and the interface between the solder and the copper pillar have large stresses, and the equivalent stress distribution inside the solder joint is relatively uniform. It can be seen from Fig. 8 that as the number of thermal cycles increases, the equivalent stress is relatively stable and does not change much. However, it can be seen from Fig. 9 that after multiple thermal cycles, the plastic strain of the solder joints has accumulated. It can be inferred that as the thermal cycle is continuously loaded, a large deformation displacement will occur from the middle portion to the periphery, resulting in chip failure.
In order to deeply study the inelastic deformation of ip-chip solder joints under thermal cycling conditions, dangerous solder joints were selected for inelastic strain load history analysis. Figure 10 shows the relationship between inelastic strain and time of hazardous solder joints [14] . As shown in the gure, the inelastic strain keeps rising during the loading process, However, compared with the pure silver paste, the plastic strain of the silver tin paste is signi cantly smaller.
In order to study the fatigue life of solder joints in depth, the nite element prediction model was used to predict the fatigue life of the chip. Co n-Manson is a fatigue life prediction model based on equivalent strain. Engelmaier modi ed the model to add temperature and frequency data to the fatigue ductility index expression. The stress-strain curve obtained by reaching the saturated state under thermal cycling conditions is calculated by modeling and simulation. The inelastic strain increment Δε of the solder joint is found, and the shear strain increment Δγ is further obtained, and then substituted into the following equation, ie Where: ε' f is the fatigue ductility coe cient; N f is the average number of failure cycles; Δγ is the shear strain range; c 1 is the fatigue ductility index [14] .
After calculation and analysis, the fatigue life of pure nano-silver solder joints and silver tin paste solder joints is shown in Table 5. It can be found that the fatigue life of the silver tin paste is signi cantly higher than that of the nano silver paste, mainly due to the addition of the alloying element Sn. After the silver tin paste is welded, Ag 3 Sn particles are produced. This hard and brittle phase IMC will produce a second phase strengthening effect. During the working process, the small IMC will pin the dislocation, thereby increasing the shear strength of the solder joint and prolonging its fatigue life. Therefore, for the nano silver paste solder joints, the doping of low melting point elements can prolong the fatigue life of the solder joints. for the nite element analysis of particle-enhanced nano-solder. 2. Through experiments and nite element simulations, it is determined that the maximum displacement of the ip chip is concentrated at the center solder joint of the chip. After thermal cycling, the plastic strain increases cumulatively, while the equivalent stress remains substantially constant.
3. Through nite element prediction, it is found that the fatigue life of silver tin paste is signi cantly higher than that of nano silver paste, indicating that adding a certain amount of Sn in the nano silver paste can reduce the plastic strain and improve the service life of the solder joint.

Declarations
Data Availability Statement