A Novel Modified Global/Local Approach using the Concept of Optimal Equivalent Solder for Fatigue Reliability Optimization of Stacked Chip BGA Packaging Systems

• Main Authors: Chao-Yang Mao, 毛昭陽
• Other Authors: Rong-Sheng Chen
• Format: Others
• Language: zh-TW
• Published: 2008
• Online Access: http://ndltd.ncl.edu.tw/handle/13405859753850725218

博士 === 國立成功大學 === 工程科學系碩博士班 === 96 === A stacked die package consists of a plurality of chips stacked up one over another for the purposes of reducing occupied space, enhancing functional speed, lowering power dissipation, miniaturizing the structure, and consequently cutting down the costs of the entire package. Due to the stacked structure of the package, the coupling behavior between materials becomes complicate so that the reliability of stacked die package becomes a critical issue to be solved. To study the reliability of solder balls in a stacked die package with complex components, the finite element analysis software is always adopted in addition to the experimental tests. Once a simplified model to the solder ball array in a package can not be applied in the software analysis, the application of a global model to the analysis would cause enormous computing time due to huge amount of elements and nodes. Meanwhile, and a constitutive model which simulates the viscoplasticity of solder balls requires very fine meshing for the purpose of accurate analysis so that immense computing time, costs and data storage space would make it an impossible job. In this paper, a global/local method along with an optimization algorithm, so called the modified submodeling approach of optimal equivalent solder, is developed as a simple but effective approach to predict the deformation and the reliability of solder balls in the package. Such a method can replace the global/local method and verify that the cubic equivalent volume sub-modeling method leads to bigger errors and inaccurate displacement field. The comprisal of equivalent solder in this method is facilitated to obviously reduce the number of elements/nodes so as to not only enhance computing accuracy and efficiency but also save computing time in the analysis of optimal parameters by the design of experiment. To verify the accuracy and efficiency for the modified submodeling approach of optimal equivalent solder, a model of WB-SC stacked die package comprised of die adhesive, real chips/spacer chip, substrate, printed circuit board and solder balls (Sn63/Pb37) is simulated and analyzed. The Anand viscoplasticity constitutive model is adopted to the solder alloys. For the analysis of the strain energy density of solder balls, the Darveaux energy-based fatigue model is taken into to analyze the fatigue reliability of solder balls. Compared with the global detailed mesh method, the global/local method and the cubic equivalent volume sub-modeling method, it is found that the computing time and the hardware space required of the method adopted in this paper are only 18.8% and 9.98% of that by the global refined mesh model respectively. Moreover, under thermal cycling load, the accumulated strain energy density difference between the two models is merely 5.76 %, and the trends of two models coincide with each other. On the other hand, the adopted method is eligible to replace the global/local method since the results of two methods are completely accordant with each other. Therefore, the modified submodeling approach of optimal equivalent solder developed in this paper is recognized as an effective method in computing time and data storage space saving as well as in the analytical accuracy increasing. Additionally, one-factor-at-a-time analysis to the WB-SC BGA stacked die package is conducted in which geometric parameters such as real chip thickness, spacer chip thickness, substrate thickness, PCB thickness and material parameters such as Young’s modulus of encapslant, Young’s modulus of substrate, CTE of encapslant and CTE of substrate are considered. The effects of these 8 parameters on the strain energy density of package and the fatigue life of solder balls are investigated. Subsequently, from the viewpoint of strain energy density distribution for solder balls, the fatigue life of stacked die package is investigated. Then an integrated objective value D is proposed, which integrates the uniform distribution index of strain energy density davg, and the index of the difference between maximum strain energy density and minimum strain energy density, ddiff, into a single objective for the analysis of the experiment design method. Finally the response surface is combined with the genetic algorithm to work on the optimal design of parameters as well as analyze the effect of the interaction among parameters on the integrated objective value D. First of all, the single factor analysis indicates that thicker real chip/space chip, thicker substrate, thinner PCB, encapslant with smaller Young’s modulus, substrate with larger Young’s modulus, encapslant with smaller CTE and substrate with larger CTE, are always facilitated to increase the fatigue life of stacked die package. Next, the response surface method is adopted. To reduce the experiment frequency while geometric factors and material factors are both involved, the following actions are proposed: (1) Neglect the interaction between geometric factors and material factors and set up two individual response surfaces so-called the double response surface method. (2) Take the interaction between geometric factors and material factors into account, and apply the fractional factorial design to select design parameters; then set up a coupled response surface so-called the mixed response surface in which genetic algorithm is introduced to search for the optimal combination of parameters to obtain the optimal fatigue life of solder balls. Furthermore, both the geometric and material response surfaces from the double response surface method are affirmed to be compatible through statistics verification, and the response surface either is a reduced quadratic model, whereas the mixed response surface is recognized as a reduced cubic model. By combining the geometric response surface in the double response surface method with the genetic algorithm, the integrated objective value D is estimated to be 0.2257 MPa(or MJ/m3), which is very closed to the real experimental value D, 0.2255 MPa. This indicates that the prediction by the geometric response surface method is quite accurate. Moreover, both the double response surface method and the one-factor-at-a-time techniques result in the same optimal combination of parameters. As for the optimal design of material parameters, the integrated objective value D is estimated to be 0.1465 MPa, which is quite closed to the real experimental value D, 0.1665 MPa. This again ensures that the material response surface performs very well. Next, the geometric parameter level and the material parameter level are combined together and revised to reach an optimal value. Through the real experiment, the integrated objective value D is obtained as 0.1267MPa, which is less than that of the original package, 0.3123 MPa and the one-factor-at-a-time techniques, 0.1464 MPa. Nevertheless, the fatigue life of solder ball is 1002 cycles, which is better than 804 cycles from the one-factor-at-a-time techniques, and 123.7% greater than that of the original package. On the other hand, the effects of control factors on the integrated objective value D for the response surface method and the one-factor-at-a-time techniques are compared with each other and found to be coincident in trend. This once again verifies the reliability of the double response surface method. Accordingly, by combining the mixed response surface method with the genetic algorithm, the fatigue life of solder balls is obtained as 1041 cycles which is better than 1002 cycles from the double response surface method and 126.3% greater than that of the original package. Yet the integrated objective value D from the mixed response surface method is obtained as 0.1258 MPa which is less than 0.3123 MPa from the original package 0.1464 MPa from the one-factor-at-a-time techniques and 0.1267 MPa from the double response surface method. This indicates that the optimization of the mixed response surface method works well. Furthermore, the analysis-of-variance table shows that although the davg value of 0.0827 MPa from the mixed response surface method is greater than 0.0824 MPa from the double response surface method, thus the ddiff value of 0.1912MPa from the former method is less than 0.1914MPa from the later method. This declares that neither index davg nor index ddiff can be the optimal objective function, yet only the integrated objective value D, which is accordant with the fatigue life of the stacked die package, is proved to be more effective. In addition, the response surfaces of parameters for both the mixed response surface method and the double response surface method are consistent with the contour plots so that the mixed response surface method is again proved to be reliable. In conclusion, the analysis methods, the evaluation index of strain energy density between solder balls as well as the genetic algorithm combined with the mixed response surface method/double response surface method proposed and developed in this paper is eligible to efficiently predict the effect of the design parameters on the accumulated strain energy density of solder balls in stacked die package so that it indeed provides valuable advices for the package design.