Because solder joint interconnections are the weaknesses of microelectronic packaging, their reliability has great influence on the reliability of the entire packaging structure. Based on an accelerated life test the reliability assessment and life prediction of leadfree solder joints using Weibull distribution are investigated. The typeI interval censored lifetime data were collected from a thermal cycling test, which was implemented on microelectronic packaging with leadfree ball grid array (BGA) and finepitch ball grid array (FBGA) interconnection structures. The number of cycles to failure of leadfree solder joints is predicted by using a modified Engelmaier fatigue life model and a typeI censored data processing method. Then, the Pan model is employed to calculate the acceleration factor of this test. A comparison of life predictions between the proposed method and the ones calculated directly by Matlab and Minitab is conducted to demonstrate the practicability and effectiveness of the proposed method. At last, failure analysis and microstructure evolution of leadfree solders are carried out to provide useful guidance for the regular maintenance, replacement of substructure, and subsequent processing of electronic products.
With the development of electronic devices, the highintegrity and portability as well as the layout design have become important features of modern electronic devices. However, they are also encountered with some challenges in the electronic industry. The potential random vibrations and thermal shocks directly affect the quality and reliability of electronic devices [
With the increase of environmental protection awareness and the European Union (EU) legislation on restriction of the use of certain hazardous substances (RoHS) and waste electrical and electronic equipment (WEEE) [
The fatigue life of a solder joint is a basic merit of its reliability. Several fatigue life models, including CoffinManson model, Engelmaier model, and Solomon model, have been proposed based on plastic strain of solders [
Generally, it is hard to obtain exact failure time of modern products, especially for electronic products with high reliability. We commonly get different kinds of censored data, such as fixedtime censoring data and fixednumber censoring data, which are separately called typeI and typeII censored data. For censored data, Chen et al. [
In this paper, a thermal cycling test of leadfree ball grid array (BGA) and finepitch ball grid array (FBGA) connection structures is conducted, and failure data are collected. A fatigue life model and a typeI interval censored data processing method are used to predict the cycles to failure of leadfree solder joints. In order to verify the practicability and effectiveness of the proposed method, the results obtained by the proposed method are compared with the ones obtained by Minitab statistical software which is based on the builtin MLE method with twoparameter Weibull distribution. The Matlab curve fitting toolbox is used to check whether the lifetime of solder joint follows the Weibull distribution.
The remainder of this paper is organized as follows. The thermal cycling tests are introduced in Section
This paper focuses on the life prediction of BGA and FBGA (Sn3.0Ag0.5Cu (wt.%)) packages. Figure
Package dimension of the BGA and the FBGA: (a) the BGA package and (b) the FBGA package.
The detail package structure of the BGA (a) basic structure and (b) the details of the BGA.
The samples used in this paper were fabricated on printed circuit board assemblies (PCBAs) with qualified functionality, which have passed online testing, visual testing, and functional testing. Flame Retardant 4 (FR4) substrates with Cu pads were used to assemble various components by SnAgCu solder pasted through a standard surface mounting technology (SMT) process. The
According to the JEDEC Standard of JESD22A104C [
ATC thermal profile.
In the CoffinManson fatigue life model [
Equation (
When
In engineering practice, especially in storage reliability research, the following situation often happens. Suppose that the observation time points are denoted as
The probability density function of the twoparameter Weibull distribution is
The product life distribution function is
And the loglikelihood function is given as follows:
If the range of
When
When all
In order to extrapolate the normal life characteristics, the life characteristics under a high stress should be used. There are four commonly used acceleration models, that is, the Arrhenius model, the inverse power law model, the Eyring model, and the temperaturehumidity model. The acceleration factor (
An extension has been developed by Norris and Landzberg [
The calculation of the
Figure
Optical images (200x) of dye penetration and dye rate. (a) 45%, (b) 100%, (c) 50% under polarized light, (d) 100% under polarized light.
Crack image after 2500 thermal cycles. (a) A complete solder joint and (b) a corner of BGA side.
Figures
SEM image of the solder joint interface at the BGA side after 2500 thermal cycles.
Prior to the use of the Engelmaier fatigue model for life prediction of solder joints, the three parameters in (
The parameters of the Engelmaier fatigue model for (
The parameters for the Engelmaier fatigue model.
Parameters  Explanation  BGA (SAC305)  FBGA (SAC305) 



23.3345  7.7666 

The nominal height of the solder joint (mm)  0.42  0.25 

Cyclic temperature 
165  165 

Empirical correction factor ([0.5, 1.5])  1  1 

Fatigue ductility coefficient  0.325  0.325 

Zero stress reference temperature (°C)  25  25 

A half cycle dwell time (mins)  15  15 
According to the previous studies, the fatigue ductility exponent
The predictions of Engelmaier fatigue model.
The result shown in Figure
Solder joint fails when its dyed area reaches up to 30% or the number of failed solder joints is no less than 10 percent of the total number at observation time
TypeI interval censored data of ATC.
BGA 

0  250  500  750  1000  1500  2000  2500 

0  0  1  0  0  1  1  0  

0  250  500  750  1000  1500  2000  2500  

0  0  0  0  1  0  0  1  


FBGA 

300  600  800  1000  1400  1800  2200  2500 

0  0  0  1  0  0  1  0  

300  600  800  1000  1400  1800  2200  2500  

0  0  0  0  1  0  0  1 
In the case of Weibull distribution, Minitab statistical software is used to analyze the experiment data (for BGA and FBGA) and calculate
The input data of Minitab.
BGA  FBGA  

Initial time (cycles)  Inspection time (cycles)  Failure frequency  Cumulative 
Initial time (cycles)  Inspection time (cycles)  Failure frequency  Cumulative 
0  250  0  0  0  300  0  0 
250  500  5  0  300  600  5  3.68 
500  750  71  0.43  600  800  9  10.29 
750  1000  129  6.58  800  1000  4  13.24 
1000  1500  168  17.75  1000  1400  10  20.59 
1500  2000  74  32.29  1400  1800  17  33.09 
2000  2500  123  41.3  1800  2200  14  43.38 
2500  *  556  51.95  2200  2500  8  49.26 
2500  *  69 
The probability plot of cycles to failure.
The cumulative failure plot of cycles to failure.
At the same time, Matlab curve fitting toolbox is used to analyze the data from this experiment. The fitted curves of the Weibull distribution for the BGA and FBGA solder joints are shown in Figure
The results obtained by using Matlab.
Parameters 


SSE 

RMSE 

BGA  1.658 (1.087, 2.229)  2919  0.0059  0.9709  0.0385 
FBGA  1.769 (1.762, 1.776)  3073  0.00096  0.9947  0.0126 
The fitting curve of Weibull distribution (the BGA and the FBGA).
Analysis of twoparameter Weibull distribution fitting (the BGA and the FBGA).
A comparison of the BGA and the FBGA solders fatigue life obtained using different methods.
Since the CoffinManson is more conservative than the NL model and the Pan model in terms of estimating the acceleration factor, the activation energy of the NL model is calibrated for SnPb solder alloys. In this paper, for SnAgCu solder alloys, the Pan model is used to calculate the acceleration factor for predicting field life. The test condition and parameters of (
Parameters for acceleration factor calculations.
Parameters 



Cycles per hour  Dwell time (mins) 

Test condition  125  −40  165  1  15 
Field condition  80  20  60  0.25  360 
The failure analysis and microstructure evolution of the solder joints in this test show that the fatigue fracture of the leadfree solder joints under thermal cycling test is creep fracture. The crack initiation always occurs in external edges of solders. Cracks are mainly grown at the interface of solder and Cu pad and have a tendency to extend along with the intermetallic compounds (IMC) layer. With the increase of thermal cycles, the IMC layers of solder joints are gradually divided into two layers, namely, Cu_{6}Sn_{5} layer and Cu_{3}Sn layer. Because of the obvious fragility caused by the increase of IMC layer and holes in solders, SnAgCu/Cu interface becomes the weak point of the whole solders with a low strength.
Figure
The basic theory of Matlab curve fitting toolbox is Powell’s Dogleg Method, which is a hybrid algorithm originating from the LevenbergMarquardt method and the Newtonsteepest descent method. Powell’s Dogleg Method is an excellent algorithm for nonlinear curve fitting, and the fitting results have high credibility [
From Table
Using the modified Engelmaier fatigue model to predict solder joint fatigue life (cycles to failure) is only associated with the total shear strain and the modified fatigue ductility exponent, where these two parameters can be obtained easily. Therefore, without considering other effect factors, this model is an effective method for the solder joint lifetime prediction. The results obtained in this paper show that the typeI interval censored data processing method which is applicable for censored data generated from accelerated life tests is an effective method to predict fatigue life of leadfree solder joints.
The modified Engelmaier fatigue model is a reasonable and effective method for estimating the fatigue life of solder interconnects. However, this model is more conservative than other models. Through the analyses of the censored lifetime data of thermal cycling tests, it is found that the typeI censored data processing method is an effective method to predict the life of solder joint. The comparison study carried out using Minitab indicates that the typeI interval censored data processing method can predict the failure life of leadfree solder joint effectively. This study shows that the fatigue fracture of leadfree solder joint under thermal cycling test is creep fracture, and the crack initiation always occurs at the interface of solder and Cu pad. The IMC layer is gradually divided into Cu_{6}Sn_{5} and Cu_{3}Sn layers, and the area close to SnAgCu/Cu interface has become the weak point of the whole solder because of the fragility introduced by the increase of IMC layer and holes in solders. Being the weaknesses of microelectronic packaging, the reliability of solder joint interconnections affects the reliability of the entire structure. The prediction of the solder joint life can offer suggestions for regular maintenance, replacement of substructure, and subsequent processing of electronics.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This research is partially supported by the National Natural Science Foundation of China under the Contract no. 11272082 and the Fundamental Research Funds for the Central Universities under the Contract no. YBXSZC20131040. The authors would like to express special thanks to the cooperation of Regional Technology Center located in Flextronics Zhu Hai Industry Park (B15) and Mr. BY Wu, Mr. C Huang in Flextronics, and Miss ZM Cao in Chongqing University for their helpful discussions. Last, the authors appreciate the reviewers for their constructive comments on this paper.