Probability of Failure for the Thermal Fatigue Life of Solder Joints in BGA Packaging using FORM and MCS Methods

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1 International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:17 No:04 1 Probability of Failure for the Thermal Fatigue Life of Solder Joints in BGA Packaging using FORM and MCS Methods Zakaria EL HADDAD, Othmane BENDAOU, Larbi EL BAKKALI Abdelmalek Essaâdi University, Faculty of Sciences, Modeling and Simulation of Mechanical Systems Laboratory BP.2121, Mhannech, 93030, Tetouan, Morocco Zakaria_elhaddad@hotmail.fr Abstract Nowadays, microelectronics plays a key role in our daily lives, such as communication, transportation, embedded systems, medicine etc, so we need to make sure that we can rely on microelectronics systems, while considering the thermal and vibratory fatigue, to make sure of that a lot of methods and simulation were introduced into the process of manufacturing. The reliability and fatigue life prediction of a system is an important problem in product design field, These problems are caused by the fatal flaw of the microelectronic packaging which contain solder joints, their reliability has a great impact on the reliability of the entire packaging structure. The cause of the fatigue failure of solder joints is usually caused by the accumulation of thermo-mechanical damages due to the operating conditions of thermal and mechanical shock. To predict the fatigue life of solder joints in ball grid array (BGA) packaging, finite element analysis methods are mostly used but this tool is not enough since they are based on a deterministic approach; the variability of the input parameters are neglected by this approach, which has an impact on the output of the model. Thus, we need to use a probabilistic approach. In this paper, we focused on the major factor of failure for solder joints as known as thermal fatigue. A finite element analysis using ANSYS APDL was used to predict the fatigue life of the most critical solder joint under thermal cycle loading. The failure probability of the most critical solder joint of the microelectronic packaging is defined using two methods of numerical study of probabilistic methods which are: The First Order Reliability Method (FORM) and Monte Carlo Simulation (MCS). Index Term-- Microelectronics; reliability; fatigue life prediction solder joints; thermo-mechanical damages; BGA packaging; thermal cycle loading; failure probability; FORM; MCS. I. INTRODUCTION In this generation, electronic products play a crucial role in our daily life. Within all the reliability concerns about electronic products, solder joints that provide mechanical and electronic connections are one of the major factor reliability concerns. In this study, the solder joints of ball grid array (BGA) packages are studied since BGA packages are extremely popular in the electronics industry [1-5]. Soldering is known from the dawn of the history as the most effective technology in the electronic industry. That is why the lifetime of the solder joints have to be predicted. It lifetime estimation is depending on the degree of modeling accuracy of the stress and strain related to the strength of the solder joint [6]. The aim of this work is to realize a statistical based simulation model which can predict the fatigue failure of solder joints under cyclic thermal loading environments. This paper presents a study of the reliability of critical solder joints in an electronic package BGA. The principal cause of failure in solder joints is mainly the thermo-mechanical stresses, caused by the differences in the coefficient of thermal expansion (CTE) between the chip and the substrate [7-9]. Also, the package variables including the package size, the die size, the pitch, the number of balls, the Distance of the solder joint from the Neutral Point (DNP), the mold compound as well as the substrate material affects the failure life of solder joints. However, it is not easy to consider all of the variables. To overcome these problems, a probabilistic model is developed and applied to evaluate the number of cycles to failure of the critical solder joint of a package-assembled circuit board of an electronic product. This model is based on Finite Element Modeling, as well as statistical methods such as the First Order Reliability Method (FORM) and Monte Carlo Simulation (MCS). II. MATERIALS AND METHODS A. Package dimensions The model is composed of 64 solder balls and 8 balls in each direction (X and Z) as shown in figure (1). The pitch is 0.8 mm, die and substrate sizes are given as (5.2*5.2*0.3) and (8*8*0.075). And the PCB size is (18*18*0.692).

2 International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:17 No:04 2 Fig. 1. The dimension and schematic of BGA Package. TABLE I SHOWS THE PACKAGE PARAMETER FOR EACH COMPONENT Parameter Substrate Solder Joint standoff heights Solder Joint Pitch PCB FR4 PCB Polymide PCB Die Die attach Molding compound Solder mask Adhesive Copper pad diameter Copper pad thickness Dimensions (mm) 8*8*0.075 mm mm 0.8 mm 18*18*0.692 mm3 18*18*0.592 mm3 18*18*0.05 mm3 5.2*5.2*0.3 mm3 5.2*5.2*0.07 mm3 8*8*0.730 mm3 8*8*0.048 mm3 8*8*0.012 mm mm mm TABLE II MATERIAL PROPERTIES Young s Material Modulus CTE (ppm/ C) Poisson s Ratio (MPa) Substrate Solder (SnPb) Copper Die (Si) FR Polyimide dhesive Solder Mask Die-attach Mold C. FEA modeling In our problem, we used the Finite Element Methods (FEM) to predict the numerical value of the mechanical solder joint s degradation caused by the repeated thermal power cycling, leading to fissure and cracking of the solder joint. In this part, we are going to describe the analysis steps for creating a nonlinear global model with a nonlinear sub-model. The following steps are created in ANSYS Step 1: global model The goal of global modeling is to identify the most critical solder joints and to provide a deriving boundary condition for the sub-modeling analysis. The symmetrical plane of the global model is comprised of one-eighth of the entire package as shown in figure (3). B. Package materials and properties The model is a 3D dimensional model of a triangular shape consisting of the following materials: Solder joint, substrate, PCB, Die, Die attach, copper pad, solder mask, adhesive and molding compound. Their properties are detailed in figure (2), table (2) and table (3) Fig. 3. global Finite Element Model of BGA package. The symmetrical boundary conditions are applied along the center line of the PCB, and node of diagonal bottom center of PCB is constrained with boundary condition Ux=Uy=Uz=0 to prevent free body translation. Step 2: Sub-modeling The sub-modeling contains the most critical solder joint, located in the package, where the maximum accumulated Plastic work (NLPLWK) of the end of the last thermal cycle takes place. As shown in figure (4) Fig. 2. Side view of BGA package model

3 International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:17 No:04 3 In this equation, N f represents the number of cycles to failure and ε p is the plastic (inelastic) strain range and K and n are the model constants. As Coffin-Manson is a general relation for the metals, numerous researchers have modified this equation to cover different parameters and interactions, which have impacts in the fatigue behavior, and calculating the relevant constants. The following equation shows the modified version of Coffin Manson used for the low cycle fatigue of the Sn/Pb solders D. Temperature Cycle Profiles Fig. 4. Local sub-model The thermal cycle profile is applied to the thermal loading of the global model. According to the JEDEC Standard of JESD22-A104C [10], we used the cycle temperature profile alternates from -40 C for low temperature, and 125 C for high temperature and 15 minutes for ramp and dwell time as presented in the figure (5). N f = 1 ( γ 2 2ε ) (1 c ) (2) f Where, Nf =mean cycles to failure Δγ= The cyclic shear strain range ε f = fatigue ductility coefficient C= fatigue ductility exponent C Ts ln 1 td Where, Ts = mean cyclic solder joint temperature t D = half-cycle dwell time (min) =15min The cyclic shear strain range is given by F. LD.. T (4) h (3) Fig. 5.Thermal cycle loading III. FATIGUE LIFE MODEL The generally, mechatronic devices experience failure due to solder joint fatigue provoked by thermo mechanical damage mechanisms during the component operation life. To predict the life of these solder joints we used combining finite element simulations and the thermal fatigue model. Which is obtained by the use of experimental data and accelerated testing. The model will help us to determine the number of cycles a component could resist before its fatigue life. There are several fatigue life models proposed by various investigators such as: Draveaux, Farooq, Perkins, Park, Engelmaier the model we will be using in this study is the Coffin Manson Fatigue model, because of the results given in modeling the crack growth in solders, and its success with repetition in temperature cycling. Coffin Manson has taken into account three major factors: maximum temperature T max, temperature change ΔT, and cycling frequency. The equation, which was introduced in the 1950 s, has been used in fatigue life prediction applications. N f = Kε p n (1) Where, F = empirical nonideal factor indicative of deviations of real solder joints from idealizing assumptions and accounting for secondary and frequently untractable effects F 1.27 for column-like leadless solder attachments, F 1.0 for solder attachments utilizing compliant leads LD = Distance of the solder joint from the Neutral Point (DNP) h = solder joint height, solder diameter Δα= absolute difference in coefficients of thermal expansion of solder joint and substrate, CTE ΔT = cyclic temperature swing Thus, from combining (2), and (5), the cyclic life of surface mount solder attachment is obtained as [13] 1 1 F. LD.. T C N f (5) 2 2 '. h IV. PROBABILISTIC METHODS In The aim of probabilistic methods is to deal with the uncertainties emerging from the random changes in geometry dimension of packaging assembly; material properties and thermal expansion mismatch (CTE). These approaches are used to increase the design s robustness and to estimate the impact of parameter uncertainties in the system response. Furthermore, the combination between the probabilistic methods and the

4 International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:17 No:04 4 finite element simulation does not allow the establishment of the scope and the boundaries of the usual deterministic approach but it also gives it an improvement by giving more information and increasing the effectiveness of the use of the empirical data. The probabilistic structural methods lie in the determination failure probability of a given structural system. This approach represents the next step of the deterministic analysis inputs for random variables. The Monte Carlo simulations (MCS) and the First Order Reliability Method (FORM) are widely used to outline the random response and the probability density function (PDF) of the response. To proceed with this method, we have firstly to define the design variables Xi (i=1, 2,., n) having an important level of fluctuation. Secondly, we have to define the number of potential failure scenarios, each one of them needs a performance function G(xi), which splits the space into two regions of the variables: safety domain G(xi) > 0 and failure domain G(xi) 0. The limit between these two domains is defined by G(x) = 0, which is called the limit state function. The failure probability is given by: P Pr ob G( X ) 0 f ( X ) dx (6) f GX ( ) 0 Where fx 1,,Xn (x 1,, x n) is the joint density of probability of the variables Xi. The evaluation of this integral is very costly in time calculation, because it comes to be a very small quantity and because all the necessary information on the joint density of probability is not available. And it is very rare that this integral can be studied analytically. Traditionally, we distinguish two main methods: the methods based on simulations such as Monte Carlo simulation and those using approximate methods such as First Order Reliability Methods (FORM), this approximation method is based on the determination of the reliability index β, which allows access to an approximate value of probability of failure P f, and they are illustrated in figure (6) around the design point [12-14]. A. First Order Reliability Method (FORM) The FORM method (First Order Reliability Method) is being used for the approximation of the probability of failure; in this method, we firstly restate the problem according to its normal standard space using the isoprobabilistic transformations, for this we transform a physical variable X into a random variable reduced centered and independent U, then we determine the basic vectors of the normal space and this is how the space becomes perfect for a simple line calculation figure (6). Fig. 6. Physical and normalize spaces The However, the difficulty stands when the identification domain of the physical variable however it is going to be avoided due to the infinite support of the Gaussian Density. Recently this method has been used by several researchers; this method is useful in the determination of the reliability index and the failure probability. The FORM is based on the first order Taylor series approximation for a limit state function, which is stated as follows: Z = R-S (7) Where, R is the capacity (or resistance) normal variable, and S is the demand (load) normal variable. And that is supposing the resistance and the load variables are statistically independent, hence the variables are also obtained through normal (or Gaussian) distribution. Therefore, when the resistance is larger than the load variable the failure (or fracture) occurs. (R<S or Z<0) In general, the relationship between the failure probability and reliability by using the cumulative distribution function of a variable in the standard coordinates of the system which rests on the probability density function of the normal distribution which is obtained as follows: Z z Pf 1 R PZ 0 exp dz z 2 2 z (8) 2 1 U exp du 2 2 Where Φ is the cumulative distribution function for a standard normal variable and β is the safety index or reliability index [16-19]. B. Monte Carlo Simulation (MCS) The Monte Carlo Simulation method is named after the Monte Carlo Casino in Monaco. This method was used back in

5 International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:17 No: In 1950s this approach was used in tasks which had relation with the development of Hydrogen Bombs. Then, the method was generalized and started to be used in several domains such as computational physics, physical chemistry and related applied fields. Random variables TABLE III STATISTICAL PROPERTIES OF RANDOM VARIABLES Mean Standard Deviation Type of Distribution L D (DNP) (m) NRMAL This approach generalized the evaluations of the failure probability. So, it is crucial to evaluate the probability of failure, because the calculation of the probability of failure is time consuming and very complex and that is why we need the Monte Carlo Simulation technique, moreover this method helps us also to have an idea about the PDF of the response of the system. Furthermore, this method involves random sampling from the distribution of the inputs, and successive model runs until a statistical significant distribution of the output is obtained. The probability of failure Pr is calculated using the following equation: P f N f N Where N f is the number of the case where the failure has occurred in the case of G(X) < 0 and N is the total number of the samples [21-22]. V. CASE STUDY The varying boundary conditions affect the failure probability of the solder joint, and the LSF (Limit State Function) including varying boundary conditions we can define to estimate the impact of boundary conditions to the failure probability. In this study, the modified Manson-Coffin plastic strain fatigue life relationship is used to formulate the LSF equation as given below: (9) Δα (ppm/ C) NORMAL ΔT( C) NORMAL h(m) NORMAL C NORMAL F A. Deterministic results NORMAL VI. RESULTS AND DISCUSSIONS The Figure (7) shows the results of the deterministic analysis of a BGA Package under the thermal cycle loading. By using finite element simulation we ve been able to determine the major parameter in the failure mechanism, which is the local maximum elastic and plastic strain accumulation that leads to the crack initiation at any given region of the joint. After we determine the most critical solder joint in the BGA Package as shown in figure (8). Then table (4) shows the deterministic analysis results. G X N f N (10) Where, N= the number of cycle before failure. For estimating the failure probability of the solder joint we ve been utilizing the random variables presented in table (3) Fig. 7. the plastic work for solder joints.

6 International Journal of Mechanical & Mechatronics Engineering IJMME-IJENS Vol:17 No:04 6 Fig. 8. the most critical solder joint. TABLE IV DETERMINISTIC ANALYSIS RESULTS Parameter Value Inelastic work of solder,δw ave(mpa) Cycles to crack initiation,n 0 (cycles) 275 fatigue life predicted N f, α(cycles) 1412 B. Probabilistic results Table (5) shows the results of the failure probabilities obtained by using FORM and MC. TABLE V RESULTS OF FORM AND MC Methods Probability of failure P f Reliability index β FORM Monte Carlo simulation ( samples) VII. CONCLUSION In this paper we introduced a combined approach between a probabilistic approach and a non linear thermo mechanical finite element analysis to predict the probability of failure of thermal fatigue life of solder joints of BGA Packaging using FORM and MC methods. This efficient probabilistic approach ensures more design robustness, because it takes on the consideration of uncertainties related to the material properties such as thermal expansion coefficient mismatch, young's modulus, and of the variability of the geometry. [2] J. H. Lau, Y. -H. Pao, Solder joint reliability of BGA, CSP, flip chip, and fine pitch SMT assemblies. New York: McGraw-Hill, 1997 [3] G. Q. Zhang, W. D. Van Driel, X. J. Fan, Mechanics of Microelectronics. Netherlands: Springer, 2006 [4] J. K. Shang, Q. L. Zeng, L. Zhang, Q. S. Zhu, Mechanical fatigue of Sn-rich Pb-free solder alloys, J. Mater. Sci.: Mater. Electron, vol. 18, pp , [5] Z. El Haddad, O. Bendaou, L.El Bakkali A Study on Stochastic Thermal Characterization of Electronic Packages Int. Journal of Engineering Research and Application, Vol. 6, Issue 8, ( Part -1) August 2016, pp [6] Ouk Sub Lee, a, Man Jae Hur, b,yeon Chang Park Comparison of Reliability of Solder Joints by FORM and SORM Key Engineering Materials Vols (2007) pp [7] Y. X. Ning, K. L. Pan, and N. Li, Failure analysis of solder joints in electronic assemblies, Equipment for Electronic Products Manufacturing, vol. 36, no. 9, pp , [8] Jinhua Mi, Yan-Feng Li, Yuan-Jian Yang,Weiwen Peng, and Hong-Zhong Huang Thermal Cycling Life Prediction of Sn- 3.0Ag-0.5Cu Solder Joint Using Type-I Censored Data Hindawi Publishing Corporation the Scientific World Journal Volume 2014, Article ID , 11 pages [9] K. Zhang, Q. S. Zhu,H. F. Zou, andz.f.zhang, Fatigue fracture mechanisms of Cu/lead-free solders interfaces, Materials Science and Engineering A, vol. 527, no. 6, pp , [10] JEDEC Solid State Technology Association, JESD22- A104C.Temperature cycling, [11] J.H.Lau, Solder Joint Reliability Theory and Application, Van Nostrand Reinhold, 1991, pp [12] Madsen HO, Krenk S, Lind NC. Methods of structural safety [13] M. Lemaire, A. Chateauneuf, and J.C. Mitteau. Fiabilite des structures. Couplage Mecano-fiabiliste statique. Hermes,2005. [14] F. Guerin, M. Barreau, A. Charki, and A. Todosko. Bayesian estimation of failure probability in mechanical systems using monte carlo simulation. Quality Technology & Quantitative Management QTQM, 4 :51-70, [15] Lee, O. S., Kim, D. H., and Choi, S. S., Reliability of Buried Pipeline using a Theory of Probability of Failure, Solid State Phenomena, Vol. 110, pp , [16] A. Delbariani-Nejad,Saeed Adib Nazari Effects of Loading Modes on Reliability of Cracked Structures Using FORM and MCS International Journal of Precision Engineering And Manufacturing Vol. 18, No. 1, Pp January 2017 / 63 [17] Mahadevan, S. and Haldar, A., Probability, Reliability, and Statistical Methods in Engineering Design, John Wiley & Sons, [18] Tanaka, K., Fatigue Crack Propagation from a Crack Inclined to the Cyclic Tensile Axis, Engineering Fracture Mechanics, Vol. 6, No. 3, pp , [19] Z. El Haddad, O. Bendaou, L.El Bakkali Numerical Approximation of Structural Reliability Analysis Methods International Journal of Innovation and Applied Studies ISSN Vol. 19 No. 2 Feb. 2017, pp [20] Bruno Sudreta and Armen Der Kiureghian, Comparison of finite element reliability methods, Probab. Engg. Mech. 17 (2002), The results of the probability of failure of the solder joint by using FORM method was supported by the results obtained by the MC method. REFERENCES [1] J. H. Lau (Ed.), Solder Joint Reliability: Theory and Applications. New York: Van Nostrand Reinhold, 1991.