When soldered to a substrate or PCB, BGAs can reduce substrate interconnection area, complexity and cost, as well as facilitate assembly automation. However, because of a general lack of compliance in BGA solder joints, their failure in a military vibration environment becomes a serious design concern.
By T.E. Wong, F.W. Palmieri, B.A. Reed and H.M. Cohen
The objective of this article is to develop a vibration-fatigue damage model for ball grid array (BGA) solder joints in which a 3-D global/local modeling technique simulates the vibration responses of the packages soldered on a printed circuit board (PCB). Linear static and dynamic finite-element models (FEM), combined with a volume-weighted average technique, are conducted to calculate the effective strains on the solder joints. In the calculation process, several proprietary Fortran programs, in conjunction with the outputs obtained from static and frequency-response analyses, are used.
Figure 1. Microsection of the BGA solder joint assembly used. The package features 600 pins at 1.27 mm pitch.
Next, a vibration-fatigue life model, evolved from an empirically derived formula of universal slopes based on high-cycle fatigue test data, is established.1 The model, combined with a three-band technique2 and the derived solder effective strain, predicts BGA solder joint survivability and durability, which are then compared to test results to validate the proposed BGA solder joint vibration-fatigue damage model.
Some understanding of solder joint vibration fatigue and life-predicting capabilities2-10, as well as a theoretical background of random vibration11-15M, can be obtained from available literature. In this article, an example of a 600-pin BGA (package size, 45.7 mm2) is illustrated. The package features 35 Sn63/Pb37 solder bumps along each periphery plus five rows along each side (their pitch is 1.27 mm). The BGA is soldered on a polyimide board on which some reinforcement-type stiffeners are mounted. A microsection of the solder joint assembly, with a height of approximately 0.5 mm, is shown in Figure 1.16
A 3-D modeling technique is used to estimate the stresses and strains on the BGA solder joints. The FEMs are constructed with a MSC/PATRAN code and the linear dynamic and static analyses are performed with a finite element code. Table 1 lists the material properties of aluminum, polyimide/glass, copper, Sn63/Pb37 solder, dry-film soldermask, polyimide tape, silicon, mold compound and epoxy adhesive.16-19
A 3-D global FEM of the module (Figure 2) is constructed to simulate major structural elements and to determine the dynamic responses when subjected to normal PCB excitations. Whereas three BGA mounting locations are selected and shown, only one 600-pin BGA is mounted for the study. To minimize solder vibration fatigue damage, a design option in which a doubler (or constrainer) is adhered to the backside of the PCB at the BGA mounting location is proposed and incorporated in the FEM. A 3-D finite-element local model (Figure 3), with refined mesh solid elements to simulate the local region, is also constructed to determine solder effective stress and strain.8
Figure 3. A 3-D submodel showing half of a solder joint simulates the local region for determining solder effective stress and strain.
The average effective strains upon the joints at the package/solder interface can be derived using the method described in Figure 4, which includes two stages:
- The cross-correlation of output displacement responses vs. frequency for each of the degrees of freedom of the connection points of the local model to the global structure is developed via a frequency response analysis of the global model.
- A static analysis generates the transfer functions that correspond to each strain component for each input-loading condition. Next, to calculate the power spectral for each component, the transfer functions are statistically correlated with the degree of correlation determined by the cross-spectral density in the first stage.
The effective solder joint strains are then derived using a type of von Mises relationship and a volume-weighted average technique.20 In the methodology process, several proprietary Fortran programs, in conjunction with the outputs obtained from static and frequency-response analyses, perform the required computations.9
Vibration-fatigue Damage Model
To estimate solder joint fatigue life, an empirically derived formula of universal slopes based on high-cycle fatigue-test data is used1:
where e = strain amplitude; De = total strain range; Su = ultimate tensile strength = 37.9 MPa for eutectic solder; and E = modulus of elasticity = 30.2 GPa for eutectic solder.
The solder vibration fatigue curve is then described as:
Figure 2. A global FEM showing only the main PCB and BGA at location 1. The model simulates major structural elements to determine dynamic responses to normal PCB excitations.
Equation 2 relates the amount of solder strain amplitude, e, developed during one vibration cycle to the number of cycles needed to induce solder failure, N. (To determine N from Equation 2, an estimate of e is necessary.) During the vibration, solder effective strains can be obtained from the finite-element analysis described. The strains are then substituted into Equation 2 to calculate solder vibration fatigue life.
To evaluate random vibration fatigue failure, a three-band technique is used.2 The basis for this technique is the Gaussian distribution. The 1, 2 and 3 s strains occur 68.31, 27.1 and 4.33 percent of the time, respectively. The vibration-fatigue lives of the solder with those strains can be obtained as:
where i = 1, 2 and 3.
The corresponding number of fatigue cycles of random vibration is obtained by multiplying the times by the maximum number of positive zero crossings (N+0) of the global model's 10 displacements from the random response. Thus, for a total of T hours of random vibration, the number of applied cycles is calculated from the following equations:
The cumulative damage index (CDI), using Miner's Law and assuming a linear summation of damage, can be obtained as:
Figure 4. Flow chart for evaluating BGA solder joint vibration-fatigue damage.
"Failure" is predicted when the CDI reflects a value greater than or equal to a critical value, usually chosen as 1 (or 0.5 for a conservative stance). Table 2 summarizes the calculation of the CDIs for the "critical-corner" solder joints of the BGA at locations 1 through 3 under the random-vibration exposures. It indicates that the BGA at 1 (close to the wedge lock of the PCB) would result in a smaller CDI value for the critical-corner solder joint. Therefore, it would have a better chance to survive the random-vibration environment.
A 3-D global/local modeling technique estimates the strains on BGA solder joints stemming from exposure to random-vibration environments. This technique uses several proprietary Fortran computer programs that, in conjunction with the outputs obtained from static and frequency response analyses, perform the required computations. The Fortran computer codes permit users to obtain the average effective strains of the BGA solder joints.
A vibration-fatigue damage model is also established. This model, combined with a three-band technique and the derived solder effective strains, predicts BGA solder joint survivability and durability. Analysis indicates that the solder joints of the BGA closed to the wedge lock of the PCB exhibit less damage during the random vibration and could survive in such an environment.
This article is adapted from a presentation originally given at APEX 2000.
The authors thank D.W. Chu, T.Y. Jue, K.T. Teshiba and M.D. Walley of Raytheon Systems Co. for providing support; and Dr. D.E. Helling (Hughes Electronics Co.), Dr. E. Jih (Ford Motor Co.) and Prof. J.M. Pitarresi (SUNY/Binghamton) for valuable technical discussions.
A list of references are available from T.E. WONG, F.W. PALMIERI, B.A. REED and H.M. COHEN at Raytheon Electronic Systems, 2000 E. El Segundo Blvd., El Segundo, CA 90245; (310) 334-5668; Fax: (310) 334-5249; E-mail: email@example.com.