The field reliability of solder joints depends on the manufacturing process tolerance of design parameters and on the capability of manufacturing processes to achieve the tolerance. This process capability is usually expressed through measures such as “six-sigma.” In this paper, a systematic procedure to estimate the reliability of solder joints due to manufacturing process induced variations on the design is presented. The reliability is calculated using the stochastic finite element method and is most naturally expressed in terms of a mean life and a standard deviation in life. An integrated finite element solution procedure for predicting solder joint profile (during reflow) and life is also presented in the paper. A physico-neural approach in which the finite element models are used to build an artificial neural network model is next developed to combine the accuracy of the finite element models with the computational efficiency of neural networks. This physico-neural approach is shown to reduce the computational time required per design evaluation by four orders of magnitude without significant loss of accuracy. The developed procedures are applied to the 72 I/O OMPAC BGA package from Motorola, Inc. It is shown that a ±10 percent process tolerance on solder joint height, volume and pad sizes with a “six-sigma” process capability on these variables will result in solder joint with over ±20 percent variations in life about the mean life at ±6σ level. It is also shown that variations in life of BGA solder joints are most sensitive to variations in solder joint height. Variations in PWB pad size, solder volume, and substrate pad size are relatively less important, but in the order listed.

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In this paper, we present a statistical-neural network modeling approach to process optimization of fine pitch stencil printing for solder paste deposition on pads of printed circuit boards (PCB). The overall objective was to determine the optimum settings of the design parameters that would result in minimum solder paste height variation for the new board designs with 20-mil, 25-mil, and 50-mil pitch pad patterns. As a first step, a Taguchi orthogonal array, L27, was designed to capture the main effects of the six important printing machinery parameters and the PCBs pad conditions. Some of their interactions were also included. Fifty-four experimental runs (two per setting) were conducted. These data were then used to construct neural network models relating the desired quality characteristics to the input design parameters. Our modular approach was used to select the appropriate architecture for these models. These models in conjunction with the gradient descent algorithm enabled us to determine the optimum settings for minimum solder paste height variation. Confirming experiments on the production line validated the optimum settings predicted by the model. In addition to the combination of all the three pad patterns, i.e., 20, 25, and 50 mil pitch pads, we also built neural network models for individual and dual combinations of the three pad patterns. The simulations indicate different optimum settings for different pad pattern combinations.

As a follow-up and conclusion to previous work in stencil printing process modeling and optimization (Li et al., 1996), we investigate the effect of stencil printing optimization on the reliability of the ceramic and plastic ball grid arrays. For ceramic ball grid arrays, the eutectic solder fillet shape is calculated using a series of simple mathematical equations. The thermal strain distributions within the solder joints after two cycles of accelerated thermal cycling test are estimated using three-dimensional finite element models. The modified Coffin-Manson relationship is applied to calculate the mean fatigue lives of the solder joints. The results reveal that an optimized stencil printing process significantly reduces variation in the fatigue life of ceramic ball grid arrays. The results also show that the fatigue life of ceramic ball grid arrays is very sensitive to the card-side solder volume. The maximum strain region shifts from the card-side eutectic solder to the module side as the card-side eutectic solder volume increases. This shift in maximum strain suggests that there exists an optimum ratio between the card-side solder volume and the module-side solder volume for the reliability of a given ceramic ball grid array design. The implications of this for the package developers and users are discussed. The calculations indicate that the fatigue life of plastic ball grid arrays is almost insensitive to the card-side solder volume.

In this paper, we first present a mathematical method that can be used to predict the eutectic solder fillet shape for ceramic ball grid array joints. An underlying assumption is that the solder fillets on both the module and the card sides can be represented as arcs. The fillets’ profiles are then calculated for the factors affecting the shape including solder volume, pad size, solder ball size, the wetting angle between eutectic solder and solder ball, and the gap between solder ball and pad. The second part of the paper focuses on design for reliability and investigates the effect of the interactions between the card-side and the module-side solder fillets on CBGA solder joint reliability. To this end, a central composite design of experiment is set up to systematically vary the pad size and the eutectic solder volume on both the module and the card sides. For each of the design settings, the proposed mathematical method is used to calculate the solder fillet shape. Using ABAQUS and the modified Coffin-Manson relationship, the mean fatigue life is predicted. The implications of the simulations are discussed. In addition, a response surface model is presented to find the optimum settings for maximum reliability. Finally, a comparison is made for the fatigue life predictions obtained using the proposed mathematical method and the linear solder fillet assumption.