An approximate mathematical model is developed for predicting the shapes of solder joints in an array-type interconnect (e.g., a ball-grid array or flip-chip interconnect). The model is based on the assumption that the geometry of each joint may be represented by a surface of revolution whose generating meridian is a circular arc. This leads to simple, closed-form expressions relating stand-off height, solder volume, contact pad radii, molten joint reaction force (exerted on the component), meridian curvature, and solder surface tension. The qualitative joint shapes predicted by the model include concave (hourglass-shaped), convex (barrel-shaped, with a truncated sphere as a special case), and truncated-cone geometries. Theoretical results include formulas for determining the maximum and minimum solder volumes that can be supported by a particular pair of contact pads. The model is used to create dimensionless plots which summarize the general solution in the case of a uniform array (i.e., one comprising geometrically identical joints) for which the contact pads on the component and substrate are of the same size. These results relate the values of joint height and width (after reflow) to the solder joint volume and the molten-joint force for arbitrary values of the pad radius and solder surface tension. The graphs may be applied to both upright and inverted reflow, and can be used to control stand-off for higher reliability or to reduce bridging and necking problems causing low yields. A major advantage of the model is that it is numerically efficient (involving only simple, closed-form expressions), yet generates results that are in excellent agreement with experimental data and more complex models. Thus, the model is ideally suited to performing parametric studies, the results of which may be cast in a convenient form for use by practicing engineers. Although in the present paper the array is assumed to be doubly-symmetric, i.e., possess two orthogonal planes of symmetry, the model may be extended to analyze arrays of arbitrary layout. The motivation for predicting joint geometries in array-type interconnects is two-fold: (1) to achieve optimal joint geometries from the standpoint of improved yield and better reliability under thermal cycling and (2) to take full advantage of the flexibility of new methods of dispensing solder, such as solder-jet and solder-injection technologies, which enable the volume of each individual joint to be controlled in a precise manner. Use of dispensing methods of these types permits the solder volumes in the array to be distributed in a non-uniform manner. Results such as those presented here (in combination with appropriate fatigue studies) can be used to determine the optimal arrangement of solder volumes.

Creep and cyclic deformation behavior of two lead-free high temperature solder alloys, 95Sn-5Ag and 99Sn-l.OCu, a high lead alloy 97.5Pb-1.5Ag-l.OSn. and an Ag-modified eutectic alloy 62.5Sn-36.1Pb-I.4Ag, were studied. Room temperature and high (100°C and 150°C) temperature fatigue tests (with cyclic strain amplitude up to 6.0%) for the four solders were conducted, with the fatigue lives ranging from a few cycles to more than 100, OOO cycles. It is shown that among the alloys studied, 62.5Sn-36.1Pb-1.4Ag (the modified Sn-Pb eutectic alloy) has the lowest fatigue resistance in term of low cycle fatigue life (strain controlled). The high lead alloy, 97.5Pb-l.5Ael.OSn, has the highest strain fatigue resistance in the large strain region (A& > 2.0%). Temperature has a significant effect on alloys 95Sn-5Ag and 99Sn-l.OCu, hut has a negligible effect on the Ag modified Sn-Pb eutectic alloy 62.5Sn-36.1Pte1.4Ag and 97.5Pb1.5Ag-l.OSn. Creep studies show that these alloys generally have a very significant primary creep regime (up to 20%); thus, any realistic constitutive relation has to take such a primary creep phase into consideration. Cyclic deformation of alloy 95Sn-5Ag was simulated by using a constitutive relation built upon a 2-cell model, which covers both primary and secondary creep. This model provides a good estimate of the peak stresses (the minimum stress and the maximum stress in each cycle); it agrees with experimental results when the applied cyclic strain is small and/or the applied strain rate is very low.

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Creep of two lead-free high temperature solder alloys, 95Sn-5Ag and 99Sn-1.0Cu was studied in this investigation. Room and high temperature creep tests were performed to examine deformation mechanisms and to establish mathematical models of creep deformation for the alloys. A state variable creep model was introduced to model both primary and secondary creep deformation of these two alloys which show a very significant primary creep. Fatigue life models of the alloys were established based on an energy-based failure criteria, which was deduced from variable strain amplitude tests at a constant strain rate of 0.003/sec, and from variable strain rates tests with two constant strain amplitudes of 0.005 and 0.01. Applications of the creep model includes determination of peak loads and hysteresis strain energy density in strain-controlled fatigue tests. It is demonstrated that the creep model can be very helpful to establish fatigue failure criteria and to assess fatigue lives of these two alloys.