PREDICTION OF SOLDER JOINT GEOMETRIES IN ARRAY-TYPE INTERCONNECTS

An approximate mathematical model is developed for predicting the shap es of solder joints in an array-type interconnect (e.g., a ball-grid a rray or flip-chip interconnect). The model is based on the assumption that the geometry of each joint may be represented by a surface of rev olution whose generating meridian is a circular arc. This leads to sim ple, closed-form expressions relating stand-off height, solder volume, contact pad radii, molten joint reaction force (exerted on the compon ent), 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), a nd truncated-cone geometries. Theoretical results included formulas fo r determining the maximum and minimum solder volumes that can be suppo rted 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 joint s) for which the contact pads on the components and substrate are of t he same size. These results relate the values of joint height and widt h (after reflow) to the solder joint volume and the molten-joint force for arbitrary values of the pad radius and solder surface tension. Th e graphs may be applied to both upright and inverted reflow, and can b e used to control stand-off for higher reliability or to reduce bridgi ng and necking problems causing low yields. A major advantage of the m odel is that it is numerically efficient (involving only simple, close d-form expressions), yet generates results that are in excellent agree ment with experimental data and more complex models. Thus, the model i s ideally suited to preforming parametric studies, the results of whic h may be cast in a convenient form for use by practicing engineers. Al though in the present paper the array is assumed to be doubly-symmetri c, i.e., posses two orthogonal planes of symmetry, the model may be ex tended to analyze arrays of arbitrary layout. The motivation for predi cting joint geometries in array-type interconnects is two-fold: (1) to achieve optimal joint geometries from the standpoint of improved yiel d and better reliability under thermal cycling and (2) to take full ad vantage of the flexibility of new methods of dispensing solder, such a s solder-jet and solder-injection technologies, which enable the volum e of each individual joint to be controlled in a precise manner. Use o f 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.