| description abstract | An analytical model of solder joint formation during a surface mount reflow process is developed for two-dimensional fillets whose flow may be restricted due to “finite” metallizations on a leadless component and the printed circuit board. Although these height and length constraints on the fillet geometry may result in obtuse contact angles, the solution is obtained in the form of an explicit integral, similar to that previously derived by the authors for the case of acute contact angles. This solution may also be recast into the form of elliptic integrals of the first and second kinds, thereby permitting one to evaluate the fillet geometry using mathematical tables or special function software, if desired, rather than resorting to a computer-based numerical quadrature. In addition an approximate zero-gravity solution is given by means of simple closed-form expressions relating the height, length, contact angles, and cross-sectional area of the fillet. Numerical results generated by implementing the “exact” integral solution for the joint profile are given in the form of dimensionless plots, relating fillet geometry to the solder properties (surface tension and density), amount of solder, chip height, and pad length. Also presented in dimensionless form are the approximate results from the zero-gravity model, which are independent of solder properties, yet are of sufficient accuracy for “small” joints. Because of their dimensionless nature, the results of the present paper may be of maximum utility to process engineers aiming to achieve desired joint geometries (e.g., to maximize fatigue life or to eliminate bridging problems), or to board designers responsible for selecting efficient footprint patterns to maximize board density. Models of solder joint formation, such as the one presented here, may be of most value when used in conjunction with stress analysis packages (e.g., finite element programs) and appropriate fatigue models. In this way an integrated approach to the design of solder joints and circuit boards may be taken, resulting in improved product reliability and performance. | |
