A Constitutive Model for Lead Free Solder Including Aging Effects and Its Application to Microelectronic Packaging

Abstract

The microstructure, mechanical response, and failure behavior of lead free solder joints in electronic assemblies are constantly evolving when exposed to isothermal aging and/or thermal cycling environments. Traditional finite element based predictions for solder joint reliability during thermal cycling accelerated life testing are based on solder constitutive equations (e.g. Anand viscoplastic model) and failure models (e.g. energy dissipation per cycle model) that do not evolve with material aging. Thus, there will be significant errors in the calculations with lead free SAC alloys that illustrate dramatic aging phenomena. In this research, a new reliability prediction procedure has been developed that utilizes constitutive relations and failure criteria that incorporate aging effects, and then validated the new approach through correlation with thermal cycling accelerated life testing experimental data. In this study, a revised set of Anand viscoplastic stress-strain relations for solder that include material parameters that evolve with the thermal history of the solder material has been developed. The effects of aging on the nine Anand model parameters have been examined by performing stress-strain tests on SAC305 samples that have been aged for various durations (0-12 months) at a temperature of 100 C. For each aging time, stress-strain data have been measured at three strain rates (0.001, 0.0001, and 0.00001 1/sec) and five temperatures (25, 50, 75, 100, and 125 C). Using the measured stress-strain data, the Anand model material parameters have been determined for various aging conditions. Mathematical expressions were then developed to model the evolution of the Anand model parameter with aging time. The results show that 2 of the 9 constants remain essentially constant during aging, while the other 6 show large changes (30-70%) with up to 12 months of aging at 100 C. Also the theoretical equations for the creep response of solder have been derived from the Anand viscoplastic model. Procedures for extracting the Anand model constants from experimental stress-strain and creep data have also been established. The two developed methods have been then applied to find the Anand constants for SAC305 (Sn-3.0Ag-0.5Cu) lead free solder using two completely different sets of experimental test data. The first set of Anand parameters were extracted from uniaxial stress strain data measured over a wide range of strain rates ( = 0.001, 0.0001, and 0.00001 sec-1) and temperatures (T = 25, 50, 75, 100, and 125 oC). The second set of Anand parameters were calculated from creep test data measured at several stress levels ( = 6, 8, 10, 12 and 15 MPa and temperatures (T = 25, 50, 75, 100, and 125 oC). New aging aware failure criteria have also been developed based on fatigue data from a parallel study for lead free solder uniaxial specimens aged at elevated temperature for various durations prior to mechanical cycling. Using the measured fatigue data, mathematical expressions have been developed for the evolution of the solder fatigue failure criterion constants with aging for Morrow-Darveaux (dissipated energy based) type fatigue criteria. After development of the tools needed to include aging effects in solder joint reliability models, these approaches have been applied to predict reliability of PBGA components attached to FR-406 glass epoxy laminated printed circuit boards that were subjected to thermal cycling. Finite element modeling has been performed to predict the stress-strain histories during thermal cycling of both non-aged and aged PBGA assemblies, where the aging at constant temperature occurred before the assemblies were subjected to thermal cycling. The results from the finite element calculations have been combined with the aging aware fatigue models to estimate the reliability (cycles to failure) for the non-aged and aged assemblies. As expected, the predictions show significant degradations in the solder joint life for assemblies that had been pre-aged before thermal cycling. To validate the new reliability models, the finite element results have been compared with the experimental reliability data for fine pitch PBGA daisy chain components. Before thermal cycling began, the assembled test boards were divided up into groups and were subjected to several sets of aging conditions (preconditioning) including different aging temperatures (T = 25, 55, 85 and 125 C) and different aging times (no aging, and 6 and 12 months). After aging, the assemblies were subjected to thermal cycling (-40 to +125 C) until failure occurred. As with the finite element predictions, the Weibull data failure plots have demonstrated that the thermal cycling reliabilities of pre-aged assemblies were significantly less than those of non-aged assemblies. Good correlation was obtained between the new reliability modeling procedure that includes aging and the measured solder joint reliability data.