| dc.description.abstract | With the ongoing miniaturization of microelectronic devices, the size of compliant solder in microscale solder joints has significantly reduced, proportion of brittle phases has increased, and the microscale joints have become highly constrained to deform because of their geometry and stiffness mismatch with substrates. Due to the varied nature of microstructure, a mere understanding of the mechanical behaviour of bulk alloys cannot be directly extended to judiciously predict the same in miniature joints. Accordingly, the aim of this work is to develop a comprehensive understanding of the effect of microstructure and size of Sn based joints on the mechanical behavior and microstructure from bulk specimens to microscale joints. This was first addressed by investigating the joint size dependence of the tensile properties of Sn-Cu joints. Maximum strength increased as the joint size reduced, and the mode of failure changed from necking in thick joints to constrained necking with cavitation in microscale Sn-Cu joints and solder-IMC failure in miniature Sn-Ag-Cu/Cu joints. The cause of this tensile strengthening was captured by crystal plasticity (CP) modeling along with existing analytical models to capture the size dependence of the tensile strength. Subsequently the effect of length scale on the creep properties of the Sn-Cu joints was investigated. This was addressed by first evaluating the creep behaviour of bulk Sn and Sn-Ag-Cu solder alloys over a range of temperature to compute the activation energy, QC, and stress exponent, n. The creep rate decreased with increasing Ag content. The creep mechanism was dislocation climb controlled by core diffusion at T<150 oC and lattice diffusion at T>150 oC with QC and n changing from 55 kJ/mol and 7 to 100 kJ/mol and 5. Subsequently the size of deformable Sn and solder was reduced by constraining metal layers of different size (from 1.4 mm to ~170 µm) and aspect ratio between Cu substrates as joints. The secondary creep rate decreased by three orders of magnitude with an order of magnitude decrease in joint size at same stress. However, no change in creep mechanism was evident in the joints. Using Finite Element Analysis this creep strengthening can be partly attributed to geometric constraints imposed by Cu which reduces the effective stress and increases the triaxiality in joints. While FE results were in close agreement with experiment in thick joints and bulk specimen, the former overpredicted the creep rate of small joints due to difference in microstructure between bulk Sn which has multiple grains and miniature joints having 2-3 grains, as confirmed by electron backscattered diffraction. This microstructural effect was captured by dislocation based crystal plasticity modeling from which it was evident that orientation anisotropy of Sn and constraints imposed by substrates on dislocation motion can lead to additional strengthening in small joints and reduce the prefactor B in Norton power law. Subsequently, a unified model was developed to quantify both these effects and predict the creep rate of arbitrary joints. In the tertiary creep stage bulk specimens exhibited strain localization by necking in pure Sn along with cavitation in precipitate containing Sn-Ag-Cu alloys. Moreover, the extent of necking and cavitation in Sn-Cu joints was sensitive to the joint size. A combined necking and cavitation based creep failure model was developed and the effect of initial geometry of instability, creep stress exponent and cavity fraction on strain localization was analyzed. The model showed that the strain at the onset of complete localization in neck will be independent of stress in pure Sn whereas it decreases with stress in Sn-Ag-Cu alloy and the predictions were found to qualitatively agree with experiment. The model also was adapted to capture the joint size dependence of tertiary creep due to necking and cavitation in the Sn-Cu and SAC-Cu joints. The model predictions and experiments showed a decrease in strain accumulated in tertiary stage with decrease in joint size, as the strain due to necking reduced and the strain due to cavitation increased from bulk Sn and solders to the very thin joints. | en_US |
