Unified constitutive modelling of interfaces and materials in semiconductor devices

A unified constitutive modelling approach is developed based on the disturbed state concept (DSC) with the hierarchical single surface plasticity (HiSS) based models. With this approach, various factors such as plastic and creep strains effects, and damage due to microcracking and fracture are considered as disturbances, and incorporated in a basic reference model in a progressive manner. As a result, the approach provides flexibility to adopt various versions of the model depending on the need of users. The thermoplastic model, δ_θ, presented here describes hardening response of materials/interfaces during monotonic as well as cyclic thermomechanical loads. In addition to the thermoplastic model, a thermoviscoplastic model, δ_θv, presented here was used to simulate creep and stress relaxation mechanisms at elevated temperatures; here the rate effect on the hysteretic response is incorporated in the incremental constitutive equations. This model can allow for any stress-strain history and can be used for investigation of the time dependence of low-cycle fatigue life prediction of solder materials. The temperature dependence of material constants are found using available laboratory tests, and is represented by using simple power functions. These models have the merit of being relatively simple, and they can be readily adapted in nonlinear finite element codes. Preliminary verification of the above two versions of model is obtained for solder materials in semiconductor devices.