Constitutive modeling of thermomechanical response of materials in semiconductor devices with emphasis on interface behavior.

Abstract

A unified constitutive modeling approach is developed based on the disturbed state concept (DSC) with the hierarchical single yield surface plasticity (HiSS) based models. With this approach, various factors such as elastic, plastic, and creep strain, as well as damage due to microcracking and fracture are considered as disturbances, and incorporated in a basic model in a hierarchical manner. As a result, the approach provides flexibility to adopt various versions of the model depending on the need of users. Two thermomechanical constitutive models are developed as the special versions of the reference DSC model. The thermoplastic model, δ(θ), presented here describes the hardening response of materials/interfaces during monotonic as well as cyclic thermomechanical loads. In addition to the thermoplastic model, a thermoviscoplastic model, δ(vθ), presented here is used to simulate creep and stress relaxation mechanisms at elevated temperatures; here the rate effect on the hysteresis response is incorporated in the incremental constitutive equations. This model can allow for arbitrary stress-strain histories 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 are expressed 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. Verifications and applications of different versions of DSC model are obtained for solder materials in semiconductor devices. Novel applications in fatigue life prediction are described, including different fatigue failure criteria that may not be readily captured by most previously proposed constitutive models.