Modeling of time-variant heterogeneous objects in micro-system packages

Abstract

UBM (under bump metallurgy) of micro-system packages consists of several heterogeneous layers such as solder wetting, diffusion barrier, adhesion, and IMC (inter-metallic compound) layers. In particular, the IMC layer, formed between the solder wetting layer (e.g., Cu or Ni) and the solder, grows gradually and thus its composition changes with time (i.e., time-variant). The primary failure mechanism of the solder joints in micro-system packages is widely known as the fatigue failure caused by thermal fatigue and electro-migration damage. However, these phenomena have thus far been viewed from experimental investigations. Therefore, finite element analysis (FEA) becomes an important step for the optimal design and reliability analysis of heterogeneous objects such as in micro-system packages. However, the accuracy of the FEA wholly depends on the quality of finite element models. There thus exists an increasing need for generating finite element models adaptive to both geometric complexity and material distribution. In this sense, this paper presents a new method for modeling of time-variant heterogeneous objects such as in micro-system packages whose composition changes with time. Heterogeneous Boolean operators based on the diffusion process are proposed to construct time-variant heterogeneous objects. Once a time-variant heterogeneous solid model is constructed, it is then discretized into an object model onto which appropriate material properties are mapped. Discretization converts continuous material variations inside an object into stepwise variations. Next, the object model is adaptively meshed and converted into a finite element model. FEA using commercial software is finally performed to check failure criteria. An example (UBM in micro-system package) is shown to illustrate the entire modeling procedure.