Ji Eun Park e-mail: ji.e.park@lmco.com Lockheed Martin Aeronautics Company, 86 South Cobb Dr., Dept. 6E5M Zone 0987, Marietta, GA 30063-0915 Iwona Jasiuk e-mail: iwona.jasiuk@me.gatech.edu Georgia Institute of Technology, The G. W. W. School of Mechanical Engineering, Atlanta, GA 30332-0405 Aleksander Zubelewicz e-mail: alek@lanl.gov Los Alamos National Laboratory, MST-8, MS G755, Los Alamos, NM 87545 Interfacial Stress Analysis and Fracture of a Bi-Material Strip With a Heterogeneous Underfill Flip chip assemblies used in electronic packaging consist of three main components (layers): chip, underfill, and substrate. In this paper, the flip chip assembly is represented as a bi-material strip consisting of the chip and underfill. Our analysis is focused on delamination along the chip-underfill interface due to thermal loading. The underfill is modeled as a composite material made of a polymer matrix and silica particles. Interfa- cial stresses are studied for several particle configurations: cases of one, two, or three particles near the interface and 30 different random particle arrangements. Interfacial fracture is investigated by evaluating the J integral and stress intensity factors. Statistics of random particle arrangements in the underfill are also discussed. The interfacial stress and fracture analyses give the same trends. DOI: 10.1115/1.1602480 1 Introduction The flip chip assembly used in electronic packaging applica- tions consists of three main components layers: a chip, an un- derfill also called encapsulant, and a substrate. The assembly is cured at about 130°C and cooled down to a room temperature. It also undergoes thermal cycling during its operation. Since the components of the assembly have different coefficients of thermal expansion CTE, several types of failure may occur. In this paper we focus on one of these failure modes, delamination between the chip and underfill. In order to make the underfill properties com- patible with the rest of the assembly, silica particles are often dispersed in the encapsulant. In this paper the underfill is modeled as a matrix-inclusion composite material, and the analysis ad- dresses stresses and fracture along the chip-underfill interface. Our original contribution lies in the explicit treatment of micro- structural details of the underfill. This issue is important because fracture is a local phenomenon occurring at small scales, and thus the heterogeneity of the underfill plays a significant role when fracture occurs. We address this problem numerically, via a finite element method. We use a simple geometric model involving a finite bi-material strip with equal length of layers, as shown in Fig. 1, consisting only of the chip and underfill. We study the interfacial stresses and fracture using the J integral and stress intensity factors at the bi-material interface between two layers in such a strip. Related problems involving interfacial stress studies in two fi- nite perfectly bonded homogeneous strips were addressed analyti- cally by Suhir 1,2 and Kuo 3, and numerically, using finite elements, by Lau 4, among others. Lee and Jasiuk 5 and Eis- chen et al. 6 studied the asymptotic behavior of stresses at the interface at the edge of a bi-material strip. We conduct our fracture analysis using the J-integral method. Rice 7 and Eshelby 8 formulated the J integral for homoge- neous materials. Smelser and Gurtin 9 used the J-integral method for bi-material bodies and they showed that the J-integral formulation could be used without any changes for bi-materials as long as the bond line is straight. Park and Earmme 10 and others also studied fracture at bi-material interfaces using the J-integral method. Sun and Wu 11 employed the J integral for periodically layered composites. Weichert and Schulz 12 used the J integral approach for multiphase materials, while Haddi and Weichert 13,14 modified the J integral for the case of inhomogeneous materials. We also study fracture by calculating stress intensity factors from crack surface displacements. The studies, which addressed stress intensity factors for mixed-mode crack problems involving bi-material strips, include those due to Charalambides et al. 15, Hamoush and Ahmad 16, Pao and Pan 17, Matos et al. 18, and others. Numerous papers addressed thermal stresses and fracture in electronic packaging assemblies. For a list of references in this area see, for example, Park et al. 19. Since our study addresses the effect of particle arrangement in the underfill and its influence on the interfacial stresses and frac- ture, we also recall here several elasticity solutions of inclusion problems. These include the celebrated work of Eshelby 20, who solved the problem of an ellipsoidal inclusion in an infinite body, and the solutions of Shioya 21, Richardson 22, Lee et al. 23, and Al-Ostaz et al. 24, among others, who studied elastic stress fields due to a circular inclusion in an elastic half plane. Yu and Sanday 25 solved the three-dimensional case of a bi-material with a spherical inclusion near the interface. The objective of this paper is to investigate the effect of under- fill microstructure particles on the interfacial stresses and frac- ture at the chip-underfill interface in electronic packaging assem- blies. In more general terms, this study addresses the interfacial stresses and fracture in a two-layer strip, which has inclusions in one of the layers. 2 Problem Statement In this paper we study stress fields and fracture along the chip- underfill interface in a flip-chip assembly. We use the simplified model of the flip-chip device involving a bi-material strip com- posed of the chip and underfill only. Thus, we do not account for the substrate and solder bumps. In our previous work 19,26 we have found that it is reasonable to use the bi-material strip model for the investigation of interfacial stresses and fracture in a flip- chip assembly since it gives the same trends as three-layer mod- els. However, the actual magnitudes are influenced by the pres- ence of substrate and the geometry of the layered model see Refs. 19, 26 for a more detailed discussion. Our analysis is con- ducted in the context of linear uncoupled thermoelasticity assum- ing plane strain. Thus, our two-dimensional 2D model represents a section taken from the middle of the package. The plane strain model is confirmed to be acceptably good when compared with 3D numerical analyses of Michaelides and Sitaraman 27, Hanna Contributed by the Electronic and Photonic Packaging Division for publication in the JOURNAL OF ELECTRONIC PACKAGING. Manuscript received Sept. 2002. Associate Editor: Z. Suo. 400 Õ Vol. 125, SEPTEMBER 2003 Copyright © 2003 by ASME Transactions of the ASME