3D Modeling of electromigration combined with thermal–mechanical effect for IC device and package

Abstract

This paper studies the numerical simulation method for electromigration in IC device and solder joint in a package under the combination of high current density, thermal load and mechanical load. The three dimensional electromigration finite element model for IC device/interconnects and solder joint reliability are developed and tested. Numerical experiment is carried out to obtain the electrical, thermal and stress fields with the migration failure under high current density loads. The direct coupled analysis and in-direct coupled analysis that include electrical, thermal and stress fields are investigated and discussed. The viscoplastic ANAND constitutive material model with both SnPb and SnAgCu lead-free solder materials is considered in the paper. An IC device is studied to show the modeling methodology and the comparison with previous test data. A global CSP package with PCB is modeled using relative coarse elements. In order to reduce the computational costs and to improve the calculation accuracy, a refined mesh sub-model is constructed. The sub-model technique is studied in a direct and indirect coupled multiple fields. The comparison of voids generation through numerical example in this paper and previous experimental result is given.

Introduction

It is well known that as the electronics industry continues to push for high performance and miniaturization, the demand higher current densities, which may cause electromigration failures, not only in a IC interconnect but also in solder bumps of a IC package [1]. Early studies of electromigration mostly concentrated on interconnects of integrated circuit packages such as Al–Cu alloy interconnect wire or pure Cu interconnect wire [2], [3], [4]. In classical electromigration studies, Black’s equation [2] has been successful in characterizing the operation life of aluminum and copper traces on a chip, but a lot of experimental work and modeling have shown that the Black’s theory is not enough accurate to evaluate the reliability or unable to reasonably simulate the failure due to void formation [5], [6], [7]. Black’s equation assumes that the current density in aluminum is constant [2], which is not true in solder bumps in which current density varies in different location. In recent years the researchers have found the phenomenon of electromigration occurs inside the solder which is adjacent to the under bump metallization (UBM) layer. The void propagates along the interface between solder and the UBM, which would induce open failures of the joints. The electromigration failure mechanism in solder balls is distinctly different from that in Al or Cu interconnects [8], [9], [10], [11].

There are a few papers that proposed an algorithm for 3D void simulation with consideration of the electromigration, the thermomigration and the stress migration [12], [13], [14]. Although these works can simulate the void formation in the interconnect lines of integrated circuits, the limit of their algorithms makes it unable to provide an accurate solution to the life prediction of IC interconnect lines. Further, their work has not yet been applied to solder joint reliability analysis. We have done some initial work to consider both the thermal and electromigration in power cycling [15]. Afterward, we presented a numerical study of electromigration in solder joints under the combination of high direct current density, thermal loads and mechanical loads [16], [17], but only a simple traces–bump model is studied and the solder bump material is assumed to be elastic. In fact, the simple traces-and-bump model does not get an appropriate thermal field and the thermal mismatch in a whole package with PCB system. Because the solder bumps have viscoplastic deformation at high temperature, the simple trace–bump model will induce the errors in multi-physics electromigration analysis.

This paper further develops the fully 3D electromigration model with consideration of both IC interconnects in a device and solder joints in a package by FEA modeling. It considers the combination analysis of electric-thermal–structural coupled fields based on ANSYS multi-physics simulation platform. The atomic flux divergence calculation method considers three mechanisms which includes the electromigration, the thermomigration and the stress migration. It also considers the void generation, and location. Evolution of the parameters corresponding to void growth and electricity is recorded during simulation. Meanwhile, the corresponding time to failure life is studied. The direct coupled and in-direct coupled analysis that include electrical, thermal and structure fields are presented and discussed. A sub-model technique is introduced in the 3D multiple physics analysis. A global chip scale package (CSP) with PCB is modeled using relative coarse elements, and a refined mesh sub-model is constructed for the detailed electromigration, thermomigration and stress-migration coupled analysis. Finally, the numerical examples for IC device and solder joints in a flip chip CSP are presented, and the comparison with the measurement result is discussed.