Cohesive zone modeling for structural integrity analysis of IC interconnects

doi:10.1016/j.microrel.2006.08.017

Microelectronics Reliability

Volume 47, Issue 8, August 2007, Pages 1251-1261

https://doi.org/10.1016/j.microrel.2006.08.017 Get rights and content

Abstract

Due to the miniaturization of integrated circuits, their thermo-mechanical reliability tends to become a truly critical design criterion. Especially the introduction of copper and low-k dielectric materials cause some reliability problems. Numerical simulation tools can assist developers to meet this challenge. This paper considers the first bond integrity during wire bond qualification testing. During testing, metal peel off may occur. This mechanical failure mode is caused by delamination of several layers of the interconnect structure. An interfacial damage model is employed for simulating delamination. However, the fact that the considered interfaces are brittle triggers some reported numerical difficulties. This paper illustrates the potential of the interface damage mechanics approach for simulating metal peel off and it highlights the computational aspects to be developed to render a practically applicable approach.

Introduction

The ongoing miniaturization of integrated circuits (ICs) requires the introduction of new materials in the interconnect structure, such as copper and low-k dielectrics. These materials have substantially different mechanical properties compared with the conventionally used materials. In particular, the low-k dielectric materials have a lower mechanical stiffness compared with the conventionally used SiO₂ and their adhesion to other materials is weaker [1], [2]. Due to both the reduced feature sizes and the altered material properties, thermo-mechanical reliability tends to become one of the critical design criteria. Current design rules need to be improved to account for this compromised thermo-mechanical reliability. Proper interfacial damage models can assist IC developers to improve and optimize their design methods in this respect [3], [4], [5], [6].

This paper focuses on the first bond integrity of wire bonded ICs. The wire bonds and the bond pads are subjected to critical loading conditions (possibly inducing damage) during different stages of the manufacturing process, for example in the bonding process, during qualification testing and during encapsulation. Here, the mechanical reliability of the bond pad during qualification testing is considered, more particularly during wire pull testing [7]. The wire bond passes this destructive test if the wire breaks in the heat affected zone above the ball at a specified strength. This is referred to as neck break. However, for some advanced ICs with fine pitch bond pads and with copper/low-k interconnects a different failure mode is sometimes observed, in which the ball is lifted from the pad and part of the interconnect structure is torn from the IC [4], [5], [8], [9], [10]. This failure mode is referred to as metal peel off. Metal peel off is caused by the delamination of several layers in the interconnect structure. This failure mode is not allowed since the associated maximum load is usually below the qualification limit. Fig. 1 shows the result of several wire pull tests in which both failure modes can clearly be distinguished.

Much effort is put into the development of methodologies to simulate and predict the interface delamination of the interconnect structure in an accurate manner. Several approaches have thereby been adopted, of which the three most relevant are:

•
Stress based approaches
Static linear elastic finite element (FE) simulations provide interface stresses [3] or first principal stresses [4]. Comparison with critical stress levels indicates the regions most prone to fracture. This approach assumes perfect adhesion between materials and therefore overestimates the strength of copper/low-k interconnects. To take poor adhesion or initial defects into account, another approach must be followed.
•
Linear elastic fracture mechanics (LEFM) based approaches
LEFM based approaches require the presence of initial defects. Explicit knowledge of the location and the size of an initial interface crack is thereby necessary. Furthermore, brittle fracture is assumed, as has indeed been observed for low-k dielectric films [2]. FE simulations provide the crack driving forces associated with the discrete interface cracks [3], [6]. An interface delaminates if this crack driving force exceeds the fracture toughness of the considered interface. Furthermore, comparison of the crack driving forces in several interfaces provides a qualitative impression of the most vulnerable interfaces.
•
Area release energy approach
The major disadvantage of LEFM based approaches is that initial crack locations and sizes must be known. Recently, the use of the area release energy value as a fracture criterion has been proposed [5]. This quantity approximates for each node on the interface of interest the work of separation by releasing nodes adjacent to the considered node, as described a.o. in [11]. The difference with standard nodal release methods is that all nodes on the interface within a predefined distance from the considered node are released. This reduces the mesh dependency of the approximated energy values. The spatial distribution of the area energy release values shows where the critical areas for delamination are located.

None of the above approaches is able to simulate both the nucleation and growth of interface cracks in a unified manner. However, both aspects need to be considered to assess the first bond integrity, since initial cracks may not be present or their location may be unknown. Furthermore, cracks may be arrested and/or several cracks may evolve simultaneously. This situation is also not easily dealt with by the above methods. Therefore, this paper considers an interface damage mechanics approach, which takes the nucleation and evolution of interface cracks into account. It describes the gradual degradation of the adhesion between two materials using a cohesive zone model.

Cohesive zone modeling has proven its added value in many applications for ductile fracture [12], [13], [14], [15] and for quasi-brittle fracture [16], [17]. However, its application to brittle fracture still poses substantial computational challenges, which currently attract considerable attention [18], [19], [20]. In view of these research activities, this paper reports on the rather unexplored application of cohesive zone modeling for evaluating the mechanical reliability of IC interconnect structures. The objective here is to prove its feasibility for simulating interface delamination in copper/low-k interconnects, despite the numerical difficulties associated with brittle fracture. A simplified two-dimensional (2D) plane strain model of a characteristic part of the interconnect structure is constructed for this purpose. The load–displacement response of the model exhibits limit points, where the rate of the load or of the displacement switches sign. The existence of limit points requires a more sophisticated solution procedure than the commonly used load- or displacement-controlled Newton–Raphson procedure, e.g., the cylindrical arc-length method [21]. FE simulations reveal the nucleation and growth of several interface cracks. Furthermore, the simulations clearly indicate which aspects of the interface damage mechanics approach and the numerical solution procedure need to be developed further.

Section snippets

Cohesive zone model

Interface damage mechanics models the nucleation and growth of interface cracks. This approach does not require that the zone of influence near the crack tip is small compared with the crack size as in case of LEFM. Therefore, interface damage mechanics is applicable to ductile fracture processes as well [12], [13], [14], [15]. A cohesive zone model describes the gradual degradation of the adhesion between two materials Ω_a and Ω_b along their common interface Γ. The nonlinear response of the

Implementation and computational requirements

The geometrically linear version of this cohesive zone model has been implemented in a 2D four-node user defined element in the commercial FE code MSC.Marc^®. Fig. 4 depicts the element conventions. The shear direction is from node 1 to node 2 in the undeformed configuration. The normal direction is perpendicular to the shear direction. Initially, the cohesive zone element is collapsed, i.e., it has a zero thickness. The nodal displacements form the element degrees of freedom (DOFs). This allows

Cylindrical arc-length method

Consider a multi-DOF nonlinear system, which is governed by the following equilibrium equation: $f_{i} (u) = f_{e} = α {\bar{f}}_{e} .$ This relation indicates that the internal force vector f_i, which is a nonlinear function of the solution vector u (or indeed a functional for the history-dependent behavior considered here), equals the external force vector f_e. The external force vector f_e can be expressed as the product of a scalar load factor α and the unit force vector ${\bar{f}}_{e}$ . In a load-controlled Newton–Raphson solution

Modeling of copper/low-k interconnects below bond pads

The copper/low-k interconnect structure below bond pads consists of several thin stacked layers of copper lines embedded in a low-k dielectric material. Layer thicknesses are on the order of 300 nm. Also SiO₂ is used as an electrically insulating material in some layers in order to improve the mechanical reliability of the structure [3]. The use of copper as a conductor requires the deposition of very thin hardmasks (≈40 nm thick), which are used as an etch stop during wafer fabrication. The

Simulation of interface delamination

Fig. 10 shows the force–displacement response at the control node obtained with the coarse FE model and the interface data set 1, i.e., the set with the largest characteristic separations λ_c resulting in the most ductile response. The diagram shows the force F_z versus the adjoint displacement U_z and it exhibits several limit points where the rate of either F_z or U_z switches sign. Three characteristic points are indicated in the graph by a–c. Fig. 11, Fig. 12, Fig. 13 show the corresponding

Discussion

Comparison of the simulation results for three interface data sets and for two FE models shows that the current implementation exhibits increasing numerical difficulties as the characteristic separation λ_c is diminished. According to the literature [20], mesh refinement should suffice to deal with the corresponding increased brittleness, but the current simulations do not confirm this. The solution procedure breaks down in an earlier stage in case of mesh refinement. The reason for this

Conclusions

This paper presents the ability of an interface damage mechanics approach in simulating delamination in copper/low-k IC interconnect structures. This approach allows one to consider several simultaneously evolving cracks, which were not present initially and whose location is a priori unknown. The adopted cohesive zone model describes the gradual degradation of adhesion between two materials along their common interface. A linear version of the cohesive zone model due to Smith and Ferrante has

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Cohesive zone modeling for structural integrity analysis of IC interconnects

Abstract

Introduction

Section snippets

Cohesive zone model

Implementation and computational requirements

Cylindrical arc-length method

Modeling of copper/low-k interconnects below bond pads

Simulation of interface delamination

Discussion

Conclusions

Microelectron Reliab

Engrg Fract Mech

Engrg Fract Mech

Engrg Fract Mech

Int J Solids Struct

Int J Solids Structures

Wire bonding in microelectronics, materials, processes, reliability, and yield