Haixia Mei

Buckling modes of elastic thin films on elastic substrates

Two buckling modes have been observed in thin films: buckle delamination and wrinkling. This letter identifies the conditions for selecting the favored buckling modes for elastic films on elastic substrates. Transition from one buckling mode to another is predicted as the stiffness ratio between the substrate and the film or is predicted for variation of the stiffness ratio between the substrate and the film or variation of theinterfacial defect size. The theoretical results are demonstrated experimentally by observing the coexistence of both buckling modes and mode transition in one film-substrate system.

A comparison of direct and iterative methods for determining traction-separation relations

Traction-separation relations have been used to represent the adhesive interactions at bimaterial interfaces for contact and fracture analyses. There are a variety of methods for determining these relations, which are broadly sorted into iterative and direct methods. Here we compare the traction-separation relations for a silicon/epoxy interface extracted by two such methods. Interferometric measurements of the normal crack opening displacements near the crack front in a double-cantilever beam specimen were exploited along with an augmented analytical solution for J-integral as an illustration of the direct method. As an example of the iterative method, we relied on comparisons of measured crack length and normal crack opening displacements with numerical simulations obtained from two types of candidate traction-separation relations. It was found that the shape of the traction-separation relation, in addition to the interfacial toughness and strength, was needed to bring the numerical solutions into optimal registration with the measurements. On the other hand, the direct method lived up to its name in terms of ease of parameter extraction while providing a reasonable set of parameters.

Initiation and propagation of interfacial delamination in integrated thin-film structures

Interfacial delamination has been a major reliability issue for both BEoL and packaging systems. The failure is often due to poor adhesion of interfaces. Thus characterization of interfacial properties is critical for material selection and process control. Conventional methods for interfacial adhesion and fracture toughness measurements are generally based on linear elastic fracture mechanics. More detailed local measurements are required to fully characterize the interfaces based on a nonlinear cohesive interface model. With the experimentally determined interfacial properties, cohesive interface modeling can be set up to predict the initiation and evolution of interfacial failure in chip-package systems. In this study, two model systems are considered by approaches of both linear elastic fracture mechanics (LEFM) and cohesive interface modeling (CIM). First, for a brittle thin film on a compliant substrate, the initiation and propagation of delamination from the root of a channel crack is simulated. The effects of the cohesive strength and fracture toughness of the interface on channel cracking of thin films on compliant substrates are analyzed. Second, a four-point bend test is considered, in comparison with experimental measurements of the local crack opening displacements.

Fracture, delamination, and buckling of elastic thin films on compliant substrates

A series of studies have been conducted for mechanical behavior of elastic thin films on compliant substrates. Under tension, the film may fracture by growing channel cracks. The driving force for channel cracking (i.e., the energy release rate) increases significantly for compliant substrates. Moreover, channel cracking may be accompanied by interfacial delamination. For a film on a relatively compliant substrate, a critical interface toughness is predicted, which separates stable and unstable delamination. For a film on a relatively stiff substrate, however, a channel crack grows with no delamination when the interface toughness is greater than a critical value. An effective energy release rate for the steady-state growth of a channel crack is defined to account for the influence of interfacial delamination on both the fracture driving force and the resistance, which can be significantly higher than the energy release rate assuming no delamination. Alternatively, when the film is under compression, it tends to buckle. Two buckling modes have been observed, one with interfacial delamination (i.e., buckle-delamination) and the other without delamination (i.e., wrinkling). By comparing the critical stresses for the onset of buckling, we give a criterion for the selection of the buckling modes, which depends on the stiffness ratio between the film and the substrate as well as the interface defects. A general conclusion from these studies is that, whether tension or compression, the interfacial properties are critical in controlling the morphology and failure of elastic thin films on compliant substrates.

Finite element modeling of stress variation in multilayer thin-film specimens for in situ transmission electron microscopy experiments

Multilayer thin-film materials with various thicknesses, compositions, and deposition methods for each layer typically exhibit residual stresses. In situ transmission electron microscopy (TEM) is a powerful technique that has been used to determine correlations between residual stresses and the microstructure. However, to produce electron transparent specimens for TEM, one or more layers of the film are sacrificed, thus altering the state of stresses. By conducting a stress analysis of multilayer thin-film TEM specimens, using a finite element method, we show that the film stresses can be considerably altered after TEM sample preparation. The stress state depends on the geometry and the interactions among multiple layers.

Direct Determination of Interfacial Traction-Separation Relations in Chip-Package Systems

Microelectronic devices are multilayered structures with many different interfaces. Their mechanical reliability is of utmost importance when considering the implementation of new materials. The cohesive interface modeling approach has the capability of modeling crack nucleation and growth, provided interfacial parameters such as strength and toughness of the system are available. These parameters are obtained through the extraction of traction-separation relations, through indirect either hybrid numerical/experimental methods or direct experimental methods. The direct method promises to determine the parameters in an unambiguous manner. All methods of extracting traction-separation relations require some local feature of the crack-tip region to be measured.