Phase Field Crystal Simulation Study On Growth Behavior Of Kirkendall Voids And Microcracks In Micro-scale Metal Interconnects

The micro-scale metal interconnect is an important part of integrated circuit(IC)systems and electronic packages.With the rapid development of electronic products towards further miniaturization,multifunction and high-reliability,the electronic packaging density has been increasing,and the size and distance of the micro-scale interconnects become smaller and smaller,which brings about an increasing proportion of the interface layer in the micro-scale interconnect.As is well-known,the interfacial microstructure of micro-scale metal interconnects plays a more and more important role in the reliability of the interconnects.Notably,during the service process,a large number of Kirkendall voids and microcracks often appear at the interface due to the migration of metal atoms,which can significantly decrease mechanical and electrical properties of the micro-scale metal interconnects,and deteriorate the the reliability of the interconnects.Recently,the theoretical and experimental studies on Kirkendall voids and microcracks have attracted much attention.Heretofore,however,it is very difficult to characterize the morphological evolution of Kirkendall voids and microcrack propagation by experimental observation and measurement.In this case,the computer-aided simulation has become a powerful approach to the study of the morphological evolution and growth behavior of Kirkendall voids and microcrack.Especially,with the rapid development of computer technology and materials science,among the methods for modeling and simulating microstructural evolution and growth of materials,the phase field crystal method based on the density functional theory is one of the most effective computational methods due to its advantages of being capable of coupling physical and mechanical properties of the materials,such as elasto-plastic deformation,grain orientation and anisotropy.In this thesis study,a binary phase field crystal method is used to simulate the morphological evolution and growth of Kirkendall voids in micro-scale metal interconnects with a focus on characterization of the influences of thickness and impurity content of alloy layer,symmetry and orientation difference of the interface and deformation on the morphological evolution and growth behavior of the voids.Further,the process of microcrack propagation in micro-scale metal interconnects is studied by the phase field crystal method of pure materials,and the effects of initial notch region,biaxial tensile strain and orientation angle on microcrack propagation are analyzed.Firstly,the influences of the thickness and impurity content of the alloy layer on the growth behavior of Kirkendall voids in metal micro-interconnect are studied by the binary phase field crystal method.The results show that the growth of Kirkendall voids exhibits two stages,i.e.,theinitial growth stage and rapid growth stage.The average size of Kirkendall voids increases with time,and the coalescence of Kirkendall voids occurs in the late stage.The number of Kirkendall voids increases initially and then decreases with time.The increase of the alloy(β phase)layer thickness and impurity content in the alloy layer lead to an increase in both the average size and growth exponent of Kirkendall voids.The change in the β phase layer thickness and impurity content show no big influence on the nucleation site of Kirkendall voids,which nucleate by grain boundary nucleation mechanism after saturation.Further,the influences of the alloy interface symmetry and orientation on Kirkendall void in micro-scale metal interconnects morphology and growth behavior are characterized by simulation.The results manifest that the nucleation of Kirkendall voids takes place by grain boundary nucleation after saturation,regardless of the symmetry and misorientation of the interfaces.Kirkendall voids distribute uniformly at the interface with small misorientation angle,while showing non-uniform distribution at the interface with large misorientation angle and growing by coalescence.The number of Kirkendall voids increases initially and then decreases with time.The growth exponent of Kirkendall voids decreases initially and then increases with the increase of the small(or large)interface misorientation angle,regardless of the symmetry of the interface.The simulation results of the morphological evolution and growth behavior of Kirkendall void in micro-scale metal interconnects during the deformation process show that the nucleation of Kirkendall voids occurs at grain boundary after saturation,and the growth direction of Kirkendall voids is parallel to the interface.The average size of the Kirekendall voids increases with time and strain rate.There is an obvious coalescence of the voids at a large strain rate(≥7×10-6)when the deformation is applied along the interface under both constant and bidirectional cyclic strain rate conditions.For the constant strain rate and unidirectional cyclic strain rate applied along the interface,the growth exponent of Kirkendall voids increases with increasing the strain rate.For the bidirectional cyclic strain rate applied along the interface,the growth exponent of Kirkendall voids increases with increasing the strain rate when the strain rate is larger than 1.0×10-6,while increasing initially and then decreasing when the strain rate is smaller than 9.0×10-7.The change in the length of the cyclic period under the constant strain rate has little effect on the average size of Kirkendall voids.The growth exponent of Kirkendall voids increases initially and then decreases gradually with increasing the length of bidirectional cyclic period under a square-wave form constant strain rate.The growth exponent of Kirkendall voids decreases initially and then increases gradually with increasing the length of unidirectional cyclic period under a square-wave form constant strain rate.The effects of morphology,density of initial notch,biaxial tensile strain and grain orientation on the propagation of the microcrack in metal micro-interconnect interface are also studied by simulation using the phase field crystal method of pure materials.The results show that the length and area fraction of the microcrack gradually increase with time,while the microcrack propagation rate decreases initially and then becomes stabilized with time.For a rectangular initial notch morphology,the length,propagation rate and extension area of the microcrack are the largest,in comparison with square and circular initial notch morphologies.By contrast,for a circular initial notch morphology,the crack propagation length,propagation rate and extension area are the smallest.The area fraction and number of the microcrack branches increase with increasing the atomic density in the initial crack notch.The larger the strain is,the more favorable the propagation of microcracks and generation of secondary and tertiary cracks take place.The free energy of system decreases with time,and the cycle and distance of atoms increase with increasing the strain in the x direction and the orientation angle.