Electromigration (EM) is a crucial failure mode in Aluminum (Al) interconnection wires those are widely used in high density semiconductor packaging. This study systematically investigated the influence of EM on the mechanical properties of Al interconnects via nanoindentation experiments and molecular dynamics (MD) simulations. The results are list as follows. (1) The indentation depth gradually increases with the increase in indentation load, resulting in a gradual increase and stabilization of the Young’s modulus and hardness of the structure. Within a specific range, the influence of the loading rate on the indentation depth and mechanical properties is relatively small. (2) The region where Young’s modulus of the interconnect decreases correlates with the location where EM-induced voids initiate. EM-induced voids have a direct impact on the material’s mechanical properties, particularly the decrease in Young’s modulus. (3) These EM-induced voids affect the nucleation and formation of dislocations. With the increase in void concentration and indentation depth, The generation and slip of dislocations increase as the void concentration and indentation depth increase, leading to a decrease in the material’s mechanical properties over time. This comprehensive findings expand the knowledge on mechanical behavior degradation of Al interconnects when EM failure occurs, providing a scientific basis for designing and optimizing high density semiconductor packaging.@en

The authors regret that in the above article the Fig. 3 contains an error of cross-section image of group C at 48 h on Page 4. Fig. 3 should read: This correction does not influence the method, results and conclusions of the original article. The authors would like to apologise for any inconvenience caused.

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In this study, we combined finite element method (FEM) based on Ansys and Noesis Optimus software to investigate the effect of bump structures and loading conditions on the electromigration properties of solder bumps in WLCSP. A numerical model considering current density, vacancy concentration, stress and temperature was utilized to calculate the vacancy concentration in solder bumps. The Optimus is an optimization software which can be used to perform the design of experiment (DOE) and sensitivity analysis. To optimize the bump structure, the DOE and response surface modeling (RSM) analysis were performed by using Noesis Optimus. The design optimization based on Noesis Optimus has three main advantages. First, the sensitivity analysis based on DOE results helps to find the most contributing factors. Second, it saves huge time because hundreds of experiments can be executed automatically. Third, it is able to perform evolutionary design optimization directly on RSM to identify the design’s optimal performance point. The maximum and concentration around solder were selected as the index to evaluate the effect of parameter combination on electromigration properties.@en

This paper investigates thermomigration (TM) and electromigration (EM) in SWEAT structure. Firstly, the distribution of temperature along SWEAT structure during EM is obtained by using finite element (FE) simulation. The FE simulation results show that the temperature is almost uniformly distributed in the most region of narrow line in SWEAT structure, but temperature decreases rapidly at both sides of conductor. Accordingly, the temperature gradient in the narrow line of SWEAT structures is calculated. Then, we apply the obtained temperature and temperature gradient in the governing equation of EM in terms of atomic concentration. The numerical results show that the TM caused by temperature gradient causes the material depletion near both ends of conductor. At the same time, atoms diffuse from the middle region of conductor to both sides driven by the atomic concentration, causing the voids in middle of conductor.@en

This paper presented a comprehensive experimental and simulation study for thermomigration (TM) accompanying electromigration (EM) at elevated current densities. Both Blech and standard wafer-level electromigration acceleration test (SWEAT)-like test structures, with aluminum (Al) as a carrier, were used for testing and analysis. In Part I of our study (Cui et al., 2023a), the experimental and numerical results with the current density of 1 MA/cm² were presented. We observed that Al stripes with a SWEAT structure did not show damage in the entire length, while Blech structures showed void and hillock formations only at the cathode and anode, respectively. The temperature gradient owing to Joule heating was neglected in our previous simulations, and the predicted results agreed well with the experimental observations. However, we have not theoretically verified the effect of the temperature gradient. In this paper, we first reported the new experimental data under the elevated current densities of 3 and 5 MA/cm². In both Blech and SWEAT structures, the spreading of voids in the middle region of conductors was observed. Moreover, in Blech structures, voiding in the middle region occurred after a period of time when voids/hillocks were formed at the cathode and anode, while the SWEAT structures did not show damage at the two ends. Next, based on the coupled 3D theory (Cui et al., 2023a), new analytical one-dimensional (1D) solutions were derived for the Blech and SWEAT structures in the un-passivated configuration considering TM. We found that TM played a significant role in the EM development in the middle of conductors under the elevated current density. The numerical results were in excellent agreement with the experimental data with the consideration of TM. We further established new EM failure's threshold criteria for the SWEAT structures in the form of the product of current density and square of conductor length. This is a major departure from the original Blech's theory in which only mechanical stress gradient was considered. We also studied the acceleration factor of the current density exponent and presented an insight into failure mechanisms associated with TM.

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This paper presented integrated electromigration (EM) studies through experiment, theory, and simulation. First, extensive EM tests were performed using Blech and standard wafer-level electromigration acceleration test (SWEAT)-like structures, which were fabricated on four-inch wafers. Second, a molecular dynamics (MD) simulation-based diffusion-induced strain was incorporated into the existing coupled theory. Third, one-dimensional (1D) governing equations in terms of atomic concentration for un-passivated and passivated configurations were derived for void formation and growth, using a modified Eshelby's solution to consider the effect of passivation. Fourth, a systematic approach was established, including theoretical formulations and experimental methods, to obtain key material properties, i.e., critical atomic concentration and diffusivity. We then determined the material's properties from a specific set of experimental data, using aluminium (Al) as a carrier for demonstration. These properties were then used to predict the time to failure and void growth under various conditions. The theoretical results agreed well with the experimental data. Moreover, we theoretically determined the critical threshold products of current density and conductor length for the un-passivated and passivated configurations, respectively. Both experiment and theory showed that, in the absence of mechanical stress in un-passivated configurations, the atomic self-diffusion, which was opposite to electron wind, was significant in resisting EM development. However, when mechanical stress was present, such as in passivated configurations, stress migration played a dominant role in resisting EM development. Our numerical results showed that the current density exponent n in Black's law remained as 2 in the range of the current density greater than 0.2 MA/cm² and rapidly approached infinity at a low level of current density.

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In this paper, we apply the Eshelby's solution to study the effect of passivation layer on electromigration (EM) failure in a conductor. The passivation layer is considered as an elastic material, not a rigid layer anymore. Thus, the deformation and stress evolution in the conductor during EM are related to the mechanical property of the passivation layer. One-dimensional (1D) analytical solution for the passivated conductor is obtained. The numerical results show that the conductor covered with the stiffer passivation layer has much less EM damage. And the steady-state solution shows that the magnitude of (jL)c increases with increasing Young's modulus of passivation material. The present study provides a way to predict the EM performances taking into account various passivation materials.

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The continuous downscaling of microelectronics has introduced many reliability issues on interconnect. Electromigration and dewetting are major reliability concerns in high-temperature micro- and nanoscale devices. In this paper, the local dewetting of copper thin film during the electromigration test was first found and investigated. When the high current was applied, the dewetted copper forming around the edge was observed at the cathode of the conductor. Furthermore, the effect of temperature and conductor size on local dewetting was investigated. Our proposed mechanism for local dewetting is in good agreement with experimental findings.

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Understanding the atomic diffusion features in metallic material is significant to explain the diffusion-controlled physical processes. In this paper, using electromigration experiments and molecular dynamic (MD) simulations, we investigate the effects of grain size and temperature on the self-diffusion of polycrystalline aluminium (Al). The mass transport due to electromigration are accelerated by increasing temperature and decreasing grain size. Magnitudes of effective diffusivity (Deff) and grain boundary diffusivity (DGBs) are experimentally determined, in which theDeffchanges as a function of grain size and temperature, butDGBsis independent of the grain size, only affected by the temperature. Moreover, MD simulations of atomic diffusion in polycrystalline Al demonstrate those observations from experiments. Based on MD results, the Arrhenius equation ofDGBsand empirical formula of the thickness of grain boundaries at various temperatures are obtained. In total,DeffandDGBsobtained in the present study agree with literature results, and a comprehensive result of diffusivities related to the grain size is presented.

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In a light-emitting diode (LED) package, silicone encapsulant serves as a chip protector and enables the light to transmit, since it exhibits the advantages of high light transmittance, high refractive index, and high thermal stability. However, its reliability is still challenged under harsh operation conditions. In this study, the optical and mechanical properties of silicone encapsulant, including appearance, light transmittance, Young’s modulus, and tensile strength, were experimentally monitored during the sulfur-rich ageing process. Meanwhile, the Fourier transform infrared (FTIR) spectroscopy and molecular dynamics (MD) simulation were used to reveal its degradation mechanism. The results show that 1) in the sulfur (S₈)-rich ageing process, the severe vulcanization reaction occurred in silicone encapsulant assisted only by high temperature and high moisture, with the existence of H₂S as the reaction product of S₈ and H₂O vapor. 2) Vulcanization characterized by the formation of the sulfhydryl (-SH) group lowered both optical and mechanical properties of silicone encapsulant. 3) The hydrolysis reaction featured by the formation of the hydroxyl (-OH) group decreased the mechanical performances of silicone encapsulant but brought slight harm to its optical performances.

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In this paper, a 3D and fully coupled electromigration modeling is implemented using COMSOL. The fully coupled multi-physics theory has a unique set of partial differential equations, which cannot be directly simulated with the standard finite element software such as ABAQUS and ANSYS. With the weak form PDE modulus in COMSOL, the weak form of the governing equations is obtained and realized for a 3D finite element modeling of electromigration. The metal lines under totally constrained and stress-free conditions with a perfectly blocking condition are presented as benchmark problems, in which the finite element solutions are in excellent agreement with the analytical solutions.@en

In high power electronics packaging, sintered silver nanoparticle joints suffer from thermal-humidity- electrical-chemical joint driven corrosion in extreme environments. In this paper, we conducted aging tests on sintered silver nanoparticles under high-temperature, high-humidity, and high-sulphur conditions. The results show that: (1) the sample under the dry high-sulphur conditions at a high temperature exhibited the highest degree of sulphidation; (2) Reactive force field (ReaxFF) molecular dynamics (MD) simulations of sintered silver nanoparticle sulphidation revealed the sulphidation layer was formed by silver atoms upward migration. This work paves the way for further investigation on sintered silver nanoparticles corrosion considering multi-physics coupling effects.

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In this paper, large-scale molecular dynamic (MD) simulation is performed to investigate the concentration-dependent vacancy volume relaxation in Al, Cu, and Au, respectively. The vacancy volume relaxation factor is calculated and correlated to the microstructure change based on MD results. It is found that the vacancy volume relaxation factor is nearly a constant at low to mid-vacancy concentration level, i.e., from 10−6 to 10−3 of the lattice concentrations. However, the volume of vacancies will completely collapse at the high vacancy concentration, and the coalescence of vacancies will form massive dislocations. The simulation results are in good agreement with the existing data from both experiments and simulations in the literature. A uniform empirical equation is developed to obtain the vacancy volume relaxation factor as a function of vacancy concentration. Furthermore, the hydrostatic stress is also calculated based on MD simulations. This paper also discusses the relationship between the vacancy volume relaxation and the diffusion-induced strain, such as in the application of electromigration. For a constrained condition, the hydrostatic stresses obtained from MD-based vacancy volume relaxation and a commonly used stress-vacancy equation are compared. An insight on the critical vacancy concentration at which electromigration failure would occur is discussed in detail.@en

This paper analyzes the mechanical properties of tungsten disulfide (WS2) by means of multiscale simulation, including density functional theory (DFT), molecular dynamic (MD) analysis, and finite element analysis (FEA). We first conducted MD analysis to calculate the mechanical properties (i.e., Young's modulus and critical stress) of WS2. The influence of different defect types (i.e., point defects and line defects) on the mechanical properties are discussed. The results reveal that WS2 has a high Young's modulus and high critical stress. Next, the effects of defect density and temperature on the mechanical properties of the material were analyzed. The results show that a lower defect density results in improved performance and a higher temperature results in better ductility, which indicate that WS2 can potentially be a strain sensor. Based on this result, FEA was employed to analyze the WS2 stress sensor and then fabricate and analyze the device for benchmarking. It is found that the FEA model proposed in this work can be used for further optimization of the device. According to the DFT results, a narrower band gap WS2 is found with the existence of defects and the applied strain. The proposed multiscale simulation method can effectively analyze the mechanical properties of WS2 and optimize the design. Moreover, this method can be extended to other 2D/nanomaterials, providing a reference for a rapid and effective systematic design from the nanoscale to macroscale.

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This dissertation presents a comprehensive and integrated study, including theory development, numerical simulation and experiment, for multi-physics driven electromigration in microelectronics. Multi-scale methodologies from atomistic modeling to continuum theory-based simulation have been developed. Moreover, extensive experimental testing, from testing wafer/die design and fabrication, sample preparation and process, to the measurement setup and characterization, has been conducted. The dissertation also provides synergetic and cohesive analysis between simulation and experiment. The simulation predictions and results have been well validated by experimental data.@en

The CaAlSiN₃:Eu²⁺ red phosphor and its silicone/phosphor composite are very promising materials used in the high color rendering white light-emitting diode (LED) packaging. However, the reliabilities of CaAlSiN₃:Eu²⁺ and its composite are still being challenged by phosphor hydrolysis at high humidity application condition. A fundamental understanding of the interface adhesion between silicone and CaAlSiN₃:Eu²⁺ is significant for the developments and applications of this material. In this work, the mechanical properties of silicone/pristine CaAlSiN₃:Eu²⁺ and silicone/hydrolyzed CaAlSiN₃:Eu²⁺ composites are experimentally measured and compared firstly, in which both the tensile strength and Young's modulus of composite are increased after the hydrolysis reaction. Then, the first principles Density Functional Theory (DFT) calculations are used to investigate the adhesion behaviors of the silicone molecular on both the pristine and the hydrolyzed CaAlSiN₃[0 1 0] at atomic level. The results show that: (1) The silicone molecular is weakly adsorbed on the pristine CaAlSiN₃[0 1 0] via Van der Waals (vdW) interactions, while silicone molecular is much stronger absorbed on the hydrolyzed CaAlSiN₃[0 1 0] due to the formation of hydrogen bonding at the interface; (2) The transient state calculations indicate that the sliding energy barrier of silicone on the hydrolyzed CaAlSiN₃[0 1 0] is higher than that on the pristine one, as the increased adsorption energy and surface roughness. Generally, the findings in this paper can guide the phosphor selection, storage and process in LED packaging, and also assist in improving the reliability design of LED package used in high moisture condition.

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At present, most high-power white Light-emitting diode and laser diode (LED&LD) package is usually constructed by a blue LED&LD chip with a Cerium doped Yttrium Aluminum Garnet (YAG:Ce³⁺) yellow phosphor, but its color rendering performance is severely challenged due to the lack of red light emission spectrum. The CaAlSiN₃:Eu²⁺ red phosphor can effectively improve the color quality of traditional yellow phosphor converted white LED&LDs(pc-wLED&LDs), however, it is often susceptible to degradation under high temperature and high humidity environments, which will directly affect the color quality of pc-wLED&LDs. In this study, a series of water immersion tests on CaAlSiN₃:Eu²⁺ red phosphor are used to quantitatively study its hydrolysis reaction kinetics. Then, the degradations of its photoluminescence and photothermal performances are evaluated by characterizing the crystal structure, micromorphology and chemical element composition. Finally, an atomic level hydrolysis reaction mechanism of CaAlSiN₃:Eu²⁺ red phosphor is investigated by using the first-principles density functional theory (DFT) calculation. The results show that: (1) By modelling the in-situ monitored electrical conductivity of CaAlSiN₃:Eu²⁺ red phosphor water solution with a first-order reaction function, the calculated hydrolysis reaction rate satisfies the Arrhenius relationship and the reaction activation energy is estimated as 49.19 kJ/mol; (2) The increased self-heating effect of CaAlSiN₃:Eu²⁺ red phosphor after water immersion test attribute to its drastic drop of light emission efficiency; (3) The hydrolysis reaction mechanism of CaAlSiN₃:Eu²⁺ red phosphor is confirmed, which sequentially results in the dissolution of Ca²⁺ and OH⁻, the crash of host lattice and the accumulation of reaction residues.

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A molecular dynamics (MD) simulation was performed on the coalescence kinetics and mechanical behavior of the pressure-assisted Cu nanoparticles (NPs) sintering at low temperature. To investigate the effects of sintering pressure and temperature on the coalescence of the nanoparticles, sintering simulations of two halve Cu NPs were conducted at the pressure of 0–300 MPa and the temperature of 300–500 K. A transition of the dominant coalescence kinetics from slight surface diffusion to intensive grain boundary diffusion and dislocation driven plastic flows were found when pressure was applied. Furthermore, atomic trajectories showed the effect of temperature on sintering was strongly dependent on the microstructures of Cu NPs. The atomic diffusion around defects can be significantly promoted by the elevated temperature. Additionally, based on the sintered structures, uniaxial tension simulation was implemented with a constant strain rate. Stress–strain curves and evolution of dislocation activities were derived. Improved mechanical behaviors, including larger elastic modulus and larger tensile strength, were obtained in the structure sintered under higher pressure and temperature. Among this study, sintering temperature and pressure consistently exhibited the same relative impact on affecting both coalescence and the mechanical properties of the sintered structure.@en

In this paper, a recently developed theory - general coupling model of electromigration, is implemented in ANSYS. We first identify several errors provided in ANSYS manual for electromigration modeling. Then the general coupling model is implemented in ANSYS and the detailed description is presented. Finally, a 1-D confined metal line with a perfectly blocking condition is presented as a benchmark problem, in which the finite element solutions are in excellent agreement with the analytical solutions.

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A three-dimensional (3D) general coupling model for electromigration has been developed with the use of the mass conservation equation. The flux terms that include concentration gradient, electron wind force, stress migration, and thermal migration are considered. The constitutive equation for the electromigration strain has been derived. Then, the governing equations for one-dimensional (1D) metal lines are obtained for both totally fixed and stress-free mechanical boundary conditions. The numerical results reveal that the hydrostatic stress is significantly lower than the predicted results in the existing literature for the totally fixed configuration. Extensive discussions are presented to provide the explanations of such difference. The vacancy concentration gradient plays an important role in formulating electromigration problems. The current-driven flux can be entirely balanced by the concentration gradient that acts as an opposing force during electromigration under a stress-free condition in steady-state. The new solutions of the critical threshold jL, the product of current density, and metal line length are obtained in terms of vacancy concentration. As electromigration is eventually determined by the void growth, the critical vacancy concentration is used to reanalyze Blech's experiment data. The theoretical predictions are consistent with the experimental observations.

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