abstract: Miniaturization of microdevices comes at the cost of increased circuit complexity and operating current densities. At high current densities, the resulting electron wind imparts a large momentum to metal ions triggering electromigration which leads to degradation of interconnects and solder, ultimately resulting in circuit failure. Although electromigration-induced defects in electronic materials can manifest in several forms, the formation of voids is a common occurrence. This research aims at understanding the morphological evolution of voids under electromigration by formulating a diffuse interface approach that accounts for anisotropic mobility in the metallic interconnect. Based on an extensive parametric study, this study reports the conditions under which pancaking of voids or the novel void ‘swimming’ regimes are observed. Finally, inferences are drawn to formulate strategies using which the reliability of interconnects can be improved. / Dissertation/Thesis / Masters Thesis Materials Science and Engineering 2020

<p>A wide variety of phase evolution phenomena observed in solids such as intermetallic growth at the junction between two metals subjected to high temperature, growth of oxide on metal surfaces due to atmospheric exposure and void evolution induced by electromigration in microelectronic devices for example, can be classified as being driven by reaction-diffusion processes. These phase evolution phenomena have a significant impact on material reliability for critical applications, and therefore, there is a requirement for modeling such reaction-diffusion driven phase evolution phenomena. It is difficult to analyze these due to the complexity of modeling the evolving interface between solid phases. Additional complexity is  due to the multi-physics nature of the diffusive and reactive processes. Diffusion in solids is driven by a variety of stimuli such as current, temperature and stress, in addition to the chemical potential. Therefore, there is a need for a model that accounts for the influence of such factors on phase evolution. In this thesis,  a generalized continuum based reaction-diffusion theory for phase and void evolution in solid state is developed. The derivation starts off with generalized interface balance laws for mass, momentum and energy. The thermodynamic entropy inequality for irreversible phase growth is derived for arbitrary anisotropic and inhomogeneous surface stress. These interface relations are combined with governing relations in the material bulk for the temperature, stress, electrical and concentration fields, to develop a general model capable of analyzing and describing phase evolution in solids. This theory is then applied to a variety of intermetallic phase and void evolution phenomena observed in microelectronics.</p> <p><br></p> <p>Electromigration induced voiding in thin metal films is an example of phase evolution that is an important reliability concern in microelectronics. Studies have reported that the electromigration induced void growth rate is inversely related to the adhesion of metal thin films with the base and capping layers. Electromigration experiments are performed on fabricated test devices with Cu thin films with SiNx and TiN capping layers. The observations from electromigration experiments on thin Cu metal films at a range of temperatures indicate that the contribution of interface adhesion strength to electromigration resistance decreases with an increase in temperature. The generalized reaction-diffusion theory developed here is modified to develop an expression to account for the effect of base and passivation layer adhesion and temperature on electromigration resistance of metal thin films. The void growth rates measured in the experiments are analyzed with the expression for void growth rate to estimate the interface adhesion strength for the Cu-TiN and Cu-SiNx interfaces. </p> <p><br></p> <p>Demand for increased bandwidth, power efficiency and performance requirements have resulted in a trend of reduction in size and pitch of Cu pillar-Solder micro-bump interconnects used in heterogeneously integrated packages. As the size of micro-bumps reduce, reliability challenges due to voiding in the solder joint and the growth of Cu-Sn intermetallics are observed. The underlying reaction-diffusion mechanisms responsible for Cu-Sn intermetallic growth and voiding in solder joints are unclear at this stage and require further investigation. The current practice of material characterization in micro-bumps involve destructive cross-sectioning and polishing of the micro-bumps after testing. These processes result in loss of continuity in the samples used for the experiments, and material removal due to abrasive polishing might result in a loss of critical information. Therefore, a novel test device capable of non-destructive characterization of Cu-Sn intermetallic growth and voiding in sub-30 micron size micro-bumps is designed and fabricated in this work. The fabricated test devices are subjected to thermal aging for over 1000 h and the underlying reaction-diffusion mechanisms behind the intermetallic phase and void evolution are investigated. </p> <p><br></p> <p>A reaction-diffusion mechanism is proposed explaining the evolution of  various Cu-Sn intermetallic phases and solder joint void observed from experiments. Using the reaction-diffusion mechanism inferred from the thermal aging experiments and the generalized reaction-diffusion theory for phase evolution developed in this thesis, a sharp interface model is developed for the evolution of Cu-Sn intermetallic phases and solder joint void. The diffuse interface phase field equivalent equations for the sharp interface model governing equations are developed using matched formal asymptotic analysis. The evolution of Cu-Sn intermetallic phase and voids in the solder joint are simulated for different temperatures and current density to demonstrate the validity of the phase field and sharp interface models.  </p> <p><br></p>

The rate at which stars have formed throughout the history of theuniverse is not constant, it started out slow, increased until around redshift ∼ 2 when it reversed and became slower again. The reason for this behaviour is still being investigated with various models and simulations usually based upon dark matter halos. The aim of this study is to instead investigate whether there is a correlation between the cosmic star formation rate and the evolution of cosmic voids. This is achieved by comparing the total mass flow from voids with the amount of matter forming stars. A simple model of void mass flow is created and compared with observational data of star formation. The model is shown to exhibit the same behaviour as the star formation rate indicating that there is indeed a correlation between void evolution and star formation. This suggests it to be fruitful to create a more involved, alternative model of star formation based upon void evolution as opposed to the common halo evolution / Hur snabbt stjärnor bildas har genom universums historia förändrats över tid, det började långsamt och ökade sedan fram till rödförskutning ∼ 2 då trenden vände och saktade ner igen. Förklaringen till detta beteende utforskas fortfarande genom diverse modeller och simularingar som vanligtvis bygger på mörk materia halos. Syftet med detta arbete är att istället undersöka ifall det finns en korrelation mellan tomrumsutveckling och den kosmiska stjärnbildningen. Detta åstadkoms genom att jämföra det totala massflödet från tomrum med den massa som bildar stjärnorna. En simpel model för tomrumsutveckling skapas och jämförs med observationell data för stjärnbildningshastighet. Denna modell visar samma beteende som stjärnbildningen och tyder på att det finns en korrelation mellan denna och tommrumsutveckling. Som slutsats pekar denna studie på att det kan vara fruktbart att utveckla en mer anancerad modell för den kosmiska stjärnbildningen som bygger på tomrumsutveckling istället för mörk materia halos.