No presente trabalho, foi montado um sistema de eletrodifusão para o estudo dos efeitos da substituição de íons alcalinos, presentes no canal estrutural, por íons de hidrogênio (H POT. +), nas propriedades termoluminescentes e ópticas do quartzo. A corrente elétrica de eletrólise apresenta, na parte inicial de aquecimento, um ombro ou pico de corrente. Através da análise do comportamento deste pico e informações obtidas de dados de absorção óptica na região espectral do infravermelho, concluiu-se que o pico presente na curva inicial de eletrólise se deve ao complexo [AL POT. 3+/M POT. +]. As medidas de termoluminescência e absorção óptica na região espectral do visível e ultra-violeta foram feitas em amostras de quartzo eletrodifundidos e não eletrodifundidos e chegou-se à proposição de uma reação envolvendo os alcalinos presentes no canal. Nesta reação, os íons alcalinos fazem o papel de centros armadilhadores de íons de oxigênio O POT. produzidos pela radiação ionizante, e estabilizadores de vacâncias de oxigênio. O aquecimento, em tomo de 300 GRAUS C, provoca a desestabilização desses centros armadilhadores, liberando os íons alcalinos que reagem com os defeitos [ALO IND. 4] POT. 0 emitindo luz TL. Aproveitando a existência de canais estruturais, semelhantes ao quartzo, tentou-se eletrodifundir H POT + no berilo. Através de medidas de termoluminescência e corrente inicial de eletrólise, discute-se a possibilidade da existência do defeito [FE POT. 3+/M POT. +] no berilo. / A system of electrodiffusion was made in the laboratory to investigate effects of exchanging alkali ions, usually present in the structural channels by protons, in the optical and thermoluminescent properties of quartz. In the initial part of heating, the sweeping current presents a peak at about 350 GRAUS C. The analysis of the behaviour of this peak with additional data of optical absorption in the region of infrared, it was concluded that the peak at 350 GRAUS C of the current is due to [AL POT. 3+/M POT. +] system. Thermoluminescence and optical absorption spectra in the visible and ultraviolet light region for swept and unswept quartz were compared. Based on this comparison it was shown that, once irradiated to gama- or X-rays, alkali ions are removed from [AL POT. 3+/ M POT. +] and either couple to o ions or capture electron and become interstitial alkali atom, leaving, further, [ALO IND. 4] POT. 0 hole center. Heating at about 300 GRAUS C electrons from M POT 0 or M POT +O POT recombine with holes in [ALO IND. 4] POT. 0, emitting TL light, besides regrouping Al POT. 3+ and M POT. + to reform [Al POT. 3+/M POT. +] system by coulomb attraction. The electrodiffusion experiment was extended to beryl crystal, because beryl has also structural channels. To explain initial sweeping current behaviour as well as thermoluminescent property a mechanism involving [FE POT. 3+/M POT. +] system is proposed.

Dans cette thèse j’étudie l’impact de la géométrie de micro et nano-domaines biologiques sur les propriétés d'électrodiffusion, ceci à l'aide des équations aux dérivées partielles de Poisson-Nernst-Planck. Je considère des domaines non-triviaux ayant une forme cuspide ou elliptique. Mon objectif est de développer des modèles ainsi que des méthodes mathématiques afin d'étudier les caractéristiques électriques de ces nano/micro-domaines, et ainsi mieux comprendre comment les signaux électriques sont modulés à ces échelles. Dans la première partie j’étudie le voltage à l'équilibre pour un électrolyte dans un domaine borné, et ayant un fort excès de charges positives. Je montre que le premier temps de sortie dans une boule chargée dépend de la surface et non du volume. J’étudie ensuite la géométrie composées d'une boule à laquelle est attachée un domaine cuspide. Je construis ensuite une solution asymptotique pour le voltage dans les cas 2D et 3D et je montre qu’ils sont donnés au premier ordre par la même expression. Enfin, j’obtiens la même conclusion en considérant une géométrie formée d'une ellipse, dont je construis une solution asymptotique du voltage en 2D et 3D. La seconde partie porte sur la modélisation de la compartimentalisation électrique des épines dendritiques. A partir de simulations numériques, je mets en évidence le lien entre la polarisation de concentration dans l'épine et sa géométrie. Je compare ensuite mon modèle à des données de microscopie. Je développe une méthode de déconvolution pour extraire la dynamique rapide du voltage à partir des données de microscopie. Enfin j’estime la résistance du cou et montre que celle-ci ne suit pas la loi d'Ohm. / In this PhD I study how electro-diffusion within biological micro and nano-domains is affected by their shapes using the Poisson-Nernst-Planck (PNP) partial differential equations. I consider non-trivial shapes such as domains with cusp and ellipses. Our goal is to develop models, as well as mathematical tools, to study the electrical properties of micro and nano-domains, to understand better how electrical neuronal signaling is regulated at those scales. In the first part I estimate the steady-state voltage inside an electrolyte confined in a bounded domain, within which we assume an excess of positive charge. I show the mean first passage time in a charged ball depends on the surface and not on the volume. I further study a geometry composed of a ball with an attached cusp-shaped domain. I construct an asymptotic solution for the voltage in 2D and 3D and I show that to leading order expressions for the voltage in 2D and 3D are identical. Finally, I obtain similar conclusion considering an elliptical-shaped domain for which I construct an asymptotic solution for the voltage in 2D and 3D. In the second part, I model the electrical compartmentalization in dendritic spines. Based on numerical simulations, I show how spines non-cylindrical geometry leads to concentration polarization effects. I then compare my model to experimental data of microscopy imaging. I develop a deconvolution method to recover the fast voltage dynamic from the data. I estimate the neck resistance, and we found that, contrary to Ohm's law, the spine neck resistance can be inversely proportional to its radius.

A Partial Differential Equation (PDE) based model combining surface electromigration and wetting is developed for the analysis of the morphological instability of mono-crystalline metal films in a high temperature environment typical to operational conditions of microelectronic interconnects. The atomic mobility and surface energy of such films are anisotropic, and the model accounts for these material properties. The goal of modeling is to describe and understand the time-evolution of the shape of film surface. I will present the formulation of a nonlinear parabolic PDE problem for the height function h(x,t) of the film in the horizontal electric field, followed by the results of the linear stability analyses and computations of fully nonlinear evolution equation.

"More Than Moore's Law" is the driving principle for the electronic packaging industry. This principle focuses on system integration instead of transistor density in order to achieve faster, thinner, and smarter electronic devices at a low cost. A core area of electronics packaging is interconnection technology, which enables ultra-miniaturization and high functional density. Solder bump technology is one of the original, and most common interconnection methods for flip chips. With growing demand for finer pitch and higher number of I/Os, solder bumps have been forced to smaller dimensions and therefore, are subjected to higher current densities. However, the technology is now reaching its fundamental limitations in terms of pitch, processability, and current-handling due to electromigration. Electromigration in solder bumps is one of the major causes of device failures. It is accelerated by many factors, one of which is current crowding. Current crowding is the non-uniform distribution of current at the interface of the solder bump and under-bump metallurgy, resulting in an increase in local current density and temperature. These factors, along with the formation of intermetallic compounds, can lead to voiding and ultimately failure. Electromigration in solder bumps has prevented pitch-scaling below 180-210 microns, producing a shift in the packaging industry to other interconnection approaches, specifically copper pillars with solder. This research aims to explore the electromigration resistance of an adhesive-based copper-to-copper (Cu-Cu) interconnection method without solder, which is thermo-compression bonded at a low temperature of 180C. While solder bumps are more susceptible to electromigration, Cu is capable of handling two orders of magnitude higher current density. This makes it an ideal candidate for next generation flip chip interconnections. Using finite element analysis, the current crowding and joule heating effects were evaluated for a 30 micron diameter Cu-Cu interconnection in comparison with two existing flip chip interconnection techniques, Cu pillar with solder and Pb-free solder. A test vehicle (TV) was fabricated for experimental analysis with 760 bumps arranged in an area-array format with a bump diameter of 30 micron. Thermo-mechanical reliability of the test vehicle was validated under thermal cycling from -55C to 125C. The Cu-Cu interconnections were then subjected to high current and temperature stress from 1E4 to 1E6 amps per square centimeter at a temperature of 130C. The results establish the high thermo-mechanical reliability and high electromigration resistance of the proposed Cu-Cu interconnection technology.

To enable fast and reliable processors, advances must be made in the interconnections on the printed circuit board and in the interconnections from the chip to the printed circuit board. Processing techniques have been demonstrated to fabricate a copper-clad encapsulated air dielectric layer to enable low loss off-chip electrical signal lines using sacrificial polymers and the three dimensional patterning capabilities of imprint lithography. The inclusion of an air gap can eliminate the dielectric loss allowing the signal to propagate over longer lengths. Additionally, the low dielectric constant of air lowers the loss contributions from the conductor and increases the signal propagation velocity reducing delay. The metal shielding could minimize the crosstalk noise and radiation losses that are significant at high frequencies. The three dimensional patterning capabilities of imprint lithography fabricated curved structures and rounded terminations which can reduce reflections at discontinuities. Furthermore, imprint lithography also created planarized surfaces which simplified the buildup process. Since imprint lithography, only uses temperature and pressure to make a pattern it is an inexpensive and simple process advancement. The metal-clad encapsulated air dielectric structures were fabricated in a comparable number of registration steps to traditional transmission lines. Implementation of all copper chip to substrate interconnects would provide high conductivity electrical connections, resistance to electromigration while avoiding formation of brittle intermetallics. High aspect ratio polymer molds for copper electroplating interconnects could enable improved integrated circuit electrical performance. The properties of a new aqueous base develop, negative-tone photosensitive polynorbornene polymer have been characterized to develop mechanically compliant all copper connections between the chip and printed circuit board. High aspect ratio features of 7:1 (height:width) were produced in 70 ìm thick films in a single coat with straight side-wall profiles and high fidelity. The polymer films studied had a contrast of 11.6 and a low absorption coefficient. To evaluate the polymer's suitability to microelectronics applications, epoxy cross-linking reactions were studied as a function of processing condition through Fourier transform infrared spectroscopy, nano-indentation, and dielectric measurements. The fully cross-linked films had an elastic modulus of 2.9 GPa and hardness of 0.18 GPa which can improve the mechanical compliance of the copper interconnections. A photo-imprint lithography process was developed to improve the photo-patterning of the polynorbornene polymer for high aspect ratio hollow structures. A shallow photo-imprint stamp was developed to physically displace material in the polymer core. Since the imprint stamp displaces material in the area of the feature, the effective film thickness is reduced compared to the bulk film. The reduction in film height reduced the effects of scattering in the core and also facilitated transport of developer within the core. The photo-imprint lithography process resulted in high aspect ratio hollow core pillars that exceeded optical resolution capabilities for comparable feature sizes.

The microelectronics industry has been managing the RC delay problem arising from aggressive line scaling, by replacing aluminum (Al) by copper (Cu) and oxide dielectric by low-k dielectric. Electromigration (EM) turned out to be a serious reliability problem for Cu interconnects due to the implementation of mechanically weaker low-k dielectrics. In addition, line width and via size scaling resulted in the need of a novel diffusion barrier, which should be uniform and thin. The objective of this dissertation is to investigate the impacts of Ta barrier process, such as barrier-first and pre-clean first, and scaling of barrier and line/via on EM reliability of Cu/low-k interconnects. For this purpose, EM statistical test structures, having different number of line segments, line width, and via width, were designed. The EM test structures were fabricated by a dualdamascene process with two metal layers (M1/Via/M2), which were then packaged for EM tests. The package-level EM tests were performed in a specially designed vacuum chamber with pure nitrogen environment. The novel barrier deposition process, called barrier-first, showed a higher (jL)[subscript c] product and prolonged EM lifetime, compared with the conventional Ta barrier deposition process, known as pre-clean first. This can be attributed to the improved uniformity and thickness of the Ta layer on the via and trench, as confirmed by TEM. As for the barrier thickness effect, the (jL)c product decreased with decreasing thickness, due to reduced Cu confinement. A direct correlation between via size and EM reliability was found; namely, EM lifetime and statistics degraded with via size. This can be attributed to the fact that critical void length to cause open circuit is about the size of via width. To investigate further line scaling effect on EM reliability, SiON (siliconoxynitride) trenchfilling process was introduced to fabricate 60-nm lines, corresponding to 45-nm technology, using a conventional, wider line lithograph technology. The EM lifetime of 60-nm fine lines with SiON filling was longer than that of a standard damascene structure, which can be attributed to a distinct via/metal-1 configuration in reducing process-induced defects at the via/metal-1 interface. / text

The main goal of this dissertation was to study the bifurcation structure underlying families of low dimensional dynamical systems that model cellular excitability. One of the main contributions of this work is a mathematical characterization of profiles of electrophysiological activity in excitable cells of the same identified type, and across cell types, as a function of the relative levels of expression of ion channels coded by specific genes. In doing so, a generic formulation for transmembrane transport was derived from first principles in two different ways, expanding previous work by other researchers. The relationship between the expression of specific membrane proteins mediating transmembrane transport and the electrophysiological profile of excitable cells is well reproduced by electrodiffusion models of membrane potential involving as few as 2 state variables and as little as 2 transmembrane currents. Different forms of the generic electrodiffusion model presented here can be used to study the geometry underlying different forms of excitability in cardiocytes, neurons, and other excitable cells, and to simulate different patterns of response to constant, time-dependent, and (stochastic) time- and voltage-dependent stimuli. In all cases, an initial analysis performed on a deterministic, autonoumous version of the system of interest is presented to develop basic intuition that can be used to guide analyses of non-autonomous or stochastic versions of the model. Modifications of the biophysical models presented here can be used to study complex physiological systems involving single cells with specific membrane proteins, possibly linking different levels of biological organization and spatio-temporal scales.

The question of how ions interact with each other and with the potential energy barrier in thin lipid bilayer membranes has interested investigators for several years. The application of electrodiffusion theory to the study of this question is the central theme of this work. We have calculated current-voltage curves for barriers of various shapes and heights, in each case by means of numerically integrating the exact electrodiffusion equation as well as this same equation in the constant field approximation. We have also calculated the total charge in the membrane for the same conditions under which we have calculated the current-voltage curves.

We consider three different phenomena governing the fluid flow in the presence of charged particles: electroconvection in fluids, electroconvection in porous media, and electrodiffusion. Electroconvecton in fluids is mathematically represented by a nonlinear drift-diffusion partial differential equation describing the time evolution of a surface charge density in a two-dimensional incompressible fluid. The velocity of the fluid evolves according to Navier-Stokes equations forced nonlinearly by the electrical forces due to the presence of the charge density. The resulting model is reminiscent of the quasi-geostrophic equation, where the main difference resides in the dependence of the drift velocity on the charge density. When the fluid flows through a porous medium, the velocity and the electrical forces are related according to Darcy’s law, which yields a challenging doubly nonlinear and doubly nonlocal model describing electroconvection in porous media. A different type of particle-fluid interaction, called electrodiffusion, is also considered. This latter phenomenon is described by nonlinearly advected and nonlinearly forced continuity equations tracking the time evolution of the concentrations of many ionic species having different valences and diffusivities and interacting with an incompressible fluid. This work is based on [1, 2, 3] and addresses the global well-posedness, long-time dynamics, and other features associated with the aforementioned three models. REFERENCES:[1] E. Abdo, M. Ignatova, Long time dynamics of a model of electroconvection, Trans. Amer. Math. Soc. 374 (2021), 5849–5875. [2] E. Abdo, M. Ignatova, Long Time Finite Dimensionality in Charged Fluids, Nonlinearity 34 (9) (2021), 6173–6209. [3] E. Abdo, M. Ignatova, On Electroconvection in Porous Media, to appear in Indiana University Mathematics Journal (2023). / Mathematics

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