A phase field model for failure in interconnect lines due to coupled diffusion mechanisms

We describe a diffuse interface, or phase field model for simulating electromigration and stress-induced void evolution and growth in interconnect lines. Microstructural evolution is tracked by defining an order parameter, which takes on distinct uniform values within solid material and voids, and varying rapidly from one to the other over narrow interfacial layers associated with the void surfaces. The order parameter is governed by a form of the Cahn-Hilliard equation. An asymptotic analysis demonstrates that the zero contour of order parameter tracks the motion of a void evolving by coupled surface and lattice diffusion, driven by stress, electron wind and vacancy concentration gradients. Efficient finite element schemes are described to solve the modified Cahn-Hilliard equation, as well as the equations associated with the accompanying mechanical, electrical and bulk diffusion problems. The accuracy and convergence of the numerical scheme is investigated by comparing results to known analytical solutions. The method is applied to solve various problems involving void growth and evolution in representative interconnect geometries.     

Discrete resistance fluctuations in pressure-type point contacts

In high ohmic pressure-type metallic point contacts (resistance range 50 Ω to 3 k Ω) the point-contact resistance is observed to switch randomly between two or more discrete levels. This effect can be explained by the motion or reorientation of single defects, thereby changing their cross section for electron scattering. From the temperature- and voltage-dependence of the characteristic times of the fluctuations, electromigration parameters for a defect in silver are extracted.     

Creep flow, diffusion, and electromigration in small scale interconnects

This paper proposes a three-dimensional electromigration model for void evolution in small scale interconnects. Concurrent kinetics of creep flow and surface diffusion as well as the effect of the surrounding material is considered to provide better understanding of the evolution process. The multiple kinetics and energetics are incorporated into a diffusive interface model. A semi-implicit Fourier spectral method and the preconditioned biconjugate-gradient method are proposed for the computations to achieve high efficiency and numerical stability. We systematically studied kinetic processes in diffusion dominated to creep dominated regime. Which process dominates, as revealed by the analysis, is determined by a combination of viscosity, mobility, interconnect thickness, and void radius. Previous studies on electromigration suggest that a circular void subjected to an electron wind force and surface diffusion is always stable against any small shape perturbation. Our simulations show that a shape that is stable in surface diffusion can become unstable in a creep dominated process, which leads to a quite different void morphology. A spherical void can evolve into a bowl shape and further break into smaller voids. It is also shown that the interconnect geometry has an important effect.     

A thermodynamic model for electrical current induced damage

Electromigration-induced damage, which is in principal an irreversible mass diffusion under high current density, has been a concern for VLSI design for a long time. Miniaturization of electronic device sizes down to nano-scale will make electromigration a concern for all conducting components. This paper uses thermodynamics, statistical mechanics and mass transport (diffusion) principals to propose a model for electromigration process and a damage evolution model to quantify the degradation in microelectronics (and micro electromechanical system) solder joints subjected to high current densities. Entropy production in the system is used as a damage metric. The irreversible thermodynamic damage model utilized in this work has previously been successfully applied to thermo-mechanical fatigue of microelectronic solder joints. In this paper we extend this model to electromigration-induced degradation.Electromigration process is modeled by the atomic vacancy flux (mass diffusion) process. The proposed unified model is compared with several existing analytical and empirical models. A comparison of the damage evolution model proposed in here agrees well with empirical models proposed in the literature.     

A simplified model of oscillating electrolytes

Unstable electrophoretic transport leading to oscillations in concentration profiles occur in certain electrolyte systems known as oscillating electrolytes whose eigenmobilities are complex valued. The study of the nonlinear behavior of such systems is of great interest but is constrained due to a high degree of complexity in the governing equations. Here we present a simplified model of unstable electrophoretic transport in a binary system that reduces the governing equations to two partial differential equations only and does away with other equations that characterize acid–base dissociation reactions and electroneutrality. We present analytical expressions for electromigration fluxes and validate the model with full nonlinear simulations. The model exhibits similar nonlinear behavior as the actual unstable electrophoretic system under various initial disturbances. For comparison, we also show that similar modeling for a stable system predicts concentration profiles that quantitatively agree with its nonoscillating dynamics. Moreover, the unique feature of electromigration flux in oscillating electrolytes that unfolds from the modeling led us to find an elegant explanation of the instability mechanism. Our theory gives a qualitative understanding of the existence and growth of large oscillation patterns in oscillating electrolytes.     

毛细管电泳电迁移扩散的定量研究

电迁移扩散是毛细管电泳中影响区带展宽的重要冈素之一。本文利用毛细管电泳电导检测装置对电迁移扩散进行了定量研究,提出一种评价电迁移扩散的方法。在该方法中引入一种描述电迁移扩散的物理量,它可通过几个易测的实验参数来计算。它不仅考虑到电迁移进样的歧视效应,而且考虑到样品浓度对电迁移扩散的影响。采用毛细管电泳中常用的两种缓冲液(磷酸和甲酸-组氨酸)对该方法进行了实验验证,结果表明它与理论预测符合良好。     

Analysis of carboxylic acids in biological fluids by capillary electrophoresis

This review article addresses the different capillary electrophoretic methods that are being used for the study of both short-chain organic acids (including anionic catecholamine metabolites) and fatty acids in biological samples. This work intends to provide an updated overview (including works published until November 2004) on the recent methodological developments and applications of such procedures together with their main advantages and drawbacks. Moreover, the usefulness of CE analysis of organic acids to study and/or monitor different diseases such as diabetes, new-borns diseases or metabolism disorders is examined. The use of microchip devices and CE-MS couplings for organic acid analysis is also discussed.     

一种移动化学反应界面的实验装置

描述了一种移动化学反应界面的实验装置，这一装置备有二台恒流泵用于连续性地驱动阴极液和阳极液，备有二根连接于计录仪的电极用于测定反应管两端的电压。用０．００５ｍｏｌ．Ｌ＾－１ＣｏＣｌ２和０．０１ｍｏｌ．Ｌ＾－１ＮａＯＨ（同时含有０．１ｍｏｌ．Ｌ＾－１背景电解质（ＫＣｌ）形成的移动化学反应界面实验了这一装置。结果表明：（１）能很好地避免电解时产生的氢离子和氢氧根离子的干扰；（２）在单根凝胶柱上可进行多     

A Novel and Optimized Method for Electro-focusing and Moving Neutralization Reaction Boundary Formed by HCl and NaOH

The theory of MCRB has been developed by C. X. Cao1-4, Deman-Rigole5,6 and Pospichal et al.7. The relations between the MCRB and IEF8,9 have also been revealed by C. X. Cao et al.10-13. The theory has been partially demonstrated by the experiments performed by the above workers5-7,14-16.But, the validity of the theory for MNRB has not been manifested, and efficient method has not been developed for the MNRB and electro-focusing that is based on the mechanism of MNRB10-12. The purp…     

Electromigration with enhanced green emission in the titanium dioxide nanotube/graphene composite

One of the most studied photoluminescence emission peaks of anatase titanium dioxide (TiO₂) is green, located at about 520 nm, which is assigned to the radiative recombination between a mobile electron in the conduction band and oxygen vacancy defect as a trapped hole in the bandgap. Composite materials of TiO₂ with graphene are normally shown by the gradual quenching of photoluminescence intensity as a result of carrier lifetime extension, which is important to enhance photocatalytic activity. Herein we report an observation of the intensity enhancement of the green PL emission in a composite TiO₂ nanotube (TNT) and graphene produced through facile hydrothermal synthesis. The heterojunction formation of graphene and TNT makes the excited photoelectrons easy to diffuse from TNT to graphene. Hence, the recombination rate of mobile electrons in graphene and trapped holes located on the nanotube surface is enhanced due to the high mobility of electrons in graphene.