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Copper electrodeposition acts as a crucial step in the manufacture of high-density interconnect board. The stability of plating solution and the uniformity of copper electrodeposit are the hotspot and difficulty for the research of electrodeposition. Because a large number of factors are included in electrodeposition, experimentally determining all parameters and electrodeposition conditions becomes unmanageable. Therefore, a multiphysics coupling technology was introduced to investigate microvia filling process, and the mechanism of copper electrodeposition was analyzed. The results provide a strong theoretical basis and technical guidance for the actual electroplating experiments. The purpose of this paper is to provide an excellent tool for quickly and cheaply studying the process behavior of copper electrodeposition without actually needing to execute time-consuming and costly experiments.

The interactions among additives used in acidic copper plating solution for microvia filling and the effect on the copper deposition potential were characterized through galvanostatic measurement (GM). The adsorption behavior and surface coverage of additives with various concentrations under different rotating speeds of working electrode were investigated using cyclic voltammetry (CV) measurements. Further, a microvia filling model was constructed using multiphysics coupling technology based on the finite element method.

GM tests showed that accelerator, inhibitor and leveler affected the potential of copper electrodeposition, and bis(3-sulfopropyl) disulfide (SPS), ethylene oxide-propylene oxide (EO/PO) co-polymer, and self-made leveler were the effective additives in acidic copper plating solution. CV tests showed that EO/PO–Cu⁺-Cl⁻ complex was adsorbed on the electrode surface by intermolecular forces, thus inhibiting copper electrodeposition. Numerical simulation indicated that the process of microvia filling included initial growth period, the outbreak period and the stable growth period, and modeling result was compared with the measured data, and a good agreement was observed.

The research is still in progress with the development of high-performance computers.

A multiphysics coupling platform is an excellent tool for quickly and cheaply studying the electrodeposited process behaviors under a variety of operating conditions.

The numerical simulation method has laid the foundation for mechanism of copper electrodeposition.

By using multiphysics coupling technology, the authors built a bridge between theoretical and experimental study for microvia filling. This method can help explain the mechanism of copper electrodeposition.

The purpose of this paper is to optimize experimental parameters and gain further insights into the plating process in the fabrication of high-density interconnections of printed circuit boards (PCBs) by the rotating disc electrode (RDE) model. Via metallization by copper electrodeposition for interconnection of PCBs has become increasingly important. In this metallization technique, copper is directly filled into the vias using special additives. To investigate electrochemical reaction mechanisms of electrodeposition in aqueous solutions, using experiments on an RDE is common practice.

An electrochemical model is presented to describe the kinetics of copper electrodeposition on an RDE, which builds a bridge between the theoretical and experimental study for non-uniform copper electrodeposition in PCB manufacturing. Comsol Multiphysics, a multiphysics simulation platform, is invited to modeling flow field and potential distribution based on a two-dimensional (2D) axisymmetric physical modeling. The flow pattern in the electrolyte is determined by the 2D Navier–Stokes equations. Primary, secondary and tertiary current distributions are performed by the finite element method of multiphysics coupling.

The ion concentration gradient near the cathode and the thickness of the diffusion layer under different rotating velocities are achieved by the finite element method of multiphysics coupling. The calculated concentration and boundary layer thicknesses agree well with those from the theoretical Levich equation. The effect of fluid flow on the current distribution over the electrode surface is also investigated in this model. The results reveal the impact of flow parameters on the current density distribution and thickness of plating layer, which are most concerned in the production of PCBs.

By RDE electrochemical model, we build a bridge between the theoretical and experimental study for control of uniformity of plating layer by concentration boundary layer in PCB manufacturing. By means of a multiphysics coupling platform, we can accurately analyze and forecast the characteristic of the entire electrochemical system. These results reveal theoretical connections of current density distribution and plating thickness, with controlled parameters in the plating process to further help us comprehensively understand the mechanism of copper electrodeposition.

Optimized plating conditions, included proper designs of insulating shield (IS), auxiliary cathode (AC) and different patterns, contribute to the uniformity enhancement of copper deposition.

Plating experiments were implemented in vertical continuous plating (VCP) line for manufacturing in different conditions. Multiphysics coupling simulation was brought to investigate and predict the plating uniformity improvement of copper pattern. In addition, the numerical model was based on VCP to approach the practical application.

With disproportionate current distribution, different plating pattern design formed diverse copper thickness distribution (CTD). IS and AC improved plating uniformity of copper pattern because of current redistribution. Moreover, optimized plating condition for effectively depositing more uniformed plating copper layer in varied pattern designs were derived by simulation and verified by plating experiment.

The comparison between experiment and simulation revealed that multiphysics coupling is an efficient, reliable and of course environment-friendly tool to perform research on the uniformity of pattern plating in manufacturing.

Acoustic noise is a crucial performance index in the design of electrical machines. Due to the challenges associated with modelling a complete motor, the stator is often used to estimate the sound power in the prototyping stage. While this approach greatly reduces lengthy simulations, the actual sound power of the motor may not be known. But, from the acoustic noise standpoint, not much is known about the correlation between the stator and complete motor. This paper, therefore, aims to use the sound pressure levels of the stator and the full motor to investigate the existence of correlations in the interior permanent magnet synchronous motor.

A multiphysics simulation framework is proposed to evaluate the sound pressure levels of multiple motor geometries in a given design space. Then, a statistical analysis is performed on the calculated sound pressure levels of each geometry over a selected speed range to compare the correlation strength between the stator and the full model.

It was established that the stator and the complete motor model are moderately correlated. As such, a reliance on the stator sound power for design and optimization routines could yield inaccurate results.

The main contribution involves the use of statistical tools to study the relationship between sound pressure levels associated with the stator geometry and the complete electric motor by increasing the motor sample size to capture subtle acoustic correlation trends in the design space of the interior permanent magnet synchronous motor.

This paper gives a bibliographical review of the finite element and boundary element parallel processing techniques from the theoretical and application points of view. Topics include: theory – domain decomposition/partitioning, load balancing, parallel solvers/algorithms, parallel mesh generation, adaptive methods, and visualization/graphics; applications – structural mechanics problems, dynamic problems, material/geometrical non‐linear problems, contact problems, fracture mechanics, field problems, coupled problems, sensitivity and optimization, and other problems; hardware and software environments – hardware environments, programming techniques, and software development and presentations. The bibliography at the end of this paper contains 850 references to papers, conference proceedings and theses/dissertations dealing with presented subjects that were published between 1996 and 2002.

The uniformity of electrodeposition is the key to successful application of pattern plating because the quality of electrodeposited copper layer has a huge impact on the performance of printed circuit boards (PCBs). The multi-physics coupling technology was used to accurately analyze and forecast the characteristics of electrochemical system. Further, an optimized plating bath was used to achieve a uniform electrodeposition.

A multi-physics coupling numerical simulation based on the finite element method was used to optimize electrodeposition conditions in pattern plating process. The influences of geometric and electrochemical factors on uniformity of current distribution and electrodeposited layer thickness were discussed by multi-physics coupling.

The model results showed that the distance between cathode and anode and the insulating shield had a great impact on uniformity of electrodeposition. By numerical simulation, it had been proved that using an auxiliary cathode was an effective and simple way to improve uniformity of electrodeposition due to redistributing of the current. This helped to achieve more uniform surface of the copper patterns by preventing the edge effect and the roughness of the copper layer was reduced to 1 per cent in the secondary current distribution model.

The research is still in progress with the development of high-performance computers.

A multi-physics coupling platform is an excellent tool for quickly and cheaply studying the process behaviors under a variety of operating conditions.

The numerical simulation method has laid the foundation for the design and improvement of the plating bath.

By multi-physics coupling technology, we built a bridge between theoretical and experimental study for control of uniformity of pattern plating in PCB manufacturing. This method can help optimize the design of plating bath and uniformity of pattern plating in PCB manufacturing.

The paper seeks to present a methodology of computer simulation of coupled magneto‐thermo‐mechanical processes in various electrical engineering devices. The methodology allows determining their parameters, characteristics and behaviour in various operation regimes.

The mathematical model consisting of three equations describing magnetic field, temperature field and field of mechanical strains and stresses (or thermoelastic displacements) is solved numerically, partially in the hard‐coupled formulation.

The methodology seems to be sufficiently robust, reliable and applicable to a wide spectrum of devices.

At this stage of research, the hard‐coupled formulation of thermo‐mechanical (or thermoelastic) problems is still possible only in 2D.

The methodology can successfully be used for design of numerous machines, apparatus and devices from the area of low‐frequency electrical engineering ranging from small actuators to large synchronous generators.

Complete numerical analysis of coupled magneto‐thermo‐mechanical phenomena in electrical devices.

To investigate transverse vibration of the eccentric rotor in a 12/8 poles switched reluctance motor (SRM), a transverse analytical vibration model is built by finite element method (FEM) under the interaction of radial magnetic resultant and vibration displacement. External forces, including radial magnetic resultant and centrifugal force, are also derived in detail, according to the variation of airgap and current and other intermediate parameters with rotation angle.

The transverse vibration response of the eccentric rotor including radial magnetic resultant and vibration displacement is solved by Newmark-β method, after inputting the currents of three phase windings under angle position control strategy. The basic characteristics of radial magnetic resultant and vibration displacement are reflected in time and frequency domain.

The magnetic resultant vector of the eccentric rotor presents multi-petals star geometric shape. The frequency distribution of magnetic resultant relates to rotation speed, current waveform and the least common multiple of the stator and rotor teeth. However, the frequency distribution of the vibration displacement also relates closely to the first-order critical whirl speed of the rotor. When the rotor is running at certain speeds, it will display superharmonic resonance and show abundant displacement locus.

By using this analytical model and solving process proposed in this paper, the nonlinear coupled vibration response of the eccentric rotor in SRM can be analyzed and discussed rapidly; only the stator’s winding currents obtained by experiment or electromagnetic simulation is needed as input.

The purpose of this study is to investigate the synergism of convection, current density distribution and additives by numerical simulation and electrochemical experiments for good throwing power (TP) of copper electro-deposition in printed circuit board (PCB) manufacture.

The flow field of THs and current density distribution on various AR of THs are calculated and analyzed. Meanwhile, corresponding simulation is used to study the performance of plating electrolytes on TP. Two electrochemical parameters, overpotential (η) and potential difference (△η), are chosen to evaluate the electrochemical properties of different plating solutions by galvanostatic measurement and potentiodynamic cathode polarization at different rotating speeds.

By combining both the results of simulation and practical plating, these two electrochemical properties of electrolytes exhibit significant impact to the system at varied conditions. Especially, the electrolyte with higher polarizing η and △η values lead to the elevated TP for AR of more than 2:1.

The harring cell model is built as a bridge between the theoretical and experimental study for control of uniformity of plating THs in PCB manufacturing. This dual-parameter evaluation is validated to be a promising decisive method to guide the THs plating with particular AR in industry.

Multiphysics problems are solved either with monolithic or segregated approaches. For accomplishing contrary discretisation requirements of the physics, disparate meshes are essential. This paper is comparing experimental results of different interpolation methods for a segregated coupling with monolithic approaches, implemented using a global and a local nearest neighbour method. The results show the significant influence of discretisation for multiphysics simulation.

Applying disparate meshes to the monolithic as well as the segregated calculation of finite element problems and evaluating the related numerical error is content of the contribution. This is done by an experimental evaluation of a source and a material coupling applied to a multiphysics problem. After an introduction to the topic, the evaluated multiphysics model is described based on two bidirectional coupled problems and its finite element representation. Afterwards, the considered methods for approximating the coupling are introduced. Then, the evaluated methods are described and the experimental results are discussed. A summary concludes this work.

An experimental evaluation of the numerical errors for different multiphysics coupling methods using disparate meshes is presented based on a bidirectional electro-thermal simulation. Different methods approximating the coupling values are introduced and challenges of applying these methods are given. It is also shown, that the approximation of the coupling integrals is expensive. Arguments for applying the different methods to the monolithic and the segregated solution strategies are given and applied on the example. The significant influence of the mesh density within the coupled meshes is shown. Since the projection and the interpolation methods do influence the result, a careful decision is advised.

In this contribution, existing coupling methods are described, applied and compared on their application for coupling disparate meshes within a multiphysics simulation. Knowing their performance is relevant when deciding for a monolithic or a segregated calculation approach with respect to physics dependent contrary discretisation requirements. To the authors’ knowledge, it is the first time these methods are compared with a focus on an application in multiphysics simulations and experimental results are discussed.