Numerical algorithms for modelling electrodeposition: Tracking the deposition front under forced convection from megasonic agitation

Electrodeposition is a widely used technique for the fabrication of high aspect ratio microstructures. In recent years, much research has been focused within this area aiming to understand the physics behind the filling of high aspect ratio vias and trenches on substrates and in particular how they can be made without the formation of voids in the deposited material. This paper reports on the fundamental work towards the advancement of numerical algorithms that can predict the electrodeposition process in micron scaled features. Two different numerical approaches have been developed, which capture the motion of the deposition interface and 2-D simulations are presented for both methods under two deposition regimes: those where surface kinetics is governed by Ohm’s law and the Butler–Volmer equation, respectively. In the last part of this paper the modelling of acoustic forces and their subsequent impact on the deposition profile through convection is examined.

Mathematical modelling of the solidification of liquid tin with electromagnetic stirring

It is well known that during alloy solidification, convection currents close to the so-lidification front have an influence on the structure of dendrites, the local solute concentration, the pattern of solid segregation, and eventually the microstructure of the casting and hence its mechanical properties. Controlled stirring of the melt in continuous casting or in ingot solidification is thought to have a beneficial effect. Free convection currents occur naturally due to temperature differences in the melt and for any given configuration, their strength is a function of the degree of superheat present. A more controlled forced convection current can be induced using electro-magnetic stirring. The authors have applied their Control-Volume based MHD method [1, 2] to the problem of tin solidification in an annular crucible with a water-cooled inner wall and a resistance heated outer one, for both free and forced convection situations and for various degrees of superheat. This problem was studied experimentally by Vives and Perry [3] who obtained temperature measurements, front positions and maps of electro-magnetic body force for a range of superheat values. The results of the mathematical model are compared critically against the experimental ones, in order to validate the model and also to demonstrate the usefulness of the coupled solution technique followed, as a predictive tool and a design aid. Figs 6, refs 19.

Accuracy of turbulence models and CFD for thermal characterisation of electronic systems

A major percentage of the heat emitted from electronic packages can be extracted by air cooling whether by means of natural or forced convection. This flow of air throughout an electronic system and the heat extracted is highly dependable on the nature of turbulence present in the flow field. This paper will discuss results from an investigation into the accuracy of turbulence models to predict air cooling for electronic packages and systems.

Investigation into the performance of turbulence models for fluid flow and heat transfer phenomena in electronic applications

Heat is extracted away from an electronic package by convection, conduction, and/or radiation. The amount of heat extracted by forced convection using air is highly dependent on the characteristics of the airflow around the package which includes its velocity and direction. Turbulence in the air is also important and is required to be modeled accurately in thermal design codes that use computational fluid dynamics (CFD). During air cooling the flow can be classified as laminar, transitional, or turbulent. In electronics systems, the flow around the packages is usually in the transition region, which lies between laminar and turbulent flow. This requires a low-Reynolds number numerical model to fully capture the impact of turbulence on the fluid flow calculations. This paper provides comparisons between a number of turbulence models with experimental data. These models included the distance from the nearest wall and the local velocity (LVEL), Wolfshtein, Norris and Reynolds, k-ε, k-ω, shear-stress transport (SST), and kε/kl models. Results show that in terms of the fluid flow calculations most of the models capture the difficult wake recirculation region behind the package reasonably well, although for packages whose heights cause a high degree of recirculation behind the package the SST model appears to struggle. The paper also demonstrates the sensitivity of the models to changes in the mesh density; this study is aimed specifically at thermal design engineers as mesh independent simulations are rarely conducted in an industrial environment.

Modelling of jet-impingement cooling for power electronics

The use of an innovative jet impingement cooling system in a power electronics application is investigated using numerical analysis. The jet impingement system, outlined by Skuriat et al, consists of a series of cells each containing an array of holes. Cooling fluid is forced through the device, forming an array of impingement jets. The jets are arranged in a manner, which induces a high degree of mixing in the interface boundary layer. This increase in turbulent mixing is intended to induce higher Nusselt numbers and effective heat transfer coefficients. Enhanced cooling efficiency enables the power electronics module to operate at a lower temperature, greatly enhancing long-term reliability. The results obtained through numerical modelling deviates markedly from the experimentally derived data. The disparity is most likely due to the turbulence model selected and further analysis is required, involving evaluation of more advanced turbulence models.

Three-dimensional simulation of the influence of convection on dendritic solidification

Bulk and interdendritic flow during solidification alters the microstructure development, potentially leading to the formation of defects. In this paper, a 3D numerical model is presented for the simulation of dendritic growth in the presence of fluid flow in both liquid and semi-solid zones during solidification. The dendritic growth was solved by the combination of a stochastic nucleation approach with a finite difference solution of the solute diffusion equation and. a projection method solution of the Navier-Stokes equations. The technique was applied first to simulate the growth of a single dendrite in 2D and 3D in an isothermal environment with forced fluid flow. Significant differences were found in the evolution of dendritic morphology when comparing the 2D and 3D results. In 3D the upstream arm has a faster growth velocity due to easier flow around the perpendicular arms. This also promotes secondary arm formation on the upstream arm. The effect of fluid flow on columnar dendritic growth and micro-segregation in constrained solidification conditions is then simulated. For constrained growth, 2D simulations lead to even greater inaccuracies as compared to 3D.

HPLC-ESI-MS method development for the elucidation of nicardipine degradation products

Purpose: Nicardipine is a member of a family of calcium channel blockers named dihydropiridines that are known to be photolabile and may cause phototoxicity. It is therefore vital to develop analytical method which can study the photodegradation of nicardipine. Method: Forced acid degradation of nicardipine was conducted by heating 12 ml of 1 mg/ml nicardipine with 3 ml of 2.5 M HCl for two hours. A gradient HPLC medthod was developed using Agilent Technologies 1200 series quaternary system. Separation was achieved with a Hichrome (250 x 4.6 mm) 5 μm C18 reversed phase column and mobile phase composition of 70% A(100%v/v water) and 30% B(99%v/v acetonitrile + 1%v/v formic acid) at time zero, composition of A and B was then charged to 60%v/v A;40%v/v B at 10minutes, 50%v/v A; 50%v/v B at 30minutes and 70%v/v A; 30%v/v B at 35minutes. 20μl of 0.8mg/ml of nicardipine degradation was injected at room temperature (25oC). The gradient method was transferred onto a HPLC-ESI-MS system (HP 1050 series - AQUAMAX mass detector) and analysis conducted with an acid degradation concentration of 0.25mg/ml and 20μl injection volume. ESI spectra were acquired in positive ionisation mode with MRM 0-600 m/z. Results: Eleven nicardipine degradation products were detected in the HPLC analysis and the resolution (RS) between the respective degradants where 1.0, 1.2, 6.0, 0.4, 1.7, 3.7, 1.8, 1.0, and 1.7 respectively. Nine degradation products were identified in the ESI spectra with the respective m/z ratio; 171.0, 166.1, 441.2, 423.2, 455.2, 455.2, 331.1, 273.1, and 290.1. The possible molecular formulae for each degradants were ambiguously determined. Conclusion: A sensitive and specific method was developed for the analysis of nicardipine degradants. Method enables detection and quantification of nicardipine degradation products that can be used for the study of the kinetics of nicardipine degradation processes.