Numerical modelling of electrodeposition phenomena

Electrodeposition is a widely used technique for the fabrication of high aspect ratio microstructure components. In recent years much research has been focused within this area with an aim to understanding the physics behind the filling of high-aspect ratio vias and trenches on PCB's and in particular how they can be made without the formation of voids in the deposited material. This paper describes some of the fundamental work towards the advancement of numerical models that can predict the electrodeposition process and addresses: i) A novel technique for interface motion based on a variation of a donor-acceptor technique ii) A methodology for the investigation of stress profiles in deposits iii) The implementation of acoustic forces to generate replenishing electrolytic flow circulation in recessed features.

Influence of megasonic agitation on the electrodeposition of high aspect ratio blind vias

This paper presents preliminary studies in electroplating using megasonic agitation to avoid the formation of voids within high aspect ratio microvias that are used for the redistribution of interconnects in high density interconnection technology in printed circuit boards. Through this technique, uniform deposition of metal on the side walls of the vias is possible. High frequency acoustic streaming at megasonic frequencies enables the decrease of the Nernst diffusion layer down to the sub-micron range, allowing thereby conformal electrodeposition in deep grooves. This effect enables the normally convection free liquid near the surface to be agitated. Higher throughput and better control of the material properties of the deposits can be achieved for the manufacturing of embedded interconnections and metal-based MEMS. For optimal filling performance of the microvias, a full design of experiments (DOE) and a multi-physics numerical simulation have been conducted to analyse the influence of megasonic agitation on the plating quality of the microvias. Megasonic based deposition has been found to increase the deposition rate as well as improving the quality of the metal deposits.

Megasonic agitation for enhanced electrodeposition of copper

In this paper we propose an agitation method based on megasonic acoustic streaming to overcome the limitations in plating rate and uniformity of the metal deposits during the electroplating process. Megasonic agitation at a frequency of 1 MHz allows the reduction of the thickness of the Nernst diffusion layer to less than 600 nm. Two applications that demonstrate the benefits of megasonic acoustic streaming are presented: the formation of uniform ultra-fine pitch flip-chip bumps and the metallisation of high aspect ratio microvias. For the latter application, a multi-physics based numerical simulation is implemented to describe the hydrodynamics introduced by the acoustic waves as they travel inside the deep microvias.

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.

Zinc polycarboxylate dental cement for the controlled release of an active organic substance: proof of concept

The potential of employing zinc polycarboxylate dental cement as a controlled release material has been studied. Benzalkonium chloride was used as the active ingredient, and incorporated at concentrations of 1, 2 and 3% by mass within the cement. At these levels, there was no observable effect on the speed of setting. Release was followed using an ion-selective electrode to determine changes in chloride ion concentration with time. This technique showed that the additive was released when the cured cement was placed in water, with release occurring by a diffusion mechanism for the first 3 h, but continuing beyond that for up to 1 week. Diffusion coefficients were in the range 5.62 × 10(−6) cm(2) s(−1) (for 1% concentration) to 10.90 × 10(−6) cm(2) s(−1) (for 3% concentration). Up to 3% of the total loading of benzalkonium chloride was released from the zinc polycarboxylate after a week, which is similar to that found in previous studies with glass-ionomer cement. It is concluded that zinc polycarboxylate cement is capable of acting as a useful material for the controlled release of active organic compounds.

The kinetics of water loss from zinc phosphate and zinc polycarboxylate dental cements

The water desorption behaviour of three different zinc oxide dental cements (two polycarboxylates, one phosphate) has been studied in detail. Disc-shaped specimens of each material were prepared and allowed to lose water by being subjected to a low humidity desiccating atmosphere over concentrated sulfuric acid. In all three cements, water loss was found to follow Fick's second law for at least 6 h (until M(t)/M(infinity) values were around 0.5), with diffusion coefficients ranging from 6.03 x 10(-8 )cm(2 )s(-1) (for the zinc phosphate) to 2.056 x 10(-7 )cm(2 )s(-1) (for one of the zinc polycarboxylates, Poly F Plus). Equilibration times for desorption were of the order of 8 weeks, and equilibrium water losses ranged from 7.1% for zinc phosphate to 16.9% and 17.4% for the two zinc polycarboxylates.

The interaction of zinc oxide-based dental cements with aqueous solutions of potassium fluoride

The ability of zinc oxide-based dental cements (zinc phosphate and zinc polycarboxylate) to take up fluoride from aqueous solution has been studied. Only zinc phosphate cement was found to take up any measurable fluoride after 5 h exposure to the solutions. The zinc oxide filler of the zinc phosphate also failed to take up fluoride from solution. The key interaction for this uptake was thus shown to involve the phosphate groups of the set cement. However, whether this took the form of phosphate/fluoride exchange, or the formation of oxyfluoro-phosphate groups was not clear. Fluoride uptake followed radicaltime kinetics for about 2 h in some cases, but was generally better modelled by the Elovich equation, dq(t)/dt = alpha exp(-beta q(t)). Values for alpha varied from 3.80 to 2.48 x 10(4), and for beta from 7.19 x 10(-3) to 0.1946, though only beta showed any sort of trend, becoming smaller with increasing fluoride concentration. Fluoride was released from the zinc phosphate cements in processes that were diffusion based up to M(t)/M(infinity) of about 0.4. No further release occurred when specimens were placed in fresh volumes of deionised water. Only a fraction of the fluoride taken up was re-released, demonstrating that most of the fluoride taken up becomes irreversibly bound within the cement.

Water transport in zinc oxy-chloride cements

The water uptake and water loss behaviour in three different formulations of zinc oxy-chloride cement have been studied in detail. Specimens of each material were subjected to a high humidity atmosphere (93% RH) over saturated aqueous sodium sulfate, and a low humidity desiccating atmosphere over concentrated sulfuric acid. In high humidity, the cement formulated from the nominal 75% ZnCl2 solutions gained mass, eventually becoming too sticky to weigh further. The specimens at 25% and 50% ZnCl2 by contrast lost mass by a diffusion process, though by 1 week the 50% cement had stated to gain mass and was also too sticky to weigh. In low humidity, all three cements lost mass, again by a diffusion process. Both water gain and water loss followed Fick's law for a considerable time. In the case of water loss under desiccating conditions, this corresponded to values of Mt/MĄ well above 0.5. However, plots did not go through the origin, showing that there was an induction period before true diffusion began. Diffusion coefficients varied from 1.56 x 10-5 (75% ZnCl2) to 2.75 x 10-5 cm2/s (50% ZnCl2), and appeared to be influenced not simply by composition. The drying of the 25% and 50% ZnCl2 cements in high humidity conditions occurred at a much lower rate, with a value of D of 2.5 x 10-8 cm2/s for the 25% ZnCl2 cement. This cement was found to equilibrate slowly, but total water loss did not differ significantly from that of the cements stored under desiccating conditions. Equilibration times for water loss in desiccating conditions were of the order of 2-4 hours, depending on ZnCl2 content; equilibrium water losses were respectively 28.8 [25% ZnCl2], 16.2 [50%] and 12.4 [75%] which followed the order of ZnCl2 content. It is concluded that the water transport processes are strongly influenced by the ZnCl2 content of the cement.

Breast milk levels of zinc and omega-6 polyunsaturated fatty acids and growth of healthy Chinese infants

AIM: To examine the concentrations of zinc and omega-6 polyunsaturated fatty acids (omega-6 PUFAs) in breast milk, the impact of zinc on omega-6 PUFA metabolism, and the growth rate of infants. METHODS: Forty-one mother-term infant pairs from a rural area of northern Beijing, China, who were 1 month (n = 18, group I) and 3 months (n = 23, group II) old and exclusively breastfed, were studied. The dietary records and the concentrations of zinc and omega-6 PUFAs in the milk of lactating women and the increase in weight and length of their infants during 1 and 3 postnatal months were analysed. RESULTS: The dietary intakes of mothers in the two groups were the same, i.e. high in carbohydrate and low in fat, protein and energy. The maternal zinc intake was 7.5mg/d and thus reached only 34.6% of the current Recommended Nutrient Intake (RNI). The levels of zinc and arachidonic acid (AA, C20:4 omega-6) in the milk of group I were significantly higher than those in group II. Furthermore, significant positive correlations were found between the concentrations of zinc and AA in the breast milk and between the level of milk AA and weight gain. CONCLUSION: Zinc may be a co-factor and essential for essential fatty acids (EFA) metabolism. Thus suboptimal zinc intake may cause EFA imbalance. Further studies of Chinese rural mother-infant pairs are necessary to determine whether zinc supplementation should be recommended when lactation exceeds 3 months.