Kinetically-limited Regime Research Articles

Defect-Free Metallization of through-Glass Vias (TGV) with Engineered Geometry

Metallized through-glass vias (TGVs) have attracted interest in recent years due to their promise in enabling 2.5D and 3D electronic architectures and high-density MEMS devices. However, unlike metallization of PCB, metallization of TGV is challenging, and the electroplating processes are not well-established. This is mostly due to the form factor associated with TGVs - high length (L) and small diameter (Φ). During electrolytic process, for example electroplating of Copper inside the TGVs, such form factor often leads to severe transport limitation and subsequent formation of defects such as seams or voids in the samples. This has led to intense research in the past decade to develop special additives and processes to achieve defect-free filling of TGVs. It has been accepted that defect-free filling of TGVs is not possible without specialized additives in the solution. We will first demonstrate through simplified theoretical analysis and numerical modeling why that is the case when the geometry of the TGV has uniform cross-section. Even when the electroplating is carried out in in fully kinetic-controlled regime (Thiele modulus, μ ≤ 1), it will be clear from the analysis that a complete defect-free metallization is not achievable as long as the TGV cross-section is uniform. Next, we will report a novel metallization technique using an engineered via with an X-shape in the middle and operating in the kinetic-limited regime without the requirement of any specialized additives. This leads to Cu bridging of the vias at the waist, after which continued conformal plating ensures void-free filling. It would be emphasized that by combining these two effects – novel shape of TGV and kinetic controlled electroplating – void-free filling is achievable even in the absence of any additives. While additive-based bath is required and will continue to be used to optimize between plating speed, low stress and roughness of plated copper, the objective of this talk is to demonstrate the advantage of engineered vias in which even an additive-free bath could provide defect-free metallization. At very low current densities, an anomalous increase in thickness in the middle compared to the top of the via was observed. This cannot be explained by a simple 1D model and is an interesting next step in understanding additive-free electroplating.

Characteristics of particulate emissions from coal char combustion: Char fragmentation and ash coalescence behaviors

Air pollution from fossil fuel combustion motivated the extensive and in-depth investigation on particulate matter (PM) to meet the stringent emission norms. The relationship between char fragmentation/mineral coalescence and PM formation is elucidated in this paper. To separately investigate their contributions to PM formation, the effects of particle bursting during devolatilization and fragmentation of excluded minerals have been stripped off. We prepared size-graded and density-fractionated chars with varying ash content levels and conducted combustion experiments in a drop-tube furnace at 1300/1600/1800 K. The mass particle size distributions (PSDs) of collected ash were measured by an Electrical Low Pressure Impactor (for PM10) and a laser particle-size analyzer (for PM10+). The micro- morphologies and elemental compositions analyses were also shown for particles of different sizes. The results indicate that char fragmentation significantly increases the number of ash particles in fine-fragmentation mode (FFM), and the ash peak in the coarse mode comes from the char particles that show fewer fragmentation behaviors. Dense char structure disadvantages char fragmentation but enhances coalescence of included minerals. The distribution of fly ash at 1600/1800 K exhibits bi-modal with two peaks around 10 and 105 μm, while the distribution at 1300 K/50%O2 exhibits uni-modal with one peak. This can be well explained by the percolation theory that the char combustion in the kinetically-limited regime is dominated by uniform fragmentation, while particles at 1600/1800 K mainly undergo perimeter fragmentation. The effect of ash content is more related to the mineral grains distributions within the char particles.

Removal of toluene in a biotrickling filter in the presence of methanol vapors: Experimental study, mathematical modeling, and kinetic parameters optimization

The performance of biotrickling filters (BTFs) has been significantly affected during the co-treatment of volatile organic compounds (VOCs) with different hydrophilicities. Removal of toluene vapor as a hydrophobic compound in the absence and presence of methanol as a hydrophilic pollutant was studied in a BTF. The inlet loading ranges were 18−36 g.m−3.h−1 for toluene and 0−225 g.m−3.h−1 for methanol at constant empty bed residence time (EBRT) of 60 s. The removal efficiency of toluene (RET) varied from 30 to 80 %, while RE of methanol (REM) remained almost constant at > 90 % within different phases of experiments due to the unlimited solubility in water. A comprehensive dynamic mathematical model consisting of mass transfer through gas, liquid, and biofilm phases with the kinetic of biodegradation in the BTF and accumulation of methanol in liquid was developed. The interaction parameters were optimized by genetic algorithm and validated by experimental data. Sensitivity analysis on the optimized parameters showed that biofilm thickness and methanol interaction parameter had the most effects on RET as 45 % and 38 %, respectively. Model simulation showed that 43–90 % of biofilm depth was active for toluene degradation at different inlet gas-phase concentrations, indicating a diffusion-limited condition in the process. In contrast, all depth of biofilm was fully active for methanol degradation, showing a kinetic-limited regime dominant for methanol removal in the BTF under all operating conditions. Results showed that the developed model could effectively predict the dynamics of VOCs removals along with the determination of kinetic constants.

Defect-free metallization of through-glass vias with engineered geometry in additive-free electrolyte

Defect-free metallization of through-glass vias (TGVs) with copper using an additive-free electrolyte is presented in this communication. Engineered vias with an X-shape in the middle were electroplated in the kinetic-limited regime (Thiele modulus, μ ≤ 1) to achieve pinching of the vias at the waist, after which continued conformal plating ensured void-free filling. Thiele modulus analysis and an 1D steady-state model predicted that the deposition front moves uniformly within the via when plating is carried out in the kinetic-limited regime. It was hypothesized that engineering the via geometry to an X-shape could enable pinching in the middle. However, neither of the two conditions are enough on their own to achieve defect-free filling. Combining these two allows conformal movement of the plating front and pinching in the middle, which results in complete filling of the via. While additive-based bath is required and will continue to be used to optimize between plating speed, low stress and roughness of plated copper, the objective of this article is to demonstrate the advantage of engineered vias in which even an additive-free bath could provide defect-free metallization. At very low current densities, an anomalous increase in thickness in the middle compared to the top of the via was observed. This cannot be explained by a simple 1D model and is an interesting next step in understanding additive-free electroplating.

Reaction Mechanism Analysis of Zn Electrodeposition Process in Acidic Sulphate Bath Using Potentiodynamic Polarization Technique

Zinc (Zn) metal is commonly known as a sacrificial anode, and is widely used as corrosion protection coating for ferrous materials. Electrodeposition of Zn is a popular method of coating substrates and it can be performed in acidic or alkaline conditions [1]. Zn electrodeposition is a two electron multi step reaction, and it is accompanied by hydrogen evolution reaction in acidic conditions. Hydrogen bubble formation during Zn deposition can affect mass transport of different species in the electrolyte bath [2]. In addition, mass transfer of cations can limit the reaction rate at typical deposition conditions. Zn electrodeposition process has been modeled in the literature [3-6].The models employ either a single step simple electron transfer reaction with mass transfer effects or multi-step reactions which neglect mass transfer limitations. In this work, we present experimental results of Zn electrodeposition in aqueous acidic sulphate solution, and propose a model to explain the observed results. The model (Figure 1a) involves a multi step mechanism with diffusional mass transfer effects, Hydrogen evolution reaction (HER) occurring in parallel with the Zn electrodeposition process. All the electrochemical experiments were carried out using a Zn rotating disk electrode (rde) in a conventional three electrode cell and conducted with IVIUMSTAT electrochemical workstation. Pt mesh was used as the counter electrode and Hg/Hg2SO4 (saturated K2SO4) was used as the reference electrode. The kinetics and mass transfer effects of the process were studied by potentiodynamic polarization (PDP) technique. PDP experiments were performed as a function of Zn salt concentration, electrolyte bath pH and electrode rotational speed. The concentration of Zn salt was varied from 0.01 M to 1 M. The electrolyte bath pH was varied from 2 to 4. The electrode rotational speed was varied from 400 to 1600 rpm to characterize mass transfer effects during the process. A supporting electrolyte (Na2SO4) at 1 M concentration was used to reduce the effects of solution resistance. A few experiments were also conducted without Zn salt (blank solution at pH 2) to quantify the Hydrogen evolution on Zn rde. Figure 1b shows the PDP curves obtained for blank solution at pH 2 and different rotational speeds to quantify the hydrogen evolution rate alone. Figure 1c shows the PDP curves of Zn electrodeposition process at pH 2 and different rotational speeds. As expected, the current magnitude increases with an increase in cathodic bias, and saturates at large cathodic potentials. The saturation current increases with an increase in electrode rotational speed. Reaction mechanism analysis was employed to describe the deposition mechanism of Zn in acidic sulphate baths. Several multi step mechanisms were evaluated to model the polarization data acquired in kinetic limited regime. A seven step mechanism [4] as mentioned in figure 1a involving three deposition steps and Volmer Heyrovsky (VH) steps for hydrogen evolution reaction was found to be the best mechanism in the kinetic limited regime. Further analysis on mechanistic investigation to include mass transfer effects during the Zn electrodeposition is in progress.

Uniformity of GaAs solar cells grown in a kinetically-limited regime by dynamic hydride vapor phase epitaxy

We demonstrate solar cell devices grown on 50 mm diameter GaAs substrates by dynamic hydride vapor phase epitaxy (D-HVPE). In contrast to our prior D-HVPE devices, grown at 650 °C in a transport-limited regime, these devices were grown at 700 °C in a kinetically-limited growth regime in which the growth rate uniformity is controlled by thermally-activated surface reactions. These devices exhibit open-circuit voltages up to 1.07 V, nearly identical performance to the devices grown at lower temperature in a different growth regime. We evaluate the uniformity of device performance and find only a 1% variation in absolute, device efficiency across the majority of the wafer in devices without anti-reflection coating. We analyze the GaAs and GaInP thickness uniformity and GaInP compositional uniformity, using high-tresolution x-ray diffraction mapping, and find that any non-uniformity in device efficiency is not related to variations in these structural parameters. We combine three-dimensional computational fluid dynamics modeling of our reactor with a kinetic model for GaAs growth, and use the combined model to predict spatial GaAs growth rate over a 50 mm wafer area. We compare these predictions with experimental data from our D-HVPE reactor and find excellent agreement. We use the model to the gain insight into the specific mechanisms that control GaAs spatial uniformity in the kinetically-limitedgrowth regime. These results suggest a large parameter window for the growth of high-performance optoelectronic devices by D-HVPE, possibly with large area uniformity.

Silicate weathering rate and its controlling factors: A study from small granitic watersheds in the Jiuhua Mountains

Silicate weathering is intimately linked to global climate. To investigate the controlling factors of silicate weathering rate, we collected monthly or half-monthly river water samples from ten small granitic watersheds in the Jiuhua Mountains. Mass balance calculation shows that agricultural activity, atmospheric input, silicate weathering, carbonate weathering and evaporite dissolution contribute 2.0%, 16.9%, 58.7%, 13.5% and 8.9% cations to the river water, respectively. The disproportionate contribution of carbonate rocks with an exposed area of <5% demonstrates the importance of trace carbonate minerals in these small granitic watersheds. The average silicate weathering and CO2 consumption rates at our sites are 7.0 t km−2 y−1 and 3.4 × 105 mol km−2 y−1, respectively.There is no correlation between silicate weathering rates (SWR) and the suspended solid concentrations (an index of physical erosion rate), but there is a strong positive correlation between SWR and temperature, consistent with the kinetic-limited chemical weathering regime in alpine areas. A compilation of literature data from global small granitic watersheds in different climatic zones shows positive correlations between temperature, runoff and SWR. A multiple linear regression between SWR, temperature and runoff yielded an adjusted R-squared of 0.61, showing that climatic factors can account for 61% of the variation in SWR. In addition, for catchments where the elevation difference between the highest point of the headwater and sampling point (an approximate topographical parameter) exceeds 400 m, the R-squared value obtained from the temperature and SWR regression analysis is significantly increased, indicating that temperature is likely the most important factor controlling silicate weathering in the alpine region where a kinetic-limited regime dominates.

On the role of heterogeneous reactions in aluminum combustion

This work addresses the role of heterogeneous reactions occurring during aluminum combustion. Direct numerical simulations are conducted on a single aluminum burning particle accounting for both detailed gas-phase and surface kinetic mechanism. A surface kinetic solver has been developed to take into account surface and gas/surface interactions. The model is validated against experimental measurements and appears to be predictive. Calculations are performed through different pressure regimes (1 and 10 bar), atmospheres (O2, CO2, CO and H2O) and droplet sizes (from 1 to 400 µm). Flames structures (temperature and AlO profile) computed by the model are consistent with experimental measurements and observations. The reaction zones for CO and H2O atmospheres are computed to be very close to the surface which is an evidence of a combustion mostly driven by chemical surface phenomena. In some cases surface reactions promote self-sustained combustion for smaller size particles at low pressure regimes. Calculated burning times are also consistent with experimental measurements. In O2/Ar, surface chemistry is more important when particles are small (under 20 µm) which guides the combustion to a more kinetically-limited regime than a diffusion-limited regime. The importance of surface reactivity is different regarding the particle size and the atmosphere of interest. Calculations of alumina residue size reveals that surface reactions could explain alumina residue formation. The model predicts a strong oxidizer effect on alumina residue size. According to the model, CO2 environment lead to large residue size while H2O environment lead to small residue size. This work definitely stresses the potential role of heterogeneous reactions in aluminum combustion.

Electrochemical Oxidation of Phenol Using Boron-Doped Diamond Electrodes

The oxidation of phenol is compared for two different boron doped diamond (BDD) electrodes; a niobium supported BDD planar electrode and a BDD coated Ti mesh. Raman spectroscopy and cyclic voltammetry were used to compare the two electrodes. Continuous oxidation of phenol utilized a flow cell configuration that circulated a fixed volume of solution, scaled to the electrode area, with an initial concentration of 10 mM phenol in 0.1M H2SO4. The conversion of phenol to CO2 was monitored by scheduled collection of aliquots and subsequent total organic carbon (TOC) analysis. The two electrodes were found to have similar conversion rates, with the total carbon decreasing from ~1% to <0.1%. Treatment of a more concentrated solution, 87 mM phenol in 0.1M H2SO4, was examined for the planar electrode and resulted in greater efficiency, which was attributed to greater localization between reactants and hydroxyl radicals in the kinetic limited regime.

On “how to start a fire”, or transverse forced-convection, hyperbaric laser chemical vapor deposition of fibers and textiles

This work explores the transverse forced flow of precursor gases during hyperbaric pressure laser chemical vapor deposition (HP-LCVD). Axial and mass growth rates of carbon fibers are measured experimentally, and a numerical model is developed that provides fiber growth rates in both the mass-transport-limited (MTL) and kinetically limited (KL) regimes. It is found that the fiber’s transport-limited rate increases as the square root of the flow velocity, while simultaneously, the temperature drops with the inverse square root of the flow velocity. Growth is enhanced by forced flow so long as the reaction zone remains within the MTL regime; upon reaching a critical temperature and flow rate, however, fibers enter the KL regime, and the growth rate declines with rising flow rate. Molecular properties of the precursors employed and gas concentrations ultimately determine the range of the MTL and the locations of the critical temperature and flow rate. The growth rates of fibers can indeed be enhanced by transverse forced convection—to at least three times the zero-flow steady-state rate, provided an MTL regime exists. Complex three-dimensional structures may be grown from these fibers in a freeform manner, and the more rapidly such microstructures can be fabricated, the more practical HP-LCVD becomes for industrial use, including the fabrication of novel textiles.

On the transition from diffusion-limited to kinetic-limited regimes of alloy solidification

An abrupt transition from diffusion-limited solidification to diffusionless, kinetic-limited solidification with complete solute trapping is explained as a critical phenomenon which arises due to local non-equilibrium diffusion effects in the bulk liquid. The transition occurs when the interface velocity V passes through the critical point V=VD, where V=VD is the bulk liquid diffusive velocity. Analytical expressions are developed for velocity–temperature and velocity–undercooling functions, using local non-equilibrium partition coefficient based on the Jackson et al. kinetic model and the local non-equilibrium diffusion model of Sobolev. The calculated functions demonstrate a sharp break in the velocity–undercooling and velocity–temperature relationships at the critical point V=VD. At this point the local non-equilibrium solidus and liquidus lines coincide with the T0 temperature. The relationship to pertinent experiments and the influence of the local non-equilibrium diffusion effects on grain refinement and disorder trapping phenomena are discussed.

Thermochemical Erosion Analysis for Chraphite/Carbon-Carbon Rocket Nozzles

A study is conducted to predict graphite/carbon–carbon nozzle erosion behavior in solid rocket motors for wide variations of propellant formulations. The numerical model considers the solution of Reynolds-averaged Navier– Stokes equations in the nozzle, heterogeneous chemical reactions at the nozzle surface, variable transport and thermodynamic properties, andheat conduction in the nozzlematerial. Twodifferent ablationmodels are considered and compared: a surface equilibriumapproach and afinite-ratemodel. Results show that the erosion rate is diffusion limited for metallized propellants, ensuring sufficiently high wall temperatures, and it is kinetic limited for nonmetallized propellants. For low surface temperatures, the twomodels are consistent with each other and predict the same erosion rate, while the surface equilibrium model overpredicts the recession at low surface temperatures. The calculated results show an excellent agreement with the experimental data from the ballistic test and evaluation system motor firings, and the finite-rate model actually improves the predictions when the kinetic-limited regime is approached.

One-dimensional model of evaporation and condensation in the presence of a noncondensable gas with applications to cryogenic fluid storage

This paper considers the one-dimensional flow of vapor between two liquid surfaces due to evaporation and condensation taking into account diffusion through a noncondensable gas and nonequilibrium interfacial kinetics. An explicit relationship is developed for the mass flux J as a function of the characteristic mole ratio of noncondensable gas X, and several simplifications are made to arrive at an effective heat transfer coefficient. A characteristic mole ratio X c is also identified that demarcates the transition to a kinetically-limited regime when X ≪ X c from a diffusively-limited regime when X ≫ X c . Numerical results obtained over a wide range of parameters show that even with a small amount of noncondensable gas, the interfacial temperature drop can be quite significant primarily because of diffusional resistance, an observation that has important practical implications, especially in the field of cryogenic fluid storage.

Growth and magnetism of self-organized arrays of Fe(1 1 0) wires formed by deposition on kinetically grooved W(1 1 0)

Homoepitaxy of W(1 1 0) and Mo(1 1 0) is performed in a kinetically-limited regime to yield a nanotemplate in the form of a uniaxial array of hills and grooves aligned along the [0 0 1] direction. The topography and organization of the grooves were studied with RHEED and STM. The nanofacets, of type {2 1 0}, are tilted ∼18° away from (1 1 0). The lateral period could be varied from 4 to 12 nm by tuning the deposition temperature. Magnetic nanowires were formed in the grooves by deposition of Fe at 150 °C on such templates. Fe/W wires display an easy axis along [0 0 1] and a mean blocking temperature T B ≈ 100 K.

High temperature ignition and combustion enhancement by dimethyl ether addition to methane–air mixtures

The effects of dimethyl ether (DME) addition on the high temperature ignition and burning properties of methane–air mixtures were studied experimentally and numerically. The results showed that for a homogeneous system, a small amount of DME addition to methane resulted in a significant reduction in the high temperature ignition delay. The ignition enhancement effect by DME addition was found to exceed that possible with equivalent amounts of hydrogen addition, and it was investigated by using radical pool growth and computational singular perturbation analysis. For a non-premixed methane–air system, it was found that two different ignition enhancement regimes exist: a kinetic limited regime and a transport limited regime. In contrast to the dramatic ignition enhancement in the kinetic limited regime, the ignition enhancement in the transport limited regime was significantly less effective. Furthermore, laminar flame speeds as well as Markstein lengths were experimentally measured for methane–air flames with DME addition. The results showed that the flame speed increases almost linearly with DME addition. However, the Markstein length and the Lewis number of the binary fuel change dramatically at small DME concentrations. Moreover, comparison between experiments and numerical simulations showed that only the most recent DME mechanism well reproduced the flame speeds of both DME–air and CH 4–air flames.

Investigation of the Effects of Controlled Periodic Illumination on the Oxidation of Gaseous Trichloroethylene Using a Thin Film of TiO2

Enhancement of gas-phase photocatalytic oxidation by controlled periodic illumination (CPI) was investigated. The oxidation of trichloroethylene (TCE) was studied in a versatile reactor designed to provide periodic illumination of the TiO2 films. The reactor was operated in two different geometric configurations, tubular and annular. Multiple flow regimes were investigated: kinetic- and diffusion-limited. No enhancement on the rate or the selectivity of TCE oxidation was observed at any of the CPI conditions investigated in the kinetically limited flow regime. The ratio of TCE oxidized to dichloroacetyl chloride (DCAC) produced was 0.59 at all light and dark times investigated for kinetically limited operation. In diffusion-limited regimes, CPI increased the rate of oxidation and decreased the relative amount of DCAC in the product stream. In the kinetic-limited regimes the apparent quantum yield was constant at around 150%; however, in the diffusion-limited regimes the apparent quantum yield almost doub...

Diffusional limitations on the kinetics of dehydration reactions of hydrated barium chloride

The dehydration kinetics of BaCl 2·2H 2O powders were examined as a function of water vapor pressure, sample bed depth, particle diameter and temperature. The conversion behavior was modeled in both the kinetic and the combined diffusion and kinetic limited regimes with modified forms of the Avrami-Erofe'ev equation. Kinetic data were obtained by thermogravimetric techniques and by calorimetry. Structural data for intermediates and products were obtained by X-ray diffraction and optical microscopy. Dehydrations were conducted isothermally between 317 and 335 K either under vacuum or in controlled pure water vapor atmospheres ranging from 40 to 6.67 × 10 2 Pa. The dehydration rate decreased as the water vapor pressure, sample bed depth and particle diameter increased. The estimated effective bed diffusivity is 1.0×10 −6 cm 2 s −1. After a critical pressure was exceeded, severe reductions in rate were observed. The dehydration of BaCl 2·2H 2O proceeded stepwise via the crystalline monohydrate above about 80 Pa at 317 K; below this pressure the crystalline monohydrate was not observed. Transient increases in water vapor pressure in the sample bed caused crystallization of the monohydrate under conditions where it did not otherwise form.

Chemical Vapor Deposition of SiO2 from Ozone-Organosilane Mixtures near Atmospheric Pressure

ABSTRACTThe kinetics of deposition of SiO2 by the reaction of tetramethylsilane (TMS) with ozone (O3) has been studied over the temperature range 180 – 380° C and compared with available data for the same process using tetraethoxysilane (TEOS). Both processes exhibit the same activation energy (17 kcal/mole) below 300 ° C which falls-off at higher temperatures due to transport limitations. Transition from first- to zero-order kinetics occurs with increasing concentrations of TMS and O3, which gives an overall O3/TMS consumption ratio of 10 at 258° C and5 at 325° C. TEOS is estimated to be 5 times more reactive than TMS above 300° C and over 10 times more reactive in the kinetically-limited regime below 300° C. Results suggest that O3-induced SiO2 deposition proceeds via surface reactions and is limited by heterogeneous decomposition of ozone.