Abstract: Single-file diffusion (SFD) of an infinite one-dimensional chain of interacting particles has a long-time mean-square displacement ∝t1/2, independent of the type of interparticle repulsive interaction. This behavior is also observed in finite-size chains, although only for certain intervals of time t depending on the chain length L, followed by the ∝t for t→∞, as we demonstrate for a closed circular chain of diffusing interacting particles. Here, we show that spatial correlation of noise slows down SFD and can result, depending on the amount of correlated noise, in either subdiffusive behavior ∝tα, where 0<α<1/2, or even in a total suppression of diffusion (in the limit N→∞). Spatial correlation can explain the subdiffusive behavior in recent SFD experiments in circular channels.

Abstract: In this paper, an O2 inductively coupled plasma used for plasma enhanced atomic layer deposition of Al2O3 thin films is investigated by means of modeling. This work intends to provide more information about basic plasma properties such as species densities and species fluxes to the substrate as a function of power and pressure, which might be hard to measure experimentally. For this purpose, a hybrid model developed by Kushner et al is applied to calculate the plasma characteristics in the reactor volume for different chamber pressures ranging from 1 to 10 mTorr and different coil powers ranging from 50 to 500 W. Density profiles of the various oxygen containing plasma species are reported as well as fluxes to the substrate under various operating conditions. Furthermore, different orientations of the substrate, which can be placed vertically or horizontally in the reactor, are taken into account. In addition, special attention is paid to the recombination process of atomic oxygen on the different reactor walls under the stated operating conditions. From this work it can be concluded that the plasma properties change significantly in different locations of the reactor. The plasma density near the cylindrical coil is high, while it is almost negligible in the neighborhood of the substrate. Ion and excited species fluxes to the substrate are found to be very low and negligible. Finally, the orientation of the substrate has a minor effect on the flux of O2, while it has a significant effect on the flux of O. In the horizontal configuration, the flux of atomic oxygen can be up to one order of magnitude lower than in the vertical configuration.

Abstract: In this article, surface processes occurring during the etching of Si with a Cl2/O2/Ar plasma are investigated by means of experiments and modeling. Cl2-based plasmas are commonly used to etch silicon, while a small fraction of O2 is added to protect the sidewalls from lateral etching during the shallow trench isolation process. When the oxygen fraction exceeds a critical value, the wafer surface process changes from an etching regime to a deposition regime, drastically reducing the etch rate. This effect is commonly referred to as the etch stop phenomenon. To gain better understanding of this mechanism, the oxygen fraction is varied in the gas mixture and special attention is paid to the effects of oxygen and of the redeposition of non-volatile etched species on the overall etch/deposition process. It is found that, when the O2 flow is increased, the etch process changes from successful etching to the formation of a rough surface, and eventually to the actual growth of an oxide layer which completely blocks the etching of the underlying Si. The size of this etch stop island was found to increase as a function of oxygen flow, while its thickness was dependent on the amount of Si etched. This suggests that the growth of the oxide layer mainly depends on the redeposition of non-volatile etch products. The abrupt change in the etch rate as a function of oxygen fraction was not found back in the oxygen content of the plasma, suggesting the competitive nature between oxidation and chlorination at the wafer. Finally, the wafer and reactor wall compositions were investigated by modeling and it was found that the surface rapidly consisted mainly of SiO2 when the O2 flow was increased above about 15 sccm.

Abstract: We investigated the mixing and segregation of a system consisting of two different species of particles, having different charges, interacting through a pure Coulomb potential, and confined in a three-dimensional parabolic trap. The structure of the cluster and its normal mode spectrum are analyzed as a function of the relative charge and the relative number of different types of particles. We found that (a) the system can be in a mixed or segregated state depending on the relative charge ratio parameter and (b) the segregation process is mediated by a first or second order structural phase transition which strongly influences the magic cluster properties of the system.

Abstract: In this paper, simulations are performed to gain a better insight into the properties of a Cl2/Ar plasma, with and without O2, during plasma etching of Si. Both plasma and surface properties are calculated in a self-consistent manner. Special attention is paid to the behavior of etch products coming from the wafer or the walls, and how the chamber walls can affect the plasma and the resulting etch process. Two modeling cases are considered. In the first case, the reactor walls are defined as clean (Al2O3), whereas in the second case a SiO2 coating is introduced on the reactor walls before the etching process, so that oxygen will be sputtered from the walls and introduced into the plasma. For this reason, a detailed reaction set is presented for a Cl2/O2/Ar plasma containing etched species, as well as an extensive reaction set for surface processes, including physical and chemical sputtering, chemical etching and deposition processes. Density and flux profiles of various species are presented for a better understanding of the bulk plasma during the etching process. Detailed information is also given on the composition of the surfaces at various locations of the reactor, on the etch products in the plasma and on the surface loss probabilities of the plasma species at the walls, with different compositions. It is found that in the clean chamber, walls are mostly chlorinated (Al2Cl3), with a thin layer of etch products residing on the wall. In the coated chamber, an oxy-chloride layer is grown on the walls for a few nanometers during the etching process. The Cl atom wall loss probability is found to decrease significantly in the coated chamber, hence increasing the etch rate. SiCl2, SiCl4 and SiCl3 are found to be the main etch products in the plasma, with the fraction of SiCl2 being always slightly higher. The simulation results compare well with experimental data available from the literature.

Abstract: The influence of an ellipsoid on the angular order of two-dimensional classical clusters is investigated through Brownian dynamics simulations. We found the following: (1) The presence of an ellipsoid does not influence the start of the angular melting, but reduces the rate at which the inner rings can rotate with respect to each other. (2) Even a small eccentricity of the ellipsoid leads to a stabilization of the angular order of the system. (3) Depending on the position of the ellipsoid in the cluster, a reentrant behavior in the angular order is observed before full radial melting of the cluster sets in. (4) The ellipsoid can lead to a two-step angular melting process: First, the rotation of the inner rings with respect to each other is hindered by the ellipsoid, but on further increasing the kinetic energy of the system, the ellipsoid just starts to behave as a spherical particle with different mobility. The effect of an ellipsoid on the molten system does not depend crucially on the interparticle interaction, but a softer parabolic confinement reduces the angular stabilization.

Abstract: Modeling results are presented to gain a better insight in the properties of a SiH4/O2/Ar inductively coupled plasma (ICP) and how it interacts with a silicon substrate (wafer), as applied in the microelectronics industry for the fabrication of electronic devices. The SiH4/O2/Ar ICP is used for the filling of microtrenches with isolating material (SiO2), as applied in shallow trench isolation (STI). In this article, a detailed reaction set that describes the plasma chemistry of SiH4/O2/Ar discharges as well as surface processes, such as sputtering, oxidation, and deposition, is presented. Results are presented on the plasma properties during the plasma enhanced chemical vapor deposition process (PECVD) for different gas ratios, as well as on the shape of the filled trenches and the surface compositions of the deposited layers. For the operating conditions under study it is found that the most important species accounting for deposition are SiH2, SiH3O, SiH3 and SiH2O, while SiH+2, SiH+3, O+2 and Ar+ are the dominant species for sputtering of the surface. By diluting the precursor gas (SiH4) in the mixture, the deposition rate versus sputtering rate can be controlled for a desired trench filling process. From the calculation results it is clear that a high deposition rate will result in undesired void formation during the trench filling, while a small deposition rate will result in undesired trench bottom and mask damage by sputtering. By varying the SiH4/O2 ratio, the chemical composition of the deposited layer will be influenced. However, even at the highest SiH4/O2 ratio investigated (i.e., 3.2:1; low oxygen content), the bulk deposited layer consists mainly of SiO2, suggesting that low-volatile silane species deposit first and subsequently become oxidized instead of being oxidized first in the plasma before deposition. Finally, it was found that the top surface of the deposited layer contained less oxygen due to preferential sputtering of O atoms, making the top layer more Si-rich. However, this effect is negligible at a SiH4/O2 ratio of 2:1 or lower.

Abstract: A numerical model for NxOy remediation in humid air plasma produced with a dielectric barrier discharge at atmospheric pressure is presented. Special emphasis is given to NO2 and N2O reduction with the decrease of O2 content in the feedstock gas. A detailed reaction mechanism including electronic and ionic processes, as well as the contribution of radicals and excited atomic/molecular species is proposed. The temporal evolution of the densities of NO, NO2 and N2O species, and some other by-products, is analyzed, and the major pathways for the NxOy remediation are discussed for one pulse. Subsequently, simulations are presented for a multi-pulses case, where three O2 contents are tested for optimization of the remediation process. It is found that when the gas mixture O2/N2/H2O/NOx has no initial O2 content, the best NOx and N2O remediation is achieved.

Abstract: In this work, a hybrid model is used to investigate the effect of different gas ratios on the Si etching and polymer film deposition characteristics in an Ar/CF4 inductively coupled plasma. The influence of the surface processes on the bulk plasma properties is studied, and also the spatial characteristics of important gas phase and etched species. The densities of F and CF2 decrease when the surface module is included in the simulations, due to the species consumption caused by etching and polymer deposition. The influence of the surface processes on the bulk plasma depends on the Ar/CF4 gas ratio. The deposited polymer becomes thicker at high CF4 content because of more abundant CFx radicals. As a result of the competition between the polymer thickness and the F flux, the etch rate first increases and then decreases upon increasing the CF4 content. The electron properties, more specifically the electron density profile, affect the Si etch characteristics substantially by determining the radical density and flux profiles. In fact, the radial profile of the etch rate is more uniform at low CF4 content since the electron density has a smooth distribution. At high CF4 content, the etch rate is less uniform with a minimum halfway along the wafer radius, because the electron density distribution is more localized. Therefore, our calculations predict that it is better to work at relatively high Ar/CF4 gas ratios, in order to obtain high etch rate and good profile uniformity for etch applications. This, in fact, corresponds to the typical experimental etch conditions in Ar/CF4 gas mixtures as found in the literature, where Ar is typically present at a much higher concentration than CF4.

Abstract: In this paper, we investigate the etch process of so-called low-k organic material by means of a N2/H2 capacitively coupled plasma, as applied in the micro-electronics industry for the manufacturing of computer chips. In recent years, such an organic material has emerged as a possible alternative for replacing bulk SiO2 as a dielectric material in the back-end-of-line, because of the smaller parasitic capacity between adjacent conducting lines, and thus a faster propagation of the electrical signals throughout the chip. Numerical simulations with a hybrid plasma model, using an extensive plasma and surface chemistry set, as well as experiments are performed, focusing on the plasma properties as well as the actual etching process, to obtain a better insight into the underlying mechanisms. Furthermore, the effects of gas pressure, applied power and gas composition are investigated to try to optimize the etch process. In general, the plasma density reaches a maximum near the wafer edge due to the so-called 'edge effect'. As a result, the etch rate is not uniform but will also reach its maximum near the wafer edge. The pressure seems not to have a big effect. A higher power increases the etch rate, but the uniformity becomes (slightly) worse. The gas mixing ratio has no significant effect on the etch process, except when a pure H2 or N2 plasma is used, illustrating the synergistic effects of a N2/H2 plasma. In fact, our calculations reveal that the N2/H2 plasma entails an ion-enhanced etch process. The simulation results are in reasonable agreement with the experimental values. The microscopic etch profile shows the desired anisotropic shape under all conditions under study.

Abstract: Simulations and experiments are performed to obtain a better insight in the plasma enhanced chemical vapor deposition process of SiO2 by SiCl4/O2/Ar plasmas for introducing a SiO2-like coating in wafer processing reactors. Reaction sets describing the plasma and surface chemistry of the SiCl4/O2/Ar mixture are presented. Typical calculation results include the bulk plasma characteristics, i.e., electrical properties, species densities, and information on important production and loss processes, as well as the chemical composition of the deposited coating, and the thickness uniformity of the film on all reactor surfaces. The film deposition characteristics, and the trends for varying discharge conditions, are explained based on the plasma behavior, as calculated by the model.

Abstract: Optical emission spectroscopy is used to investigate the nitrogen-hydrogen with trace rare gas (4% Ar) plasma generated by 50 Hz pulsed DC discharges. The filling pressure varies from 1 mbar to 5 mbar and the current density ranges from 1 mA.cm(-2) to 4 mA.cm(-2). The hydrogen concentration in the mixture plasma varies from 0% to 80%, with the objective of identifying the optimum pressure, current density and hydrogen concentration for active species ([N] and [N-2]) generation. It is observed that in an N-2-H-2 gas mixture, the concentration of N atom density decreases with filling pressure and increases with current density, with other parameters of the discharge kept unchanged. The maximum concentrations of active species were found for 40% H-2 in the mixture at 3 mbar pressure and current density of 4 mA.cm(-2).

Abstract: In this paper we analyse the gas phase production and loss pathways for several biomedically active species, i.e. N2(A), O, O3, O2(a), N, H, HO2, OH, NO, NO2, N2O5, H2O2, HNO2 and HNO3, in an argon plasma jet flowing into an open humid air atmosphere. For this purpose, we employ a zero-dimensional reaction kinetics model to mimic the typical experimental conditions by fitting several parameters to experimentally measured values. These include ambient air diffusion, the gas temperature profile and power deposition along the jet effluent. We focus in detail on how the pathways of the biomedically active species change as a function of the position in the effluent, i.e. inside the discharge device, active plasma jet effluent and afterglow region far from the nozzle. Moreover, we demonstrate how the reaction kinetics and species production are affected by different ambient air humidities, total deposited power into the plasma and gas temperature along the jet. It is shown that the dominant pathways can drastically change as a function of the distance from the nozzle exit or experimental conditions.

Abstract: Reactive molecular dynamics simulations are performed to study the interaction of reactive oxygen species, such as OH, HO2 and H2O2, with the endotoxic biomolecule lipid A of the gram-negative bacterium Escherichia coli. It is found that the aforementioned plasma species can destroy the lipid A, which consequently results in reducing its toxic activity. All bond dissociation events are initiated by hydrogen-abstraction reactions. However, the mechanisms behind these dissociations are dependent on the impinging plasma species, i.e. a clear difference is observed in the mechanisms upon impact of HO2 radicals and H2O2 molecules on one hand and OH radicals on the other hand. Our simulation results are in good agreement with experimental observations.