Abstract: Recent advances in model based quantification of electron energy loss spectra (EELS) are reported. The maximum likelihood method for the estimation of physical parameters describing an EELS spectrum, the validation of the model used in this estimation procedure, and the computation of the attainable precision, that is, the theoretical lower bound on the variance of these estimates, are discussed. Experimental examples on An and GaAs samples show the power of the maximum likelihood method and show that the theoretical prediction of the attainable precision can be closely approached even for spectra with overlapping edges where conventional EELS quantification fails. To provide end-users with a low threshold alternative to conventional quantification, a user friendly program was developed which is freely available under a GNU public license. (C) 2004 Elsevier B.V. All rights reserved.

Abstract: Dielectric properties of materials are crucial in describing the electromagnetic response of materials. As devices are becoming considerably smaller than the optical wavelength, the conventional measuring methods based on optical response are limited by their spatial resolution. Electron energy loss spectroscopy performed in a scanning transmission electron microscope is a good alternative to obtain the dielectric properties with excellent spatial resolution. Due to the overlap of diffraction discs in scanning transmission electron microscopy, it is difficult to apply conventional experimental settings to suppress retardation losses. In this contribution, a relativistic dielectric model for the loss function is presented which is used in a model based optimization scheme to estimate the complex dielectric function of a material. The method is applied to experiments on bulk diamond and SrTiO3 and shows a good agreement with optical reference data when retardation effects are included. Application of this technique to nanoparticles is possible but several theoretical assumptions made in the model of the loss function are violated and interpretation becomes problematic.

Abstract: An extension to model-based electron energy loss spectroscopy (EELS) quantification is reported to improve the possibility of modelling fine structure changes in electron energy loss spectra. An equalisation function is used in the energy loss near edge structure (ELNES) region to model the differences between a single atom differential cross section and the cross section for an atom in a crystal. The equalisation function can be shown to approximate the relative density of unoccupied states for the given excitation edge. On a set of 200 experimental h-BN spectra, this technique leads to statistically acceptable models resulting into unbiased estimates of relative concentrations and making the estimated precisions come very close to the Cramer-Rao lower bound (CRLB). The method greatly expands the useability of model-based EELS quantification to spectra with pronounced fine structure. Another benefit of this model is that one also gets an estimate of the unoccupied density of states for a given excitation edge, without having to do background removal and deconvolution, making the outcome intrinsically more reliable and less noisy. (c) 2006 Elsevier B.V. All rights reserved.

Abstract: Electron energy loss spectroscopy (EELS) is an ideal tool to obtain chemical information from nanoscale volumes. Quantification of the experimental spectra however has prevented for a long time access to the available information in a reliable and reproducible way. We present recent advances in model-based quantification of EELS spectra and show that we obtain the best possible precision for a given dataset, as well as remarkably good accuracies when applied to three different materials. The results are shown to be far superior over conventional quantification techniques and could hold a promise for standardless quantification of EELS spectra.

Abstract: In this study, we present a computational model of a cylindrical electric probe in atmospheric pressure argon plasma. The plasma properties are varied in terms of density and electron temperature. Furthermore, results for plasmas with Maxwellian and non-Maxwellian electron energy distribution functions are also obtained and compared. The model is based on the fluid description of plasma within the COMSOL software package. The results for the ion saturation current are compared and show good agreement with existing analytical Langmuir probe theories. A strong dependence between the ion saturation current and electron transport properties was observed, and attributed to the effects of ambipolar diffusion.

Abstract: A two-dimensional hybrid Monte Carlofluid model, incorporating a full-wave solution of Maxwell's equations, is employed to describe the behavior of high frequency (HF) and very high frequency capacitively coupled plasmas (CCPs), operating both at single frequency (SF) and dual frequency (DF) in a CF4/O2 gas mixture. First, the authors investigate the plasma composition, and the simulations reveal that besides CF4 and O2, also COF2, CF3, and CO2 are important neutral species, and CF+3 and F− are the most important positive and negative ions. Second, by comparing the results of the model with and without taking into account the electromagnetic effects for a SF CCP, it is clear that the electromagnetic effects are important, both at 27 and 60 MHz, because they affect the absolute values of the calculation results and also (to some extent) the spatial profiles, which accordingly affects the uniformity in plasma processing. In order to improve the plasma radial uniformity, which is important for the etch process, a low frequency (LF) source is added to the discharge. Therefore, in the major part of the paper, the plasma uniformity is investigated for both SF and DF CCPs, operating at a HF of 27 and 60 MHz and a LF of 2 MHz. For this purpose, the authors measure the etch rates as a function of position on the wafer in a wide range of LF powers, and the authors compare them with the calculated fluxes toward the wafer of the plasma species playing a role in the etch process, to explain the trends in the measured etch rate profiles. It is found that at a HF of 60 MHz, the uniformity of the etch rate is effectively improved by adding a LF power of 2 MHz and 300 W, while its absolute value increases by about 50%, thus a high etch rate with a uniform distribution is observed under this condition.

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: Hydrogenotrophic denitrification is a novel and sustainable process for nitrogen removal, which utilizes hydrogen as electron donor, and carbon dioxide as carbon source. Recent studies have shown that nitrous oxide (N2O), a highly undesirable intermediate and potent greenhouse gas, can accumulate during this process. In this work, a new mathematical model is developed to describe nitrogen oxides dynamics, especially N2O, during hydrogenotrophic denitrification for the first time. The model describes electron competition among the four steps of hydrogenotrophic denitrification through decoupling hydrogen oxidation and nitrogen reduction processes using electron carriers, in contrast to the existing models that couple these two processes and also do not consider N2O accumulation. The developed model satisfactorily describes experimental data on nitrogen oxides dynamics obtained from two independent hydrogenotrophic denitrifying cultures under various hydrogen and nitrogen oxides supplying conditions, suggesting the validity and applicability of the model. The results indicated that N2O accumulation would not be intensified under hydrogen limiting conditions, due to the higher electron competition capacity of N2O reduction in comparison to nitrate and nitrite reduction during hydrogenotrophic denitrification. The model is expected to enhance our understanding of the process during hydrogenotrophic denitrification and the ability to predict N2O accumulation.

Abstract: Our aim is to develop and optimize a model for a dielectric barrier discharge used as a chemical reactor for gas treatment. In order to determine the optimum operating conditions, we have studied the influence of the gas flow rate, reactor geometry and applied voltage parameters on the discharge characteristics. For this purpose, a two-dimensional time-dependent fluid model has been applied to an atmospheric pressure DBD in helium with nitrogen impurities, in a cylindrical geometry. The numerical model is based on the continuity and flux equations for each type of particles treated, the electron energy equation and the Poisson equation. The gas flow is incorporated in the flux equations as a source term. The set of coupled partial differential equations is solved by the so-called modified strongly implicit method. The background gas flow is numerically treated separately, assuming in the model that there is no influence of the plasma on the flow. Indeed, the gas convection velocity is calculated using the commercial code Fluent and it is used as input into the 2D fluid model. The plasma characteristics have been studied in terms of gas flow rate, applied voltage amplitude and frequency, and geometrical effects. The electric currents as a function of time for a given applied potential have been obtained, as well as the number densities and fluxes of plasma species.

Abstract: Low-temperature plasma chemical kinetic models are particularly important to the plasma community. These models typically require dozens of inputs, especially rate coefficients. The latter are not always precisely known and it is not surprising that the error on the rate coefficient data can propagate to the model output. In this paper, we present a model that uses N = 400 different combinations of rate coefficients based on the uncertainty attributed to each rate coefficient, giving a good estimation of the uncertainty on the model output due to the rate coefficients. We demonstrate that the uncertainty varies a lot with the conditions and the type of output. Relatively low uncertainties (about 15%) are found for electron density and temperature, while the uncertainty can reach more than an order of magnitude for the population of the vibrational levels in some cases and it can rise up to 100% for the CO2 conversion. The reactions that are mostly responsible for the largest uncertainties are identified. We show that the conditions of pressure, gas temperature and power density have a great effect on the uncertainty and on which reactions lead to this uncertainty. In all the cases tested here, while the absolute values may suffer from large uncertainties, the trends observed in previous modeling work are still valid. Finally, in accordance with the work of Turner, a number of ‘good practices’ is recommended.

Abstract: Graphene interconnects are being considered as a promising candidate for beyond CMOS applications, thanks to the intrinsic higher carrier mobility, lower aspect ratio and better reliability with respect to conventional Cu damascene interconnects. However, similarly to Cu, line edge roughness can seriously affect graphene resistance, something which must be taken into account when evaluating the related performance benefits. In this letter, we present a model for assessing the impact of edge scattering on the resistance of graphene interconnects. Our model allows the evaluation of the total mean free path in graphene lines as a function of graphene width, diffusive scattering probability and edge roughness standard deviation and autocorrelation length. We compare our model with other models from literature by benchmarking them using the same set of experimental data. We show that, as opposed to the considered models from literature, our model is capable to describe the mobility drop with scaling caused by significantly rough edges.