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At least 433 records · Page 24

One-dimensional hybrid simulation of the dc/RF combined driven capacitively coupled CF{sub 4} plasmas

We developed a one-dimensional hybrid model to simulate the dc/RF combined driven capacitively coupled plasma for CF{sub 4} discharges. The numerical results show the influence of the dc source on the plasma density distribution, ion energy distributions (IEDs), and ion angle distributions (IADs) on both RF and dc electrodes. The increase of dc voltage impels more ions with high energy to the electrode applied to the dc source, which makes the IEDs at the dc electrode shift toward higher energy and the peaks in IADs shift toward the small angle region. At the same time, it also decreases ion-energy at the RF electrode and enlarges the ion-angles which strike the RF electrode.

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Energy distribution of electron flux at electrodes in a low pressure capacitively coupled plasma

A one-dimensional particle-in-cell (PIC) model is used to examine the energy distribution of electron flux at electrodes [labeled g{sub e}({epsilon},t), where {epsilon} is energy and t is time] in a low pressure 60 MHz capacitively coupled Ar discharge. The effect of gas pressure and an auxiliary DC voltage on g{sub e}({epsilon},t) is also investigated. It is found that the electrons only leave the plasma for a short time period during the radio-frequency (RF) cycle when the sheath collapses at the electrode. Furthermore, majority of the exiting electrons have energies below 10 eV with a distribution g{sub e}({epsilon},t) that is narrow in both energy and time. At relatively high pressures ({>=}4.67 Pa for the conditions considered), the relationship between the time-average distribution g{sub e}({epsilon}) and electron temperature in the plasma (T{sub e}) can be easily established. Below 4.67 Pa, kinetic effects become important, making it difficult to interpret g{sub e}({epsilon}) in terms of T{sub e}. At low pressures, g{sub e}({epsilon},t) is found to broaden in both energy and time except for a narrow pressure range around 1.2 Pa where the distribution narrows temporally. These low pressure kinetic phenomena are observed when the electrons can be accelerated by expanding sheaths to speeds that allow them to traverse the inter-electrode distance quickly (<1.5 RF cycles for conditions considered) and when electrons undergo few collisions during this excursion. The mean energy of exiting electrons increases with decreasing gas pressure, especially below 1.0 Pa, due to higher T{sub e} and secondary electrons retaining a larger fraction of the energy they gained during initial sheath acceleration. For the relatively small DC voltages examined ( Double-Vertical-Line V{sub dc} Double-Vertical-Line /V{sub rf} {<=} 0.15), the application of a negative DC voltage on an electrode decreases the electron flux there but has a weak impact on the g{sub e} profile.

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Simulation benchmarks for low-pressure plasmas: Capacitive discharges

Benchmarking is generally accepted as an important element in demonstrating the correctness of computer simulations. In the modern sense, a benchmark is a computer simulation result that has evidence of correctness, is accompanied by estimates of relevant errors, and which can thus be used as a basis for judging the accuracy and efficiency of other codes. In this paper, we present four benchmark cases related to capacitively coupled discharges. These benchmarks prescribe all relevant physical and numerical parameters. We have simulated the benchmark conditions using five independently developed particle-in-cell codes. We show that the results of these simulations are statistically indistinguishable, within bounds of uncertainty that we define. We, therefore, claim that the results of these simulations represent strong benchmarks, which can be used as a basis for evaluating the accuracy of other codes. These other codes could include other approaches than particle-in-cell simulations, where benchmarking could examine not just implementation accuracy and efficiency, but also the fidelity of different physical models, such as moment or hybrid models. We discuss an example of this kind in the Appendix. Of course, the methodology that we have developed can also be readily extended to a suite of benchmarks with coverage of a wider range of physical and chemical phenomena.

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Combined effects of gas pressure and exciting frequency on electron energy distribution functions in hydrogen capacitively coupled plasmas

The combined effects of the variation of hydrogen pressure (40-400 mTorr) and exciting frequency (13.56-50 MHz) on the electron energy probability function (EEPF) and other plasma parameters in capacitively coupled hydrogen H{sub 2} discharge at fixed discharge voltage were investigated using rf-compensated Langmuir probe. At a fixed exciting frequency of 13.56 MHz, the EEPF evolved from Maxwellian-like distribution to a bi-Maxwellian distribution when the H{sub 2} pressure increased, possibly due to efficient vibrational excitation. The electron density largely increased to a peak value and then decreased with the increase of H{sub 2} pressure. Meanwhile, the electron temperature and plasma potential significantly decrease and reaching a minimum at 120 mTorr beyond, which saturated or slightly increases. On the other hand, the dissipated power and electron density markedly increased with increasing the exciting frequency at fixed H{sub 2} pressure and voltage. The electron temperatures negligibly dependent on the driving frequency. The EEPFs at low pressure 60 mTorr resemble Maxwellian-like distribution and evolve into a bi-Maxwellian type as frequency increased, due to a collisonless (stochastic) sheath-heating in the very high frequency regime, while the EEPF at hydrogen pressure {>=}120 mTorr retained a bi-Maxwellian-type distribution irrespective of the driving frequency. Such evolution of the EEPFs shape with the driving frequency and hydrogen pressure has been discussed on the basis of electron diffusion processes and low threshold-energy inelastic collision processes taking place in the discharge. The ratio of stochastic power to bulk power heating ratio is dependent on the hydrogen pressure while it is independent on the driving frequency.

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Frequency dependence of the electrical asymmetry effect in dual-frequency capacitively coupled discharges

Using experimental measurements complemented with particle-in-cell (PIC) simulations, we demonstrate a reduction in the electrical asymmetry effect in capacitively coupled discharges for low excitation frequencies (0.8 MHz < f<10 MHz). These results confirm PIC simulation predictions made by [I. Korolov, Z. Donko, U. Czarnetzki, and J. Schulze, J. Phys. D: Appl. Phys. 45, 465205 (2012)], where this effect was investigated for dual-frequency discharges in which the driving frequencies are phase-shifted harmonics. Because the reduction in electrical asymmetry is a sensitive function of the secondary electron emission coefficient, we are able to non-invasively estimate this coefficient as 0.035 for argon ions incident on aluminium electrodes.

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Narrow gap electronegative capacitive discharges

Narrow gap electronegative (EN) capacitive discharges are widely used in industry and have unique features not found in conventional discharges. In this paper, plasma parameters are determined over a range of decreasing gap length L from values for which an electropositive (EP) edge exists (2-region case) to smaller L-values for which the EN region connects directly to the sheath (1-region case). Parametric studies are performed at applied voltage V{sub rf}=500 V for pressures of 10, 25, 50, and 100 mTorr, and additionally at 50 mTorr for 1000 and 2000 V. Numerical results are given for a parallel plate oxygen discharge using a planar 1D3v (1 spatial dimension, 3 velocity components) particle-in-cell (PIC) code. New interesting phenomena are found for the case in which an EP edge does not exist. This 1-region case has not previously been investigated in detail, either numerically or analytically. In particular, attachment in the sheaths is important, and the central electron density n{sub e0} is depressed below the density n{sub esh} at the sheath edge. The sheath oscillations also extend into the EN core, creating an edge region lying within the sheath and not characterized by the standard diffusion in an EN plasma. An analytical model is developed using minimal inputs from the PIC results, and compared to the PIC results for a base case at V{sub rf}=500 V and 50 mTorr, showing good agreement. Selected comparisons are made at the other voltages and pressures. A self-consistent model is also developed and compared to the PIC results, giving reasonable agreement.

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Spectroscopy diagnostic of dual-frequency capacitively coupled CHF{sub 3}/Ar plasma

A combined spectroscopic method of absorption, actinometry, and relative optical emission intensity is employed to determine the absolute CF{sub 2} density, the relative F and H densities, H atom excitation temperature and the electron density in dual-frequency (60/2 MHz) capacitively coupled CHF{sub 3}/Ar plasmas. The effects of different control parameters, such as high-frequency (HF) power, low-frequency (LF) power, gas pressure, gap length and content of CHF{sub 3}, on the concentration of radical CF{sub 2}, F, and H and excitation temperature are discussed, respectively. It is found that the concentration of CF{sub 2} is strongly dependent on the HF power, operating pressure and the proportion of CHF{sub 3} in feed gas, while it is almost independent of the LF power and the gap length. A higher concentration ratio of F to CF{sub 2} could be obtained in dual-frequency discharge case. Finally, the generation and decay mechanisms of CF{sub 2} and F were also discussed.

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Particle-In-Cell simulation of laser photodetachment in capacitively coupled radio frequency oxygen discharges

Particle-In-Cell simulations with Monte Carlo collision of capacitively coupled radio frequency oxygen discharges are used to study the appearance and characteristics of two experimentally observed electronegative modes, the high electronegative mode for low peak-to-peak voltage, and the low electronegative mode for high peak-to-peak voltage. For the high electronegative mode, the simulated laser photodetachment signal agrees very well with the experiment. The simulation identifies the dominant transport processes for high electronegativities: electrons flow fast out of the perturbed region, where the laser pulse generates laser detachment of negative ions. Negative ions are not streaming inward, but are produced within this region by dissociative attachment after the laser pulse.

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Investigation of the effects of a thin dielectric layer on low-pressure hydrogen capacitive discharges driven by combined radio frequency and pulse power sources

Negative hydrogen ion sources, for instance for fusion devices, currently attract considerable attention. To generate the precursors—highly rovibrationally excited hydrogen molecules—for negative hydrogen ions effectively by electron excitation, a thin dielectric layer is introduced to cover the surface of the electrically grounded electrode of two parallel metal plates in a low-pressure hydrogen capacitive discharge driven by combined rf and pulse power sources. To understand the characteristics of such discharges, particle-in-cell simulations are conducted to study the effects that the single dielectric layer would bring onto the discharges. The simulation results show that the dielectric layer leads to a much higher plasma density and a much larger production rate of highly vibrationally excited hydrogen molecules compared to discharges without the dielectric layer on the electrode. Further investigation indicates that the nonlinear oscillation of the electrons induced by the nanosecond-pulse continues until it is finally damped down and does not show any dependence on the pulse plateau-time, which is in stark contrast to the case without the dielectric layer present. The physical reason for this phenomenon is explored and explained.

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Experimental investigations of electron density and ion energy distributions in dual-frequency capacitively coupled plasmas for Ar/CF{sub 4} and Ar/O{sub 2}/CF{sub 4} discharges

The electron density and ion energy distribution (IED) are investigated in low-pressure dual-frequency capacitively coupled Ar/CF{sub 4} (90%/10%) and Ar/O{sub 2}/CF{sub 4} (80%/10%/10%) plasmas. The relations between controllable parameters, such as high-frequency (HF) power, low-frequency (LF) power and gas pressure, and plasma parameters, such as electron density and IEDs, are studied in detail by utilizing a floating hairpin probe and an energy resolved quadrupole mass spectrometer, respectively. In our experiment, the electron density is mainly determined by the HF power and slightly influenced by the LF power. With increasing gas pressure, the electron density first goes up rapidly to a maximum value and then decreases at various HF and LF powers. The HF power also plays a considerable role in affecting the IEDs under certain conditions and the ion energy independently controlled by the LF source is discussed here. For clarity, some numerical results obtained from a two-dimensional fluid model are presented.

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Capacitive micromachined ultrasonic transducer arrays as tunable acoustic metamaterials

Capacitive Micromachined Ultrasonic Transducers (CMUTs) operating in immersion support dispersive evanescent waves due to the subwavelength periodic structure of electrostatically actuated membranes in the array. Evanescent wave characteristics also depend on the membrane resonance which is modified by the externally applied bias voltage, offering a mechanism to tune the CMUT array as an acoustic metamaterial. The dispersion and tunability characteristics are examined using a computationally efficient, mutual radiation impedance based approach to model a finite-size array and realistic parameters of variation. The simulations are verified, and tunability is demonstrated by experiments on a linear CMUT array operating in 2-12 MHz range.

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Hybrid model of atmospheric pressure Ar/O{sub 2}/TiCl{sub 4} radio-frequency capacitive discharge for TiO{sub 2} deposition

A hybrid global-analytical model of an atmospheric pressure radio-frequency driven capacitive discharge is applied to determine the plasma conditions for TiO{sub 2} film deposition. The feed gas is mainly argon with a small fraction of O{sub 2} and a smaller fraction of TiCl{sub 4}. Variations of the discharge parameters and species densities with O{sub 2} concentration, discharge power, and flow rate are determined. A simplified chemistry model is developed and compared with the simulation results, showing good agreement. For a base case with Ar/O{sub 2}/TiCl{sub 4} flow rates of 203/30/0.17 sccm, the results indicate that a minimum O{sub 2} fraction of 7.3 × 10{sup −4} is required for pure (un-chlorinated) TiO{sub 2} film deposition that the active precursor species is TiO{sub 2}Cl{sub 3}, with subsequent abstraction of Cl atoms by dissociative electron attachment and that the deposition rates are around 1 nm/s.

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Heating mode transition in a hybrid direct current/dual-frequency capacitively coupled CF{sub 4} discharge

Computer simulations based on the particle-in-cell/Monte Carlo collision method are performed to study the plasma characteristics and especially the transition in electron heating mechanisms in a hybrid direct current (dc)/dual-frequency (DF) capacitively coupled CF{sub 4} discharge. When applying a superposed dc voltage, the plasma density first increases, then decreases, and finally increases again, which is in good agreement with experiments. This trend can be explained by the transition between the four main heating modes, i.e., DF coupling, dc and DF coupling, dc source dominant heating, and secondary electron dominant heating.

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Direct current dielectric barrier assistant discharge to get homogeneous plasma in capacitive coupled discharge

In this paper, we propose a method to get more homogeneous plasma in the geometrically asymmetric capacitive coupled plasma (CCP) discharge. The dielectric barrier discharge (DBD) is used for the auxiliary discharge system to improve the homogeneity of the geometrically asymmetric CCP discharge. The single Langmuir probe measurement shows that the DBD can increase the electron density in the low density volume, where the DBD electrodes are mounted, when the pressure is higher than 5 Pa. By this manner, we are able to improve the homogeneity of the plasma production and increase the overall density in the target volume. At last, the finite element simulation results show that the DC bias, applied to the DBD electrodes, can increase the homogeneity of the electron density in the CCP discharge. The simulation results show a good agreement with the experiment results.

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Kinetic simulation of capacitively coupled plasmas driven by trapezoidal asymmetric voltage pulses

A kinetic Particle-In-Cell simulation with Monte Carlo Collisions was performed of a geometrically symmetric capacitively coupled, parallel-plate discharge in argon, driven by trapezoidal asymmetric voltage pulses with a period of 200 ns. The discharge was electrically asymmetric, making the ion energy distributions at the two electrodes different from one another. The fraction of the period (α), during which the voltage was kept at a constant (top-flat) positive value, was a critical control parameter. For the parameter range investigated, as α increased, the mean ion energy on the grounded electrode increased and the ions became more directional, whereas the opposite was found for the ions striking the powered electrode. The absolute value of the DC self-bias voltage decreased as α increased. Plasma instabilities, promoted by local double layers and electric field reversals during the time of the positive voltage excursion, were characterized by electron plasma waves launched from the sheath edge.

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Observation of transient electric fields in particle-in-cell simulation of capacitively coupled discharges

The analytical prediction of the presence of transient electric field regions between the bulk plasma and sheath edge in radio frequency capacitively coupled plasma (RF-CCP) discharges has been reported by Kaganovich [Phys. Rev. Lett. 89, 265006 (2002)]. In this paper, we have used the semi-infinite particle-in-cell (PIC) simulation technique to verify the theoretical prediction for the existence of transient electric field in the linear regime; it is shown that the PIC simulation results are in good agreement with the results predicted by analytical model in this regime. It is also demonstrated that the linear theory overestimates the transient electric field as one moves from linear to weakly nonlinear regime. The effect of applied RF current density and electron temperature on evolution of transition field and phase mixing regime has been explored.

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Experimental observation of standing wave effect in low-pressure very-high-frequency capacitive discharges

Radial uniformity measurements of plasma density were carried out by using a floating double probe in a cylindrical (21 cm in electrode diameter) capacitive discharge reactor driven over a wide range of frequencies (27–220 MHz). At low rf power, a multiple-node structure of standing wave effect was observed at 130 MHz. The secondary density peak caused by the standing wave effect became pronounced and shifts toward the axis as the driving frequency further to increase, indicative of a much more shortened standing-wave wavelength. With increasing rf power, the secondary density peak shift toward the radial edge, namely, the standing-wave wavelength was increased, in good qualitative agreement with the previous theory and simulation results. At higher pressures and high frequencies, the rf power was primarily deposited at the periphery of the electrode, due to the fact that the waves were strongly damped as they propagated from the discharge edge into the center.

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Experimental and numerical investigations of the phase-shift effect in capacitively coupled discharges

The phase-shift effect has been investigated by a Langmuir probe and a fluid model in Ar capacitively coupled plasmas at 50 mTorr. In the discharge, two sources with the same frequency, i.e., 27.12 MHz, are applied on the top and bottom electrodes simultaneously, and the phase shift between them varies from 0 to π. It is found that the electron density has an off-axis peak near the radial edge when the phase difference is equal to 0 due to the electrostatic edge effect, and the best radial uniformity is observed at a phase difference equal to π. Furthermore, when the voltage increases, the best radial uniformity is obtained at lower phase shift values. Moreover, the electron energy probability function has a bi-temperature structure at all the selected phase differences at r = 1–15 cm. The evolution of the plasma characteristics with the phase difference implies that the best radial uniformity can be obtained, by balancing the electrostatic edge effect and the phase shift effect.

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