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In this paper, the high-accuracy ion mobility coefficient based on the Chapman–Enskog approximation to the solution of the Boltzmann equation for low pressure radio frequency plasma discharges is presented. We employ two-dimensional fluid simulations of the argon filled axisymmetric reactor, where the effect of new ion-kinetics-based fluid closure is compared to theoretical expressions and experimental data. The spatial profiles of plasma composition in the low pressure radio frequency capacitively coupled plasma are presented, which includes the metastable reactions in the simulation. Moreover, inelastic collision integrals terms, due to charge exchange inelastic collisions between ions and neutral species, have been also considered. A Monte Carlo simulation of kinetic ion energy distribution of impinging on the radio frequency powered electrode provides a measure of accuracy of the new transport model. From our simulation, the results that mirror the influence of ion mobility coefficient obtained by the Chapman–Enskog method on plasma physical quantities under different pressures, frequencies, and electrode gaps is in good agreement with experimental measurement results and theoretical expressions. [ABSTRACT FROM AUTHOR]

A self-consistent method for computation and testing of transport coefficients in low pressure radio frequency plasma discharges is detailed by comparing the experimental fitting formula and previous results gained from the Langevin expression. In this paper, for the first time, we apply the Chapman–Enskog method for calculating transport coefficients of ions to a weakly ionized plasma which is laid in a thermodynamic non-equilibrium and chemical non-equilibrium state. The ion diffusion coefficient is obtained by using the Chapman–Enskog method expanded to the second order approximation. The corresponding ion mobility coefficient is deduced from Einstein's relation. A two-dimensional axisymmetric fluid model of capacitively coupled plasmas is employed to determine the plasma composition. Moreover, the comparison of plasma physical characteristics using ion transport coefficients calculated by the Chapman–Enskog method with those derived from theoretical and experimental methods is also investigated. The results show that the ion transport coefficients obtained by the Chapman–Enskog method and their effect on plasma physical quantities are in good agreement with the experimental measurement and theoretical expression. Furthermore, the results indicate that the set of exponential and Morse potentials is more reasonable for the ion–neutral particles' interaction. [ABSTRACT FROM AUTHOR]

In our relevant paper [Zhao S X (2021) Chin. Phys. B 30 055201], a delta distribution of negative ions is given by fluid simulation and preliminarily explained by decomposed anions transport equation. In the present work, first, the intrinsic connection between the electropositive plasma transport equation and spring oscillator dynamic equation is established. Inspired by this similarity, reformed "spring oscillator" equation with dispersing instead of restoring force that gives quasi-delta solution is devised according to the math embodied in the anion equation, which is of potential significance to the disciplines of atomic physics and astronomy as well. For solving the "diffusion confusion", the physics that determines the delta profile within the continuity equation is explored on the basis that recombination loss source term plays the role of drift flux, which is applicable for fluid model of low temperature plasma, but not the ordinary fluid dynamics. Besides, the math and physics revealed in this work predict that the ratio of recombination or attachment (for electrons) frequency versus the species diffusion coefficient is a very important parameter in determining the delta distribution, as it acts as the acceleration of object, according to the reformed oscillator equation. With this theory, the analogous delta profile of electrons density in the famous drift and ambi-polar diffusion heating mechanism of electronegative capacitively coupled plasma is interpreted. [ABSTRACT FROM AUTHOR]

One of the novel phenomena of Ar/O2 inductively coupled plasma, the delta negative ions density profile is discovered by the fluid simulation at very low electronegativity. The anions delta is found to be formed by the collaboration of successive plasma transport phases. The plasma transport itself is affected by the delta, exhibiting many new phenomena. A new type of Helmholtz equation is devised to mathematically explain the delta forming mechanism. For revealing the physics behind, a revised spring oscillator dynamic equation has been constructed according to the Helmholtz equation, in a relevant paper [Zhao S X and Li J Z (2021) Chin. Phys. B 30 055202]. The investigation about the anions delta distribution is a nice prediction of new phenomenon in low temperature electronegative plasmas, waiting for the validation of related experiments. [ABSTRACT FROM AUTHOR]

A two-dimensional fluid model was built to study the argon discharge in a capacitively coupled plasma reactor and the full set of Maxwell equations is included in the model to understand the electromagnetic effect in the capacitive discharge. Two electrical sources are applied to the top and bottom electrodes in our simulations and the phase-shift effect is focused on. We distinguish the difference of the phase-shift effect on the plasma uniformity in the traditional radio frequency discharge and in the very high frequency discharge where the standing wave effect dominates. It is found that in the discharges with frequency 13.56 MHz, the control of phase difference can less the influence of the electrostatic edge effect, and it gets the best radial uniformity of plasma density at the phase difference π. But in the very high frequency discharges, the standing wave effect plays an important role. The standing wave effect can be counteracted at the phase difference 0, and be enhanced at the phase difference π. The standing wave effect and the edge effect are balanced at some phase-shift value between 0 and π, which is determined by discharge parameters. [ABSTRACT FROM AUTHOR]

One self-consistent method combined with the electromagnetic theory and fluid model is developed to investigate the E-H mode transition of argon inductively coupled plasma (ICP) by adjusting the external electric parameters of the reactor. ICP dynamic characteristics of radial and axial space are also studied when E and H modes coexist. By regulating the radio-frequency current in the coil and voltage across the powered end of the coil and the ground, the E-H mode transition is observed, accompanied by the substantial variations in the electromagnetic field and plasma parameters (density, temperature, and deposited power). Besides, the evolution characteristics of ICP are examined when the discharge mechanism transforms from an E-mode dominated to an H-mode dominated. [ABSTRACT FROM AUTHOR]

Surface dielectric barrier discharge (SDBD), used as the plasma actuator for airflow control at atmospheric pressure, has been widely concerned over the past decades. In this work, four different electrode configurations, i.e., copper mesh, thin wire, blade, and aluminum foil, are chosen as exposed electrodes for the SDBD plasma actuator. The different effects of the four structures on the airflow acceleration behavior are experimentally investigated through the discharge current, surface potential distribution, ionic wind velocity, and mean thrust production. The result shows that the actuator with the copper mesh exposed electrode can generate the maximal induced force, while the actuator with the aluminum foil exposed electrode can generate the minimal induced force. This difference, as analyzed, is mainly due to the distinct discharge characteristics, i.e., different discharge asymmetry and surface potential, caused by the specifically designed exposed electrode configurations. This paper illustrates that the actuator with low surface potential has preferable mechanical performance. [ABSTRACT FROM PUBLISHER]

The E to H mode transitions are studied by a hairpin probe and optical emission spectroscopy in inductively coupled CF4 + Ar plasmas. Electron density, optical emission intensity of Ar, and the voltage and current are measured during the E to H mode transitions. It is found that the electron density and plasma emission intensity increase continuously at low pressure during the E to H mode transition, while they jump up discontinuously at high pressure. Meanwhile, the transition threshold power and ▵P (the power interval between E and H mode) increase by increasing the pressure. When the ratio of CF4 increases, the E to H mode transition happens at higher applied power, and meanwhile, the ▵P also significantly increases. Besides, the effects of CF4 gas ratio on the plasma properties and the circuit electrical properties in both pure E and H modes were also investigated. The electron density and plasma emission intensity both decrease upon increasing the ratio of CF4 at the two modes, due to the stronger electrons loss scheme. The applied voltages at E and H modes both increase as increasing the CF4 gas ratio, however the applied current at two modes behave just oppositely with the gas ratio. [ABSTRACT FROM AUTHOR]

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 FROM AUTHOR]

A Langmuir probe and an ICCD are employed to study the discharge mode transition in Ar inductively coupled plasma. Electron density and plasma emission intensity are measured during the E (capacitive discharge) to H (inductive discharge) mode transitions at different pressures. It is found that plasma exists with a low electron density and a weak emission intensity in the E mode, while it has a high electron density and a strong emission intensity in the H mode. Meanwhile, the plasma emission intensity spatial (2D image) profile is symmetrical in the H mode, but the 2D image is an asymmetric profile in the E mode. Moreover, the electron density and emission intensity jump up discontinuously at high pressure, but increase almost continuously at the E to H mode transition under low pressure. [ABSTRACT FROM AUTHOR]

A fluid model is self-consistently established to investigate the harmonic effects in an inductively coupled plasma, where the electromagnetic field is solved by the finite difference time domain technique. The spatiotemporal distribution of harmonic current density, harmonic potential, and other plasma quantities, such as radio frequency power deposition, plasma density, and electron temperature, have been investigated. Distinct differences in current density have been observed when calculated with and without Lorentz force, which indicates that the nonlinear Lorentz force plays an important role in the harmonic effects, especially at low frequencies. Moreover, the even harmonics are larger than the odd harmonics both in the current density and the potential. Finally, the dependence of various plasma quantities with and without the Lorentz force on various driving frequencies is also examined. It is shown that the deposited power density decreases and the depth of penetration increases slightly because of the Lorentz force. The electron density increases distinctly while the electron temperature remains almost the same when the Lorentz force is taken into account. [ABSTRACT FROM AUTHOR]

A two-dimensional self-consistent fluid model combined with the full set of Maxwell equations is developed to investigate an argon capacitively coupled plasma, focusing on the electromagnetic effects on the discharge characteristics at various discharge conditions. The results indicate that there exist distinct differences in plasma characteristics calculated with the so-called electrostatic model (i.e., without taking into account the electromagnetic effects) and the electromagnetic model (which includes the electromagnetic effects), especially at very high frequencies. Indeed, when the excitation source is in the high frequency regime and the electromagnetic effects are taken into account, the plasma density increases significantly and meanwhile the ionization rate evolves to a very different distribution when the electromagnetic effects are dominant. Furthermore, the dependence of the plasma characteristics on the voltage and pressure is also investigated, at constant frequency. It is observed that when the voltage is low, the difference between these two models becomes more obvious than at higher voltages. As the pressure increases, the plasma density profiles obtained from the electromagnetic model smoothly shift from edge-peaked over uniform to a broad maximum in the center. In addition, the edge effect becomes less pronounced with increasing frequency and pressure, and the skin effect rather than the standing-wave effect becomes dominant when the voltage is high. [ABSTRACT FROM AUTHOR]

An experimental investigation of the hysteresis during the E (capacitive coupling) and H mode (inductive coupling) transitions at various matching situation in argon inductively coupled plasma is reported. At high pressure, the results show two hysteresis loops involved the plasma density, applied power, and forward power, as well as the electrical parameters in the discharge circuit, when the series capacitance is cycled. The measured electron density versus applied power shows that the hysteresis loop shrinks with the decrease of the matching capacitance, and the same trend is discovered on the input current, voltage, and phase angle. In addition, for the case of small capacitance, the current (or voltage) jumps to a low value when the discharge passes through the E to H mode transition regime. Contrarily, for the case of large capacitance, the current jumps to a high value while the voltage is almost constant. The evolution characteristics of the plasma and circuit parameters observed imply that the nonlinear behavior of the matching situation may be one of the determined factors for hysteresis. [ABSTRACT FROM AUTHOR]

In order to include the nonlocal characteristics of electrons and investigate the inductively coupled plasma (ICP) resources more completely, we have developed a hybrid Monte Carlo (MC)/fluid hybrid model and calculated the axial and radial distributions of electron density, electron temperature, plasma potential, and electron energy distribution functions (EEDFs) of Ar discharge in a planar ICP. Furthermore, to make the model more practical, we still incorporate the effects of metastable atoms, whose sets of rate coefficients and density are, respectively, calculated through the electron MC part and fluid module. Besides, the corresponding Langmuir probe measurements are used to compare these data to validate the simulated results. Under all the selected discharge powers and pressures, the theoretically simulated and experimentally measured quantity profiles agree reasonably with each other, embodied in the generally identical magnitude ranges and spatial distributions. Furthermore, the interpretations about their detailed differences are given, which are based on the designs of both experimental schematic and model configuration. The analysis implements that the inclusions of electron-electron collision and a neutral density distribution into the hybrid model are likely to improve the comparison between the model predictions and experiment diagnostics. Furthermore, the evolution of plasma parameters and EEDFs with discharge conditions is discussed. [ABSTRACT FROM AUTHOR]

In this work, the behavior of electron temperature against the power in argon inductively coupled plasma is investigated by a fluid model. The model properly reproduces the non-monotonic variation of temperature with power observed in experiments. By means of a novel electron mean energy equation proposed for the first time in this article, this electron temperature behavior is interpreted. In the overall considered power range, the skin effect of radio frequency electric field results in localized deposited power density, responsible for an increase of electron temperature with power by means of one parameter defined as power density divided by electron density. At low powers, the rate fraction of multistep and Penning ionizations of metastables that consume electron energy two times significantly increases with power, which dominates over the skin effect and consequently leads to the decrease of temperature with power. In the middle power regime, a transition region of temperature is given by the competition between the ionizing effect of metastables and the skin effect of electric field. The power location where the temperature alters its trend moves to the low power end as increasing the pressure due to the lack of metastables. The non-monotonic curve of temperature is asymmetric at the short chamber due to the weak role of skin effect in increasing the temperature and tends symmetric when axially prolonging the chamber. Still, the validity of the fluid model in this prediction is estimated and the role of neutral gas heating is guessed. This finding is helpful for people understanding the different trends of temperature with power in the literature. [ABSTRACT FROM AUTHOR]

A new type of two-dimensional self-consistent fluid model that couples an equivalent circuit module is used to investigate the mode transition characteristics and hysteresis in hydrogen inductively coupled plasmas at different pressures, by varying the series capacitance of the matching box. The variations of the electron density, temperature, and the circuit electrical properties are presented. As cycling the matching capacitance, at high pressure both the discontinuity and hysteresis appear for the plasma parameters and the transferred impedances of both the inductive and capacitive discharge components, while at low pressure only the discontinuity is seen. The simulations predict that the sheath plays a determinative role on the presence of discontinuity and hysteresis at high pressure, by influencing the inductive coupling efficiency of applied power. Moreover, the values of the plasma transferred impedances at different pressures are compared, and the larger plasma inductance at low pressure due to less collision frequency, as analyzed, is the reason why the hysteresis is not seen at low pressure, even with a wider sheath. Besides, the behaviors of the coil voltage and current parameters during the mode transitions are investigated. They both increase (decrease) at the E to H (H to E) mode transition, indicating an improved (worsened) inductive power coupling efficiency. [ABSTRACT FROM AUTHOR]

The inflexion point of electron density and effective electron temperature curves versus radio-frequency (RF) bias voltage is observed in the H mode of inductively coupled plasmas (ICPs). The electron energy probability function (EEPF) evolves first from a Maxwellian to a Druyvesteyn-like distribution, and then to a Maxwellian distribution again as the RF bias voltage increases. This can be explained by the interaction of two distinct bias-induced mechanisms, that is: bias-induced electron heating and bias-induced ion acceleration loss and the decrease of the effective discharge volume due to the sheath expansion. Furthermore, the trend of electron density is verified by a fluid model combined with a sheath module. [ABSTRACT FROM AUTHOR]

Both geometrical and electrical asymmetry effects in capacitive argon discharges are investigated using a two-dimensional particle-in-cell coupled with Monte Carlo collision model. When changing the ratio of the top and bottom electrode surface areas and the phase shift between the two applied harmonics, the induced self-bias was found to develop separately. By adjusting the ratio between the high and low harmonic amplitudes, the electrical asymmetry effect at a fixed phase shift can be substantially optimized. However, the self-bias caused by the geometrical asymmetry hardly changed. Moreover, the separate control of these two asymmetry effects can also be demonstrated from their power absorption profiles. Both the axial and radial plasma density distributions can be modulated by the electrical asymmetry effect. [ABSTRACT FROM AUTHOR]