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The surface charging effect of positive ions at the trench bottom during the etching of dielectric materials has become a severe problem with the shrinkage of electronic feature dimensions. Pulsed plasmas have been widely used to overcome surface charging issues during plasma etching in industry. In this work, synchronized dual-level radio frequency pulsed modulation on capacitively coupled plasmas is investigated based on 1D3V particle-in-cell/Monte Carlo collision simulations. It is found that the plasma always remains a certain initial density during the dual-level pulse modulation, as the high frequency (HF) source still presents during pulse off time (with a reduced voltage amplitude), which may facilitate high processing efficiency. Meanwhile, many HF sheath oscillations are simulated at the initial stage of a pulse period, which induces vast high energy electrons to strike the electrode. When the HF voltage is maintained at a very low value during the pulse off (i.e. 0.1 V HF ), more electrons with higher energy bombard the bottom of the trench, effectively alleviating the charging effect. Furthermore, the nonlinear behavior of sheath oscillations is proved to be very sensitive to dual-frequency voltage amplitudes and pulse ramp-up times.

In this work, the electron power absorption mode transition in capacitively coupled Ar/CF4 discharges is investigated by using a one-dimensional fluid/electron Monte Carlo hybrid model. Different electron power absorption modes are observed under various external discharge conditions, which could be explained by examining the contribution of bulk electrons and secondary electrons respectively. The results indicate that as the gap increases, the electron power absorption mode changes from the drift-ambipolar (DA) mode to a α-γ-DA hybrid mode. This is ascribed to the enhanced ionization process of secondary electrons due to their sufficient collisions when the discharge region expands, as well as the weakened drift and ambipolar electric fields. By increasing the secondary electron emission coefficient, the number density of secondary electrons grows, and thus the discharge experiences a transition from a α-DA hybrid mode over a α-γ-DA hybrid mode and finally into the γ mode. Moreover, when the proportion of CF4 increases, the discharge tends to be more electronegative. As a consequence, the discharge gradually transits from a α-γ hybrid mode over a α-γ-DA hybrid mode, and finally to the DA mode. The results obtained in this work are important for improving the high aspect ratio etching process by secondary electrons.

A hybrid model, which consists of a fluid module, a sheath module and an ion Monte Carlo module, is employed to investigate the dependence of ion energy and angular distributions (IEDs and IADs) on the inductively coupled plasma (ICP) power, pressure, gas ratio, bias power and bias frequency in Ar/O2 discharges. The results indicate that the bimodal distribution appears as bias power increases or bias frequency decreases. Moreover, the low and high energy peaks of IEDs move to higher energy with the rise of bias power and O2 content. Whereas, an opposite tendency is observed with the increase of ICP power and pressure. For IADs, it is clear that a larger percentage of ions incident on the electrode have a smaller deflection angle by increasing bias power or decreasing pressure, and a similar evolution is observed with the decline of bias frequency. Besides, the better collimation of ions is obtained at larger O2 concentration, but ICP power only has little influence on IADs. In order to validate the model, a comparison between the simulated IEDs and those measured by a retarding field energy analyzer has been done, and shows a good agreement. The results obtained in this work could help us to gain more insight into the dependence of IEDs and IADs on the discharge parameters, which is of significant importance in the improvement of the etching rate and anisotropy.

Asymmetrically excited, high frequency cylindrical capacitive discharges are widely used for materials etching and thin film deposition. Two-dimensional (2D) electrostatic particle-in-cell (PIC) simulations show the existence of standing waves and wave-induced hysteresis of the plasma density, i.e. two different steady states for the same driving rf voltage amplitude, when the voltage is increased from a low value or decreased from a high value. The phenomenon is explored over a range of pressures (10–30 mTorr) and frequencies (60–80 MHz). Examined at 73 MHz, with increasing gas pressure, the hysteresis loop gradually shrinks and vanishes. To understand the hysteresis induced by z-symmetric and z-antisymmetric radial wave propagation modes, the PIC results are compared with a nonlinear transmission line model assuming uniform bulk plasma density, to determine the symmetric and antisymmetric voltage amplitudes. The model results are in good agreement with the PIC observations, showing central-low and central-high profiles of the antisymmetric mode voltage at low density and high density, respectively. The results are then used to determine the parameters of a lumped circuit model of the two modes, from which the hysteresis is induced by the density dependence of the symmetric and anti-symmetric wave mode absorbed electron powers. For the low density state, the discharge is sustained mainly by the symmetric mode excitation. At high density, the discharge is sustained by both symmetric and anti-symmetric modes, with the latter partly showing a spatial resonance. The results are also shown to be frequency dependent, with an onset of the hysteresis at about 66 MHz.

Improving plasma uniformity during plasma processing in the microelectronics industry is of critical importance to the quality of etching or deposition. Compared to continuous wave (CW) plasmas, pulsed plasmas have drawn much attention with the introduction of additional pulse parameters, which would be helpful to improve the plasma properties. In this paper, a two-dimensional fluid model is developed to investigate a pulsed radio-frequency capacitively coupled plasma (CCP) sustained in SiH4/N2/O2 mixture at fixed operating conditions of 70V rf power, 300 mTorr (40 Pa) gas pressure and an SiH4/N2/O2 gas ratio of 2.5/92.5/5. First, we study the temporal dynamics of densities of the electron, positive ion and negative ion, at different positions in the pulsed CCP. Under the operation conditions, charged particles, instead of neutral particles, may basically respond to the applied modulated power. The electron density in the bulk could approach a quasi-steady value by the end of the activeglow. However, the achievement of a quasi-steady state of plasma like that in the CW condition not only depends on enough activeglow time of the pulse discharge but also relies on the observed position in the discharge. In addition, we investigate the impact of pulse parameters on plasma characteristics, showing that the radial inhomogeneity of plasma caused by the edge effect can be effectively suppressed by controlling the duty cycle (DC) rather than the pulse repetition frequency (PRF). Improvement of the plasma uniformity in pulsed discharge is due to the competition between the edge effects during the activeglow and diffusion of charged species during the afterglow. Moreover, the electron density undergoes a local minimum value in the temporal profile before it rises sharply beyond that of CW discharge, since production of electrons is less than loss by the spatial movement at the very beginning of one pulse. Also, there appears to be a peak value of ion bombardment energy at the beginning of power, which may damage the wafer in actual industrial processes. At a certain DC, this peak may be flattened to a certain degree by adjusting the PRF.

Ion energy distributions (IEDs) of Ar+ and bombarding the grounded electrode are measured by an energy resolved quadrupole mass spectrometer in a dual-frequency capacitively coupled plasma (DF-CCP) operated in a gas mixture of Ar and O2 (90%/10%). The effects of external discharge parameters, such as the frequency and power of the low frequency (LF) source and the gas pressure, on the IEDs are investigated in detail. With the increase in the LF power, the high-energy peak shifts towards the high-energy region and the energy width ΔE between high- and low-energy peaks in the IEDs also increases. However, the increase in the LF frequency leads to the shift of the high-energy peak towards the low-energy region as well as a narrow energy width ΔE. The increase in the gas pressure results in the bimodal structure being unobvious because of intensive momentum transfer and charge exchange collisions between ions and background molecules. In addition, the distinctions between Ar+ and IEDs are also discussed. Finally, some experimental results are compared with numerical ones obtained from the particle-in-cell/Monte Carlo (PIC/MC) method and both results are in general agreement.

A two-dimensional self-consistent fluid model combined with the full set of Maxwell equations is employed to investigate an Ar/CF4 capacitively coupled plasma, focusing on the phase-shift effect on the plasma characteristics at various frequencies and gas mixture ratios. When the discharge is sustained by a single frequency at 13.56 MHz in an Ar/CF4 mixture with a ratio of 0.9/0.1, no obvious difference is detected between the electron densities obtained in the so-called electrostatic model (with only the static electric fields taken into account) and the electromagnetic model (which includes the electromagnetic effects). However, as the frequency increases to 60 and 100 MHz, the difference becomes distinct, due to the significant influence of the electromagnetic effects. The phase-shift effect on the plasma radial uniformity has also been investigated in a dual frequency discharge, i.e. when the top driven source is switched on with a phase difference φ ranging from 0 to π, in the frequency range 13.56–100 MHz. At low concentration of CF4 (10%), Ar+ ions are the major positive ions in the entire range of frequencies. When the frequency is low, i.e. 13.56 MHz, the Ar+ density exhibits an off-axis peak at φ = 0 due to the edge effect, and a better uniformity caused by the phase-shift modulation is obtained at φ = π. At 60 MHz, the Ar+ density varies from edge-peaked at φ = 0 to uniform (i.e. at φ = 0.53π), and finally at φ = π, a broad maximum is observed at the centre due to the standing-wave effect. As the frequency increases to 100 MHz, the best radial uniformity is reached at 0.25π, and the maximum moves again towards the radial wall in the reverse-phase case (φ = π) due to the dominant skin effect. When the frequency is fixed at 100 MHz, the phase-shift control shows a different behaviour at a high concentration of CF4. For instance, the density profiles shift from edge-high over uniform to centre-high, as the CF4 content increases from 10% to 90%, which indicates that the skin effect is suppressed by the high electronegativity of the Ar/CF4 = 0.1/0.9 mixture. Moreover, the ratio of the total negative ion density to electron density decreases with increasing frequency, and it increases with CF4 content. In addition, ions become the major positive ions in the discharge with 90% CF4.

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.

A two-dimensional fluid model, including the full set of Maxwell equations, has been developed and applied to investigate the effect of a phase shift between two power sources on the radial uniformity of several plasma characteristics in a hydrogen capacitively coupled plasma. This study was carried out at various frequencies in the range 13.56–200 MHz. When the frequency is low, at 13.56 MHz, the plasma density is characterized by an off-axis peak when both power sources are in-phase (φ = 0), and the best radial uniformity is obtained at φ = π. This trend can be explained because the radial nonuniformity caused by the electrostatic edge effect can be effectively suppressed by the phase-shift effect at a phase difference equal to π. When the frequency rises to 60 MHz, the plasma density profiles shift smoothly from edge-peaked over uniform to centre-peaked as the phase difference increases, due to the pronounced standing-wave effect, and the best radial uniformity is reached at φ = 0.3π. At a frequency of 100 MHz, a similar behaviour is observed, except that the maximum of the plasma density moves again towards the radial edge at the reverse-phase case (φ = π), because of the dominant skin effect. When the frequency is 200 MHz, the bulk plasma density increases significantly with increasing phase-shift values, and a better uniformity is obtained at φ = 0.4π. This is because the density in the centre increases faster than at the radial edge as the phase difference rises, due to the increasing power deposition P z in the centre and the decreasing power density P r at the radial edge. As the phase difference increases to π, the maximum near the radial edge becomes obvious again. This is because the skin effect has a predominant influence on the plasma density under this condition, resulting in a high density at the radial edge. Moreover, the axial ion flux increases monotonically with phase difference, and exhibits similar profiles to the plasma density. The calculation results illustrate that the radial uniformity of the various plasma characteristics is strongly dependent on the applied frequency and the phase shift between both power sources, which is important to realize, for controlling the uniformity of the plasma etch and deposition processes.

A two-dimensional self-consistent fluid model coupled with the full set of Maxwell equations is established to investigate the phase-shift effect on the transient behaviour of electrodynamics and power deposition in a hydrogen capacitively coupled plasma. The effect has been examined at 13.56 MHz and 100 MHz, respectively, because of the different phase-shift modulation when the electromagnetic effects are dominant. The results indicate that the spatiotemporal distributions of the plasma characteristics obtained for various phase-shift cases are obviously different both in shape and especially in absolute values. Indeed, when the phase difference varies from 0 to π, there is an increase in the electron flux, thus the power deposition becomes more pronounced. At the frequency of 13.56 MHz, the axial electron flux in the bulk plasma becomes uniform along the z-axis, and the radial electron flux exhibits two peaks within one period at the reverse-phase case, whereas the oscillation is less pronounced at the in-phase case. Furthermore, in the very high frequency discharge, the radial electron flux is alternately positive and negative with four peaks during one period, and the ionization mainly occurs in the sheath region, due to the prominent power deposition there at a phase difference equal to π.

By using an improved hybrid Monte Carlo/fluid model with the metastable solver and power deposition scheme, we investigate the dynamic characteristics of metastable atoms and their influences on plasma conditions during mode transition, and moreover explore its role in hysteresis by searching the nonlinear mechanism. The evolution behaviours of metastable atoms with power deposition at different pressures are traced. Besides, the effects of metastable atoms and multistep ionization on the variation of plasma parameters, e.g. electron density, temperature and energy distribution function, etc, during the transition are systematically examined. When cycling the inputted electrical parameters, coil current and voltages, hysteresis does not appear. The basic characteristic of plasma dynamics during mode transition is not significantly influenced by the presence of metastable atoms. Moreover, a linearly increasing slope of plasma density with the deposited power is observed and no evidence of nonlinear mechanisms is detected.

Industrial inductively coupled plasma (ICP) sources are always operated in low gas pressure 10–100 mTorr, therefore in order to accurately investigate the mode transition of ICP, we developed our pure fluid model (2009 J. Appl. Phys. 105 083306) into a hybrid fluid/Monte Carlo (MC) model, where the MC part is exploited to take in more dynamic characteristics of electrons and self-consistently calculate the rate coefficients and electron temperature used in the fluid module, and more crucially to study the electron energy distribution function (EEDF) evolution with mode transition. Due to the introduction of the nonlocal property of the electrons at relatively low pressures, the dependences of the plasma density on the coil current, including the mode transitions, are distinctly different at low and high pressures when simulated by this improved hybrid model (HM), while the trends for different pressures obtained from the original pure fluid model (PFM) are the same in all cases. Furthermore, the computed peaks of the electron density profile by the HM shift from the discharge centre in the E mode to the intense inductive field heating area (about half of the radius of the reaction chamber under the dielectric window) in H mode. In addition, the electron temperature profiles of two modes under different pressures simulated by HM are totally higher than the results of PFM. When the pressure is low, there is a minimum exhibited in the bulk plasma of the electron temperature profiles of the E mode, and along with the mode transition the distribution area of low temperature is substantially reduced. Moreover, this phenomenon disappears when the gas pressure is increased. Accompanied by this, the calculated EEDF of the E mode in the low pressure also demonstrates an absolutely dominant low energy electron fraction (about ≤5 eV); while transforming to the H discharge most of the electrons carry an energy of 1–10 eV. The tendencies of the calculated EEDF evolution with mode transition under relatively high pressures agree well with the experimental measurements of EEDF of Lee et al (2009 Appl. Phys. Lett. 90 191502), but the determination mechanisms are still in dispute and require further examination.

Gap length effects on the properties of capacitively coupled plasmas at low pressures are investigated with particle-in-cell/Monte Carlo simulations. A hysteresis, or two different steady states under the same parameters, in argon gas is observed for the first time. Simulation results show that the hysteresis may be a consequence of different energy diffusion coefficients. At smaller gaps, electron energy probability functions will have much higher energy tails, and the average electron energy loss to the electrodes will increase significantly. These imply the electrons are possibly heated by the resonance heating mechanism and therefore electron energy probability functions are anisotropic.

Stable kilohertz spark discharges with a unique waveform of discharge current were studied for high-efficiency conversion of methane to hydrogen and acetylene at atmospheric pressure for the first time. Discharge stability was confirmed by the concentration variation in the product streams with 220 min discharge time using pure methane as the feed gas. Utilizing the stable kilohertz spark discharges, the hydrogen concentration in the product stream could be as high as 72.1 vol% at an energy cost of 6.7 eV per H2 molecule produced and 81.5% of methane conversion. The acetylene concentration could reach 18.4 vol% at an energy cost of 21.2 eV per C2H2 molecule produced and 70.3% of methane conversion. For methane conversion ranging from 51.9% to 81.5%, the energy costs were 6.6‐10.7 eV per CH4 molecule converted, 4.4‐6.7 eV per H2 molecule produced and 16.9‐27.6 eV per C2H2 molecule produced. This study showed the high-concentration production of COx-free hydrogen and acetylene from methane at a low energy cost by stable kilohertz spark discharges. (Some figures in this article are in colour only in the electronic version)