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In the past three decades, first principles-based fully kinetic Particle-in-Cell Monte Carlo collision (PIC/MCC) simulations have been proven to be an important tool for the understanding of the physics of low pressure capacitive discharges. However, there is a long-standing issue that the plasma density determined by PIC/MCC simulations shows quantitative deviations from experimental measurements, even in argon discharges, indicating that certain physics may be missing in previous modelling the low pressure rf driven capacitive discharges. In this work, we report that the energetic electron-induced secondary electron emission and excited state atoms play an important role in low pressure rf capacitive argon plasma discharges. The ion-induced secondary electrons are accelerated by the high sheath field to strike the opposite electrode and produce a considerable number of secondary electrons that produce additional ionizing impacts and further increase the plasma density. Importantly, the presence of excited state species even further enhances the plasma density via excited state neutral and resonant state photon-induced secondary electron emission on the electrode surface. The PIC/MCC simulation results show good agreement with the recent experimental measurements in the low pressure range (1-10Pa) that is commonly used in the etching semiconductor industry. At the highest pressure (20Pa) and driving voltage amplitudes 250 and 350V explored here, the plasma densities from PIC/MCC simulations considering excited state neutrals and resonant photon-induced secondary electron emission are quantitatively higher than the experiments, requiring further investigation on high pressure discharges.

This article briefly reviews the theory and modeling of single-surface multipactor discharge on a dielectric, focusing on recent studies on two-frequency RF-field-induced multipactor. A novel multiparticle Monte Carlo simulation model with adaptive time steps is used to investigate the time-dependent physics of multipactor discharge. Two-frequency RF operation is found to be effective in reducing multipactor strength compared with single-frequency RF operation with the same total RF power. Strong multipactor mitigation is also demonstrated for nonsinusoidal RF fields of multiple frequencies. Migration of multipactor trajectory is shown for different configurations of the two-frequency RF field. Frequency-domain analysis shows that multipactor-induced normal surface charging electric field consists of only even harmonics of the RF frequency for single-frequency RF operation, but is dominated by strong intermodulation products of the RF carrier frequencies for two-frequency RF operation.

While the particle-in-cell (PIC) method is quite mature, verification and validation of both newly developed methods and individual codes has largely focused on an idiosyncratic choice of a few test cases. Many of these test cases involve either one- or two-dimensional simulations. This is either due to availability of (quasi) analytic solutions or historical reasons. Additionally, tests often focus on investigation of particular physics problems, such as particle emission or collisions, and do not necessarily study the combined impact of the suite of algorithms necessary for a full featured PIC code. As three dimensional (3D) codes become the norm, there is a lack of benchmarks test that can establish the validity of these codes; existing papers either do not delve into the details of the numerical experiment or provide other measurable numeric metrics (such as noise) that are outcomes of the simulation. This paper seeks to provide several test cases that can be used for validation and bench-marking of particle in cell codes in 3D. We focus on examples that are collisionless, and can be run with a reasonable amount of computational power. Four test cases are presented in significant detail; these include, basic particle motion, beam expansion, adiabatic expansion of plasma, and two stream instability. All presented cases are compared either against existing analytical data or other codes. We anticipate that these cases should help fill the void of bench-marking and validation problems and help the development of new particle in cell codes.

Multipactor, a sustained electron avalanche driven by radiofrequency (RF), has been extensively studied due to its importance in all RF vacuum electronic devices. In particular, much effort has been made in understanding the phenomenon to mitigate it in real systems. On the other hand, some have used what is often seen as a disastrous effect for benefit. In this article, we study a novel way of using multipactor discharges for harmonic generation. We take advantage of the intrinsic phase-focusing mechanism of multipactor as a natural charge-bunching mechanism. The theory along with some validating test cases will be presented. Potential (beneficial) applications and ramifications of this phenomenon will be briefly discussed.

This article presents the frequency-domain analysis of multipactor discharge on a single dielectric surface. We employ the multiparticle Monte Carlo simulation model in one dimension with adaptive time steps to obtain the temporal profiles of the normal electric field, which is due to surface charging that corresponds to the multipactor strength, induced by single- or dual-tone radio frequency (RF) electric fields acting parallel to the surface. We apply a discrete Fourier transform (DFT) to obtain the amplitude spectrum of the normal electric fields. It is found that for the single-tone RF operation, the normal electric field consists of pronounced even harmonics of the driving RF frequency. The strength of a harmonic component in the normal electric field depends on its frequency and the incident RF amplitude. An empirical relation between the strength and frequency of the harmonics and the input RF amplitude has been proposed. For dual-tone RF operation, spectral peaks are observed in the amplitude spectrum of the normal electric field at various frequencies of intermodulation product of the RF carrier frequencies. Pronounced peaks are observed at the sum and difference frequencies of the carrier frequencies, at multiples of those frequencies, and at multiples of the carrier frequencies. Empirical relations between the heights of different spectral peaks and the input RF amplitudes have been proposed.

In this Letter, the novel physics of higher harmonic (HH) generation of the normal electric field near a dielectric surface is reported in multipactor induced plasma ionization breakdown, as determined by kinetic particle-in-cell simulations. The observed HH frequency is around ten times the fundamental rf driving frequency, but lower than the electron plasma frequency. A theory is constructed which indicates that stream plasma interaction-induced instability is the mechanism of HH generation in the collisional regime. The HH frequency and its corresponding growth rate of the HH oscillation amplitude from the theory are in good agreement with kinetic particle-in-cell simulations.

Multipactor is a nonlinear AC discharge phenomenon occurring in RF systems and system components in which a high frequency RF field creates an electron avalanche sustained through secondary electron emission [1] from metallic or dielectric surfaces. This work presents a study of two-surface multipactor discharge induced by two-frequency RF fields. We employ Monte Carlo simulations [2] , [3] and Computer Simulation Technology (CST) [4] to examine the effects of the relative strength and phase of the second carrier mode on multipactor susceptibility and time dependent physics [3] .

In this work, we characterize the formation and transition behaviors of a microplasma around a microstructured surface at different gas pressures via two-dimensional particle-in-cell/Monte Carlo collision simulations. It is found that the microdischarge occurs outside the cathode microcavities at the lowest pressure and starts penetrating the microcavities with a curved sheath edge as the pressure increases. At higher pressure, coupled periodic microhollow cathode discharges (MHCDs) are formed inside the microcavities. Further increasing the gas pressure results in the disappearance of the MHCDs, and the dominant discharge shifts outside of the microcavity, locating above the protrusion tips. The effect of the space charge shielding on the discharge and the conditions for MHCD formation are discussed. The macroscopic discharge parameters versus the gas pressure and the electron energy distributions are examined. The results are helpful for better understanding the microplasma formation around nonplanar electrode surface in microgaps, which inform the scaling, design, and optimization of microplasma array devices across a wide range of gas pressure regimes.

Multipactor is a resonant RF discharge of secondary electrons from metal or dielectric surfaces. In the right conditions, this electron avalanche is a catastrophic process that can distort the original signal in the transmission line 1 , produce unwanted localized heating, and even destroy the system on hand. As a result, particular attention has been dedicated to understanding this phenomenon in order to avoid or, if inevitable, suppress it or predict its effects 2 .

Multipactor discharges are widely observed in rf accelerators, high power microwave transmission and space-based communication systems [1] - [2] . Understanding the fundamental physics of the transit multipactor and ionization breakdown is important. In this work, a novel multilayer-structured discharge (MSD) is reported in multipactor-coexisting plasma ionization breakdown by fully kinetic particle-in-cell (PIC) simulations [3] - [7] . The observed multilayer structure is originated by the response of ions to the electric field. It is found that the electron diffusion and multipactor discharge near the surface produce two electric fields in opposite directions towards and away from the dielectric surface, respectively. Thus, ions are gathered to form a locally high density profile, which is followed by the electron density. Furthermore, the relatively stronger restoring field induced by the multipactor discharge drives the ions away from the surface, and the locally high electron density diffuses away from the surface, resulting in a local electric field also away from the surface, which drives the ion density peak to propagate towards the bulk plasma. Such a process is periodically repeated, and finally, a MSD is formed, and propagate into bulk region.

Multipactor 1 is a vacuum discharge caused by secondary electron avalanche within powerful microwave devices for manifold radio-frequency applications. Especially for the aerospace community, multipactor discharge is commonly thought as the primary failure mode of the spaceborne microwave devices. Due to the produced electron cloud, multipactor may generate unexpected harmonics, increase the system noise, and even engender irreversible instrument damage when the surface outgassing further provokes more dangerous gaseous discharge 2 .

Particle-in-cell Monte Carlo collision (PIC/MCC) simulations are important for understanding low pressure low-temperature discharge dynamics, since no assumptions are needed to determine the electron energy distribution function. Benchmark work is needed to build a solid base in the correctness of PIC/MCC codes. In this work, the basic object-oriented plasma device PIC/MCC code (oopd1-v1) is strictly benchmarked against the well-established xpdp1 code over a wide range of pressures (0.03 - 15 Torr), and varying size of the blocking capacitor in the external circuit (5 – 10 5 nF). An excellent agreement between codes is obtained. By upgrading oopd1-v1, incorporating excited argon atoms, metastable and radiative Ar m , Ar r , and Ar(4p), their role in rf capacitive discharges, especially in the collisional regime, was explored. It is found that the presence of the metastable atoms Ar m enhances the plasma density by a factor of 3 - 5 at 1.6 Torr and even higher at pressure up to 5 Torr. The proportion of metastable pooling ionization and step-wise ionization as an ionization source increases with increasing pressure and becomes more important than direct electronneutral ionization at 5 – 15 Torr. Also. as the pressure is increased the ionization occurs near the plasma-sheath interfaces, with little ionization within the plasma bulk region.

Meeks’ criterion established a relationship between the fields around space charges in an electron avalanche and enabled prediction of the breakdown voltage across a gap given its distance and surrounding gas pressure. This criterion is reevaluated in this study for atmospheric pressure with a non-uniform electric field distribution where voltage up to 30 kV is applied to a ring-to-plate electrode configuration. The ring electrode is made of a stainless-steel needle with an inner diameter of 0.25 mm and an outer diameter of 0.51 mm, and is vertically placed above a copper grounding plate for various gap distances ranging from 1 to 14 mm. The breakdown voltage vs. gap distance and the V-I characteristics are obtained for both cathode-directed and anode-directed streamer discharges. The experimental results are found to be in good agreement with analytical predictions based on Meek’s criteria for self-propagating streamer accounting for a non-uniform electric field distribution across the gap. The results are also compared with Paschen’s law. Emergent behavior such as the negative polarity producing breakdown at progressively higher voltage than the positive polarity at gap distances greater than 6mm is discussed. This analysis concludes that Meeks’ criteria held throughout our results, overall, and offers suggestions for further refinements to related models and experiments.

This paper summarizes our recent studies on a gas breakdown in microgaps with a surface protrusion on the electrode with more detailed information. The breakdown voltages are quantified when the discharge enters into the subnormal glow region with negative differential resistance, using a 2-D fluid model. The breakdown characteristics are evaluated with the effects of the protrusion geometries, such as protrusion size and aspect ratio, as well as the discharge polarity. It is found that in an atmospheric-pressure microgap, the protrusion size has a more profound effect on the breakdown voltage than its aspect ratio, which is due to the competition between the current density enhancement and the effective cathode emission area. As gas pressure varies, the surface protrusion on the electrode results in a combined Paschen’s curve, which transits from long-gap behavior at low pressure to short-gap behavior at high pressure. The key parameters on the breakdown characteristics with the surface protrusion are elucidated.

Multipactor discharge near an rf window is a key limiting factor in high power microwave systems. In this work, we report special features of dielectric multipactor susceptibility under a Gaussian-type waveform as a function of the rf power density of the transverse rf electric field ([Formula: see text]) and normal restoring field ([Formula: see text]) via particle-in-cell (PIC) and multiple particle Monte Carlo (MC) simulations. The MC simulations show that, for a Gaussian waveform of a half peak width ([Formula: see text]), larger than [Formula: see text] with T = 1 ns the rf repetition period, the susceptibility boundary is similar to that of the conventional sinusoidal waveform-driven multipactor, i.e., two inclined lines in the plane of ([Formula: see text]). However, by decreasing [Formula: see text], the susceptibility boundary converts to be a closed curve at [Formula: see text] in the plane of ([Formula: see text]) and further shrinks at [Formula: see text]. PIC simulations with a self-consistent surface and space charge effects also show a reduced [Formula: see text] with increasing [Formula: see text] when [Formula: see text] exceeds a critical value, resulting in a closed curve in the plane of ([Formula: see text]), and the maximum time-averaged [Formula: see text] (multipactor strength) also decreases significantly with further decreasing [Formula: see text] in agreement with MC simulations. Accordingly, the fraction of the rf power density absorbed by the multipactor discharges also decreases nonlinearly with [Formula: see text] from the order of [Formula: see text] to [Formula: see text] (even [Formula: see text]), implying a significant improvement compared to the conventional sinusoidal waveform. The simulations also show that the multipactor susceptibility under a transverse Gaussian-type waveform for different frequencies follows the same scaling law in terms of the ratio of the electric field to the rf repetition rate.

In this work, we comprehensively investigate the generation of higher harmonic (HH) electric fields normal to the applied rf electric field in multipactor-coexisting plasma breakdown by fully kinetic particle-in-cell (PIC) simulations and a theoretical model. Firstly, a base case at driving frequency 1 GHz, transverse rf electric field amplitude 3 MV m−1, and background gas pressure 0.2 Torr, is studied in detail. The enhanced harmonic frequency observed is around ten times the fundamental rf frequency, significantly lower than the Langmuir frequency. A theoretical model reveals that the fundamental mechanism of HHs generation is stream–plasma instability, which originates from stream-like secondary electron emission interacting with plasma. The resulting HH frequency and the growth rate of its oscillating amplitude from the theoretical model, agree well with the PIC simulations. With increasing pressure, the HH oscillations are found to be significantly reduced. This is because at higher pressure the gas ionization rate is higher, which causes a more rapidly increasing plasma density, leaving less time for the growth of instability. Furthermore, the parameter space in terms of background gas pressure and rf field amplitude within which the HHs appear is revealed. Finally, the effect of the driving rf frequency on HHs is also investigated, and it is found that the instability-induced oscillating HHs field remains when the driving frequency is increased to 2 GHz, however, it is highly reduced at higher driving frequency of 5 GHz, as oscillations at the fundamental frequency start playing a more important role.

We generalize similarity theory based on the scaling and solution invariance of the Boltzmann equation, coupled with the Poisson equation, and demonstrate similarity laws for radio-frequency (rf) discharge plasmas across three nonlinear transitional regimes, namely, the alpha-gamma mode transition, the stochastic-Ohmic-heating mode transition, and the bounce-resonance-heating mode transition. Fundamental plasma parameters, e.g., the electron power absorption, under similar discharge conditions are examined via fully kinetic particle-in-cell simulations, and electron-kinetic invariance is exemplified in similar rf discharge plasmas. The results unambiguously confirm the applicability of similarity laws for rf plasmas in extended operating regimes, and strengthen the foundations and framework of similarity physics with universality.

This work presents the frequency domain analysis of multipactor discharge on a dielectric surface with rf electric fields of single or two carrier frequencies, by using a one-dimensional multiparticle Monte Carlo (MC) simulator with adaptive time steps. The study shows that the single tone rf operation produces a normal electric field to the dielectric surface consisting of pronounced even harmonics of the driving rf frequency. The strength of a harmonic component is a function of the incident rf amplitude. For dual tone operation, the amplitude spectrum of the normal electric field reveals spectral peaks at various frequencies of intermodulation products of the rf carrier frequencies. Empirical equations are proposed to approximate the temporal profiles of the normal electric field in terms of its frequency components, for rf operation with either single or two carrier frequencies.

Multipactor is a resonant AC discharge of secondary electrons driven by RF signals and has been a center point of current interest because of its detrimental effects in space satellite communications. Much effort has been placed in mitigating/suppressing or determining the onset of multipactor. However, not much attention has been directed to the effects of multipactor, should it occur, on the quality of the original signal. In this paper, we will look at different types of multipactor (single-surface and two-surface) and how they may affect a signal (single-tone and dual-tone) in planar and coaxial transmission line systems with impedance mismatches. I-Q plots that characterize the multipactor effects will also be presented.

This work investigates the time-dependent physics of multipactor discharge on a single dielectric surface with a transverse rf electric field of two carrier frequencies using a multiparticle Monte Carlo simulation model with adaptive time steps. The effects of the relative strength and phase, and the frequency separation between the two carriers are studied. Closed Lissajous curves are obtained to describe the relationship between the rf electric field parallel to the surface and the normal surface charging field in the ac saturation state. It is found that two-frequency operation can reduce the multipactor strength compared to single-frequency operation with the same total rf power, though the effect of the frequency separation is not prominent on multipactor susceptibility. Formation of beat waves is observed in the temporal profiles of the normal electric field due to surface charging with a noninteger frequency ratio between the two carrier modes. Phase space evolution of multipactor electrons is examined, revealing a periodic bunching and debunching of electrons in the surface normal direction, but a gradual debunching effect in the direction tangential to the dielectric surface. Migration of the multipactor trajectory is also demonstrated for different configurations of the two-frequency rf fields.

Similarity laws (SL) are essential for correlating the characteristics of plasmas at different dimensional scales, which have been validated for radio frequency (rf) discharges at low pressure but under limited conditions. In this work, we evaluate the effects of nonlinear collisions (e.g. stepwise ionization) on the similarity properties in capacitive rf discharges in argon across a wide range of pressure regimes via fully kinetic particle-in-cell simulations. The SL scalings of fundamental discharge parameters, e.g. the electron power absorption and electron energy probability function, are examined with and without nonlinear collisions, respectively. Without the nonlinear collisions, the similarity scalings are found to be rigorously valid. When the nonlinear collisions are considered, the similarity properties in rf discharges still exist approximately, which indicates that the violations caused by the nonlinear collisions are still minor in the studied cases. The reasons for the effectiveness of SL scalings with nonlinear collision processes are also discussed. The results from this study confirmed the validity of similarity transformations with more complex reaction kinetics, which may promote the applicability of the SL scalings for the design and fabrications of plasma devices.

The capacitive argon discharge operated in the intermediate pressure regime is studied by performing one-dimensional particle-in-cell Monte Carlo collision simulations. First, the basic object-oriented plasma device code (oopd1-v1) is strictly benchmarked against the well-established xpdp1 code over a wide range of pressure (0.05 – 15 Torr) and varying blocking capacitor of the external circuit (5 – 10^5nF), and excellent agreement is obtained. The oopd1-v1 is upgraded to v2 and v3, by adding excited atoms modeled as time- and space-evolving fluid species. The metastable Arm, the radiative Arr, and the Ar(4p) manifold, and their roles in discharge equilibrium are explored. It is found that the presence of the metastable Arm enhances the plasma density by a factor of 3 at 1.6 Torr and even higher at pressures up to 5 Torr. At low pressure (0.05 Torr), electron impact ionization from the ground state atom dominates the ionization over the whole discharge region, while metastable pooling and step-wise ionization has small contribution. The proportion of metastable pooling ionization and step-wise ionization increases with increasing pressure and becomes the dominant ionization source at 5 – 15 Torr.

The present paper examines how multipactor impact points change when a perturbative harmonic mode is present, in addition to the fundamental mode which is primarily driving the multipactor. We propose a steerability-to-zero criterion to determine under what conditions a multipactor trajectory can be controlled through the perturbative mode. Simulated results are shown for a parallel-plate geometry, and the results are expected to be generalizable to coaxial and more complicated geometries. The results show that for the second, third, and fourth harmonics examined as perturbative modes, steerability-to-zero is possible under some circumstances, typically when the harmonic mode magnetic field is much stronger than the fundamental mode magnetic field. The results also show that to a good approximation, it is only the ratio of the magnetic fields between the perturbative and fundamental modes which determines whether or not multipactor trajectories can be controlled; this is because if two magnetic fields are present and are both scaled by the same factor, then the direction of the charged particle’s deflection due to the magnetic fields will remain the same.

This work investigates the temporal physics of multipactor discharge on a single dielectric surface by one-dimensional multiparticle Monte Carlo (MC) simulator with adaptive time steps. The study shows that the presence of a second carrier frequency of the rf electric field changes the saturation level and temporal oscillation pattern of the normal surface field. It is found that the instantaneous normal surface field and the multipactor electron population remains at a lower value for a longer duration within an rf period for dual frequency operation than for single frequency operation.

Recently, there is significant interest in multipactor discharge because of its threat to satellite communications. In this paper, an analytical model is presented which assesses the distortion of a signal by multipactor. Complex, multi-tone signals will also be investigated. The I-Q plot is presented to show the effects of multipactor.

We demonstrate the formation and transition behaviors of a microplasma around microstructure arrays at different gas pressures via two-dimensional particle-in-cell/Monte Carlo collision simulations. It is found that the microdischarge occurs outside the cathode microcavities at the lowest pressure and starts penetrating the microcavities with a curved sheath edge as the pressure increases. At higher pressure, coupled periodic microhollow cathode discharges (MHCDs) are formed inside the microcavities. Further increasing the gas pressure results in the disappearance of the MHCDs, and the dominant discharge shifts outside of the microcavity, locating above the protrusion tips. The effect of the space charge shielding on the discharge and the conditions for MHCD formation are discussed. The macroscopic discharge parameter scalings with the gas pressure and the electron kinetics are also examined. The results are helpful for deeply understanding the microplasma formation with nonplanar electrodes, which inform the scaling, design, and optimization of microplasma array devices across a wide range of pressure regimes in practical applications.

The spatial visible light profiles from plasma discharges near the dielectric-air interfaces of flat and periodic triangular surfaces at varied pressure in air were studied using a high-speed ICCD camera. Intense light emitted in a sub-centimeter thickness layer above the dielectric surface was observed. With increasing pressure, the brightness and thickness of the light first increases to maximum at a pressure of about 100 Torr, and then decreases. The nonlinear variation of brightness with pressure may result from the increasing critical density of plasma with pressure while the averaged electron energy decreases with an increased rate of collision with gas atoms and molecules. At a certain range of pressure, the electron energy is close to the peak of the excitation collision cross section, together with very high electron density, leads to maximum brightness and thickness light emission. Both for the flat surface and periodic surface, the light emission duration continuously becomes shorter with increasing pressure. Compared with the flat surface, the light duration for the periodic surface is shorter, especially for pressure below 0.1 Torr, where the duration dramatically decreases and no pulse-tail erosion of breakdown waveform is found. Consequently, the duration and brightness for the flat surface is higher than those for the periodic surface in most of the pressure regime studied here. Electron energy, density, and light emission brightness are studied in the analytical electron dynamic to understand these phenomena.

We verify the similarity law (SL) and show a violation of frequency scaling (f-scaling) in low-pressure capacitive radio frequency (rf) plasmas via fully kinetic particle-in-cell simulations. The SL scaling relations for electron density and electron power absorption are first confirmed in similar rf discharges. Based on these results, with only the driving frequency varied, the f-scaling for electron density is also validated, showing almost the same trend as the SL scaling, across most of the frequency regime. However, violations of the f-scaling are observed at lower frequencies, which are found to be relevant to the electron heating mode transition from stochastic to Ohmic heating. Electron kinetic invariance is illustrated for the SL and f-scaling being valid, respectively, whereas the electron kinetic variation is observed when the f-scaling is violated.

Similarity transformations are essential for correlating discharges at different scales, which are mostly utilized with local field or local energy approximations. In this work, we report the fully kinetic results from particle-in-cell/Monte Carlo collision simulations that unambiguously demonstrate the similarity of radio frequency (rf) discharges in nonlocal regimes where the electron energy relaxation length is much larger than the gap dimension. It is found that at a constant rf voltage amplitude, discharges will be similar if the gas pressure, inverse of gap distance, and rf driving frequency are all changed by the same scaling factor. The scaling relations of fundamental parameters are illustrated for rf discharges in the alpha-mode with secondary electron emission ignored, and the temporal electron kinetics are shown to have invariance in similar discharges. The results explicitly validate the scaling laws in nonlocal kinetic regimes, indicating promising application potentials of the similarity transformations across a wide range of kinetic regimes.

This work demonstrates the presence of a small number of high-energy ballistic electrons (HEBEs) that originate from secondary electrons in low-pressure radio-frequency (rf) plasmas. The kinetic behaviors of the HEBEs are illustrated through electron energy probability functions from the fully kinetic particle-in-cell simulations, showing two wavy high-energy tails and two bifurcations during one rf cycle. Test-particle simulations and a semi-analytical method associated with nonlocal electron kinetics are performed to characterize the HEBE trajectories, which reveal the ballistic nature of the HEBEs and their typical bouncing features between the rf sheaths. Parameter dependence of the HEBEs on the discharge conditions (e.g., gas pressure, gap distance, and rf frequency) are identified, which is relevant to the plasma collisionality. With a pronounced presence of HEBEs, the overall impacts of the secondary electron emission on discharge parameters, such as electron power absorption and ionization rate, are also illustrated.

The modelling, measurement, and control of ion flux energy distributions are of growing in terest for the fabrication of complex structures in microelectronics manufacturing processes. Retarding field energy analyzers (RFEA 's) enable the direct measure of these energy distributions, and can be used to measure the ion flux spectrum incident on these structures in order to elucidate the flux contribution to critical process parameters for material deposition and pattern etching.