Ion Energy Distribution Function Research Articles

Multiscale modeling of fragmentation in an electrospray plume

We present a 3D-particle-in-cell (PIC) approach to modeling electrospray plumes typical of those formed by externally wetted emitter devices. Numerical grid-resolution techniques suitable for capturing strong electric fields in the emitter region were explored, and grid refinement criteria were quantified. The molecular dynamics simulations of the EMIM−BF4 ionic liquid system were modeled to determine the fragmentation mechanism in the presence of an electric field and dimer temperature as well as to provide fragmentation rates for the PIC simulations. An energy analysis of the molecular dynamics (MD) fragmentation demonstrated that the key mechanism for dimer fragmentation corresponds to a decrease in the Coulomb energy between the cation and anion in the system and that dimers of temperatures 300 and 600 K are extremely stable for electric fields smaller than 1.5 V/nm. Using probabilities of fragmentation consistent with the MD simulations, we implemented a dimer fragmentation model in our PIC simulations. The ion energy distribution functions obtained from the PIC simulations were used to predict retarding potential analysis (RPA) curves that were compared directly to measurements. The sensitivity of the RPA shape to the fragmentation probability was found to be significant. By comparing predicted and measured RPA curves for both negative and positive operation modes, and the fact that dimers do not fragment for electric fields less than 0.6 V/nm, we conclude that fragmentation of dimers occurs spontaneously due to their high thermal energies.

Applying the plasma physical sputtering process to SRF cavity treatment: Simulation and Experiment Study

Plasma processing is a fast-emerging surface treatment technology for superconducting radio frequency (SRF) cavities: plasma interacts with the impurity contamination and tiny burrs, resulting in an etched clean-and-smooth RF surface. Among all the variations of plasma processing method, the physical sputtering process might be applied to SRF cavities but has no clear etching profile (including distribution uniformity, ion flux, energy, and etching rate). To investigate that, this paper utilizes a two-dimensional self-consistent model combining the fluid equations and the Monte Carlo collision method. With the model, we introduced the sputtering-yield probability distribution to evaluate the physical sputtering process quantitatively; optimized the plasma distribution characteristics with three electrode structures to attain uniformly distributed plasma; built the correlation between ion flux and ion-energy distribution function (IEDF) under varied power and frequency; and studied the physical sputtering process at different positions. In the end, we performed the plasma physical sputtering experiment on small niobium samples, seeing an etching and smoothing effect. This research successfully evaluated the physical sputtering process for SRF cavities, and indicated the feasibility of pure physical sputtering etching.

Ion energy distribution function in very high frequency capacitive discharges excited by saw-tooth waveform

Tailoring the ion energy distribution function (IEDF) is vital for advanced plasma processing applications. Capacitively coupled plasma (CCP) discharges excited using a non-sinusoidal waveform have shown its capability to control IEDF through the generation of plasma asymmetry and DC self-bias. In this paper, we performed a particle-in-cell simulation study to investigate the IEDF in a symmetric capacitive discharge excited by a saw-tooth-like current waveform at a very high frequency. At a constant driving frequency of 27.12 MHz, the simulation results predict that the ion energy asymmetry in the discharge scales with the discharge current amplitude. A transition from a single narrow ion energy peak to a bi-modal type IEDF is observed with an increase in the current density amplitude. Further studies at a constant current density and varying the fundamental excitation frequency show that the ion energy asymmetry enhances with a reduction in the driving frequency. Increase in the plasma asymmetry and significant DC self-bias at a lower driving frequency is observed to be one of the principal factors responsible for the observed asymmetry in the ion energy peaks. An investigation of DC self-bias and plasma potential confirms that the powered electrode energy peak corresponds to the DC self-bias with respect to the plasma potential, and the grounded electrode peak corresponds to the plasma potential. These results suggest that although lower driving frequency is beneficial for generating the discharge asymmetry and large DC self-bias, a narrow low energy IEDF is plausible in very high frequency driven CCP systems.

2D Particle-in-cell simulations of charged particle dynamics in geometrically asymmetric low pressure capacitive RF plasmas

Understanding the spatio-temporal dynamics of charged particles in low pressure radio frequency capacitively coupled plasmas (CCP) is the basis for knowledge based process development in these plasma sources. Due to the importance of kinetic non-local effects the particle in cell/Monte Carlo collision (PIC/MCC) simulation became the primary modeling approach. However, due to computational limitations most previous PIC/MCC simulations were restricted to spatial resolution in one dimension. Additionally, most previous studies were based on oversimplified treatments of plasma-surface interactions. Overcoming these problems could clearly lead to a more realistic description of the physics of these plasma sources. In this work, the effects of the reactor geometry in combination with realistic heavy particle and electron induced secondary electron emission coefficients (SEEC) on the charged particle dynamics are revealed by GPU based 2D3V PIC/MCC simulations of argon discharges operated at 0.5 Pa and at a high voltage amplitude of 1000 V. The geometrical reactor asymmetry as well as the SEECs are found to affect the power absorption dynamics and distribution functions of electrons and ions strongly by determining the sheath voltages and widths adjacent to powered and grounded surface elements as well as via the self-excitation of the plasma series resonance. It is noticed that secondary electrons play important roles even at low pressures. Electron induced secondary electrons (δ-electrons) are found to cause up to half of the total ionization, while heavy particle induced secondary electrons (γ-electrons) do not cause much ionization directly, but induce most of the δ-electron emission from boundary surfaces. The fundamental insights obtained into the 2D-space resolved charged particle dynamics are used to understand the formation of energy distribution functions of electrons and ions for different reactor geometries and surface conditions.

Plasma Plume Characterization of a 100 kW Nested Hall Thruster

The plasma plume properties of a three-channel 100-kW-class nested Hall thruster were measured on xenon propellant for total powers up to 80 kW. The thruster was throttled through all seven available channel combinations for conditions spanning 300 to 500 V discharge voltage and three discharge current densities. A plasma diagnostics array, which included a Wien filter spectrometer, a retarding potential analyzer, and a planar Langmuir probe, was placed in the far-field plume of the thruster and used to measure the beam ion charge state, the ion energy distribution function, and the local plasma potential. These data were used to calculate thruster phenomenological efficiencies. These efficiencies are compared across the discharge voltage and channel combination, and they are compared to similar results from the NASA-300M single-channel high-power Hall thruster. An estimate of cross-channel ingestion, which is a phenomenon in the nested configuration that may improve thruster efficiency and that will be present in space, is calculated, and the results for mass utilization efficiency are corrected for this effect. These plasma diagnostic results are discussed in the context of the state of the art, as well as in that of the viability and potential benefits of the nested channel thruster configuration.

Time-resolved ion energy measurements using a retarding potential analyzer.

A retarding potential energy analyzer was used to obtain temporally resolved ion energy distribution functions (IEDFs) of a flowing laboratory plasma. The plasma of time varying ion energy was generated at 1 and 20 kHz using a commercial gridded ion source and modulated using a wideband power amplifier. Three plasma energy modulation setpoints were tested, and their IEDFs were reconstructed. This method leverages high-speed, low-noise instrumentation to obtain fast collector current measurements at discrete retarding bias levels, recombining them in the time domain using two data fusion techniques. The first method is an empirical transfer function, which determines the linear ratio of complex coefficients in Fourier space. The second method, shadow manifold interpolation, reconstructs the IEDFs point-by-point by comparing input and output datasets in a multi-dimensional phase space. Reconstructed IEDFs from the two methods are presented and compared. The two analysis methods show very good agreement.

Characterization of an RF excited broad beam ion source operating with inert gases

Ion current density distributions, mass spectra, and ion energy distribution functions (IEDFs) for the use of Ar and mixtures of Ar/He and Ar/Ne in an RF broad beam ion source have been measured as a function of the extracted ion beam current and the applied RF-power. For the measurements, an array of Faraday probes and an energy-selective mass spectrometer have been used. Regardless of the gases or gas mixtures used, a broadening of the ion current density profile is measured at constant grid voltages with increasing RF-power. The IEDFs of all species are also dependent on the applied RF-power and show a bimodal shape with an increasing energy shift for a higher RF-power. The data show a significant contribution of charge exchange processes after the ions left the ion beam source. Besides ions of the process gas, additional species of ions originating from the erosion processes of the ion beam source, can be found in the mass spectrum. The measurements show that the operating conditions of the ion source have a significant influence on the beam properties and thus can also affect the results of ultraprecise ion beam-assisted processes.

Non‐self‐sustained electron beam RF‐generated plasma in application for functional surface pretreatment

AbstractSimulation of non‐self‐sustained plasma generated by a 2‐keV electron beam in Ar with radiofrequency (RF) biasing is carried out using a one‐dimensional particle‐in‐cell Monte Carlo method. The effect of 10–30 mTorr gas pressure and different RF voltages of 0–45 V on the ion energy and angle distribution functions is analyzed and discussed. The performed ab initio dynamic simulations confirmed the possibility to eliminate methyl groups from the low‐k surfaces with low‐energy (10–20 eV) Ar ions, thereby turning these surfaces from hydrophobic into hydrophilic. The analytical model is developed to calculate the ion fluxes on two‐dimensional trench walls and bottom for conditions under study. It was shown that plasma with a pressure of 10 mTorr and a bias voltage of ≤45 V is better suited for pretreatment of the low‐k trench walls.

Hybrid simulation of radio frequency biased inductively coupled Cl2 plasmas

In the etching process, a bias source is usually applied to the bottom electrode of an inductively coupled plasma (ICP) source to control the ion energy and angular distribution function (IEADF) independently. In this work, a hybrid model, i.e., a global model combined bi-directionally with a fluid sheath model, is applied to investigate the plasma properties in biased ICPs sustained in Cl2 gases. The evolutions of the plasma properties with bias voltage are presented for various ICP powers (i.e., 200, 500, and 1000 W) at a pressure of 10 mTorr and bias frequency of 13.56 MHz. The results indicate that the Cl2 (v = 0) density decreases with ICP power, whereas the densities of electrons and Cl+ ions increase strikingly and they become the dominant charged species at 1000 W. In addition, the electron density and Cl+ density increase with bias voltage, and the increasing trend becomes more obvious at higher ICP powers. However, the evolution of the Cl2+ density and Cl− density with bias voltage depends on the ICP power. For instance, they first exhibit an increasing trend and then keep constant at 200 W, while a slight downward trend is observed at 1000 W. In addition, as the bias voltage increases, both the high-energy peak and low-energy peak of IEADFs move toward higher energy, and meanwhile the peak separation becomes wider. The results obtained in this work are of significant importance for improving the etching process.

Link between plasma properties with morphological, structural and mechanical properties of thin Ti films deposited by high power impulse magnetron sputtering

The main focus of this work is to correlate the basic plasma properties with morphological, structural and mechanical properties of thin films to bridge the gap between the energy source, the plasma and materials. For this purpose, the deposition and growth of thin titanium films deposited by high power impulse magnetron sputtering (HiPIMS) at various discharge power densities, from 0.17 kW/cm 2 to 3.5 kW/cm 2 were studied, both experimentally and by kinetic Monte Carlo simulation. Simulations of film growth were performed with a three-dimensional kinetic Monte Carlo code (NASCAM) with ion fraction and species energy determined experimentally by mass spectroscopy . Our approach, which is not purely empirically driven, intends to reveal some insights of the mechanisms underlying the synthesis process, which determine the intrinsic material properties. In order to link HiPIMS plasma parameters and Ti film properties, we used different techniques to analyse Ti films. TEM, X-ray diffraction and AFM were used to evaluate the structural and morphological properties of the films, and nano indention was used to evaluate their mechanical properties. We observed that the orientation of micro-crystals, which constitute the films, changes when the discharge power density increases. At the same time, we show that the films nano hardness changes non-monotonically with the increase of the discharge power density; it decreases first, then increases. The surface roughness behaviour is also non-monotonic; first increasing, then decreasing with the further increase of the discharge power density. 3D modelling helped to reveal that these non-monotonic evolutions are due to a transition between thermally-driven to ballistically-driven Ti atom mobility. • Evolution of the film properties with increase of discharge power density in HiPIMS deposition • Combined analysis of the film morphology by a range of experimental methods and simulations • A correlation between ion energy distribution functions and properties of the deposited Ti film is demonstrated. • The average energy per deposited atom is the driving force for the changes in morphology and structure of deposited films.

Diagnostic and modelling investigation on the ion acceleration and plasma throttling effects in a dual-emitter hollow cathode micro-thruster

Hollow cathode discharges are widely used as neutralizers for the electric propulsion systems and recently developed into micro-thrusters for the small satellites. In this work, a dual-emitter hollow cathode thruster is developed, which can be operated in two different modes—the neutralizer mode and the micro-thruster mode. For characterizing this kind of new device, the Langmuir probe, Faraday probe, and retarding potential analyzer are used to determine the electron temperature, electron density, ion flux, and ion energy distribution function. The operating parameters, including the thrust, and specific impulse, are also measured. A two-dimensional self-consistent extended fluid model is employed to calculate the spatial distribution of plasma parameters and the fluid field of electrons in the region around the emitters. By comparing the diagnostic and modelling results, it is found that the change in the electric field and ionization zone is the essential reason for the different performances of the device in the neutralizer and micro-thruster modes. Variation in the electric field leads to an ion acceleration effect in the micro-thruster mode; moving of the ionization zone raises the plasma pressure in the orifice region of the hollow cathode, and thus leads to enhanced plasma throttling and gas expanding effects. By analyzing the above mechanisms, the possible methods for improving this kind of hollow cathode micro-thruster are discussed.

Influence of magnetic field configuration on plasma characteristics and thin film properties in dual magnetron reactive high power impulse magnetron sputtering discharge with Al in Ar/O2 mixture

In this work, the influences of the magnetic field configuration (mirror-field and closed-field) on plasma parameters and ion flux dynamics of dual magnetron reactive high power impulse magnetron sputtering (R-HiPIMS) with Al targets in Ar/O2 mixture were studied by time-resolved Langmuir probe and time-averaged mass spectrometer. Compared with mirror-field configuration, the electron density (ne) in the closed-field discharge is obviously higher while the plasma potential (Vp), floating potential (Vf) and effective electron temperature (Teff) were lower. Time-averaged mass spectrometer results showed that the plasma compositions in both configurations were similar. The ion energy distribution functions (IEDFs) recorded at both discharges consisted of three components: a main narrow peak at low energy followed by a broad shoulder and then a high energy tail. Compared with the closed-field discharge, the mirror-field discharge exhibited higher peak energies but lower ion fluxes. For both discharges, the ions intensity increased immediately after the start of the negative voltage pulse. The signal for the mirror-field discharge peaked exactly at the end of the pulse, whereas fluxes of the ion species in the closed-field configuration reached the highest value 10μs after the voltage pulse termination. To investigate how changes in the magnet arrangement affect the film properties, Al2O3 thin films were deposited and characterized. It is confirmed that the magnet configuration appeared to have little influence on the deposition rate. In addition, high average energy per deposited atom in the closed-field discharge resulted in a well densified and stoichiometric crystalline Al2O3 film.

Kinetic characteristics of ions in an inertial electrostatic confinement device.

The kinetic analyses are quite important when it comes to understanding the particle behavior in any device as they start to deviate from a continuum nature. In the present study, kinetic simulations are performed using the particle-in-cell method to analyze the behavior of ions inside a cylindrical inertial electrostatic confinement fusion (IECF) device which is being developed as a tabletop neutron source. Here, the lighter ions, like deuterium, are accelerated by applying an electrostatic field between the chamber wall (anode) and the cathode (cylindrical gridded wire), placed at the center of the device. The plasma potential profiles obtained from the simulated results indicate the formation of multiple potential well structures inside the cathode grid depending upon the applied cathode potential (from -1 to -5 kV). The ion density at the core region of the device is found to be of the order of 10^{16}m^{-3}, which closely resembles the experimental observations. Spatial variation of ion energy distribution function has been measured in order to observe the characteristics of ions at different cathode voltages. Finally, the simulated results are compared and found to be in good agreement with the experimental profiles. The present analysis can serve as a reference guide to optimize the technological parameters of the discharge process in IECF devices.

Decoupling ion energy and flux in intermediate pressure capacitively coupled plasmas via tailored voltage waveforms

The discrete control of ion energy and flux is of increasing importance to industrially relevant plasma sources. The ion energy distribution functions (IEDFs) and net ion flux incident upon material surfaces in intermediate pressure (≈133 Pa, 1 Torr) radio-frequency capacitively coupled plasmas (rf CCPs) are coupled to the spatio-temporal sheath dynamics and resulting phase-averaged sheath potential. For single frequency driven discharges this co-dependence of ion energy and flux on the sheath potential limits the range of accessible operating regimes. In this work, experimentally benchmarked 2D fluid/Monte-Carlo simulations are employed to demonstrate quasi-independent control of the ion flux and IEDF incident upon plasma facing surfaces in a collisional (≈200 Pa, 1.5 Torr argon) rf hollow cathode discharge driven by multi-harmonic (n ⩾ 2) tailored voltage waveforms. The application of variable phase offset n = 5 tailored voltage waveforms affords a significant degree of control over the ion flux and mean ion energy , modulating each by factors of 2.9 and 1.6, respectively as compared to 1.8 and 1.6, achieved via n = 2 dual-frequency voltage waveforms. The disparate modulations achieved employing n = 5 tailored voltage waveforms demonstrate a significant degree of independent control over the mean ion energy and ion flux for collisional conditions, enabling access to a wider range of operational regimes. Maximising the extent to which ion energy and flux may be independently controlled enables improvements to plasma sources for technological applications such as plasma assisted material manufacture and spacecraft propulsion.

Detailed Density and Ion Energy Profiles Downstream of a Small ECR Plasma Source

The exhaust ion stream from an electron cyclotron resonance (ECR) plasma source is investigated in detail. Two sets of coils allow for different shapes of the external field under which the plasma is created. Parameters in the form of electron density $n_{e}$ , electron temperature $T_{e}$ , and ion energy distribution function (IEDF) are evaluated using Langmuir probes and retarding field energy analyzers (RFEAs). Parameters are evaluated under 10 and 20 W of microwave energy at pressures in argon between $1\times 10^{-3}$ and $2\times 10^{-3}$ mbar. In the middle of the plasma, we see electron temperatures in the range of 4–5 eV for most measurements and electron densities of up to $5\times 10^{16}/\text{m}^{3}$ in agreement with particle and power balance models. For a purely expanding magnetic field, the detailed IEDFs indicate a directed ion speed within the plasma column of up to $3.1\times 10^{3}$ m/s with respect to the low-energy background. With increasing downstream magnetic field, the low-energy part of the IEDFs vanishes downstream of the magnetic mirror. Structures with energies increasing in the radial direction appear as radial confinement improves.

Driving frequency effect on discharge parameters and higher harmonic generation in capacitive discharges at constant power densities

Very high frequency (VHF) driven capacitive discharges are now being increasingly adopted for plasma-based materials processing due to their high processing rates and lower substrate damage. Past studies related to complex plasma dynamics and higher harmonics generation in such systems were limited to constant voltage/current conditions, whereas, industrial systems are mostly driven by constant power density sources. In the present study, using particle-in-cell (PIC) simulation, we explore the dynamics of collisionless symmetric capacitive discharges that is operated at constant power densities. Our focus is on the effect of the driving frequency on the discharge parameters like the electron density/temperature, the electron energy distribution function (EEDF), the ion energy distribution function (IEDF), and the generation of higher harmonics in the device. The simulations are performed for a driving frequency from 27.12 to 100 MHz in argon plasma at a gas pressure of 1 Pa and for two values of the power density, namely, 2 kW m−3 and 20 kW m−3. It is observed that the required discharge voltage for maintaining constant power density decreases and discharge current increases with an increase in the driving frequency. A transition frequency is observed at both power densities. The density decreases (electron temperature increases) before the transition frequency and the trend is reversed after crossing the transition frequency. The EEDF shows an enhancement in the population of the mid-energy range of electrons as the driving frequency increases up to the transition frequency thereby changing the shape of EEDF from bi-Maxwellian to nearly Maxwellian, and then transforms into a nearly bi-Maxwellian at higher driving frequencies. The IEDF at the electrode surface shows bimodal behaviour at a lower driving frequency, becoming more pronounced at a power density of 20 kW m−3, and then turning into a single energy peak. The corresponding maximum ion energy is found to decrease with driving frequency.

Plasma polymerization of (2,2,6,6-tetramethylpiperidin-1-yl)oxyl in a collisional, capacitively coupled radio frequency discharge.

Plasma polymerization of (2,2,6,6-tetramethylpiperidin-1-yl)oxyl (TEMPO) yields thin films containing stable nitroxide radicals that have properties analogous to that of nitric oxide (NO) without short lifetimes. This property gives TEMPO films a wide variety of potential applications. Typically, control of the final film chemistry is difficult and the plasma discharge conditions must be tailored to in order to maximize the retention of these nitroxide groups during the polymerization and deposition process. In this study, plasma diagnostics and surface analysis of the deposited films were carried out to determine the optimal plasma conditions for the retention of nitroxide groups. These techniques included energy-resolved mass spectrometry, heated planar probe ion current measurements, deposition rate measurements, and x-ray photoelectron spectroscopy (XPS). Results show that operating the plasma with a combination of low input powers and high pressures produces a collisional discharge in which fragmentation of the TEMPO molecule is suppressed, leading to good retention of nitroxide groups. Ion energy distribution functions and quartz crystal microbalance measurements support the soft landing theory of ion deposition on the substrate within this γ-mode, in which the flux of low energy, soft landed ions form the primary contribution to film growth. XPS analysis of deposited polymers shows 75.7% retention of N-O groups in the polymer films deposited in a 25 Pa 5 W discharge.

Enhancing surface production of negative ions using nitrogen doped diamond in a deuterium plasma

The production of negative ions is of significant interest for applications including mass spectrometry, particle acceleration, material surface processing, and neutral beam injection for magnetic confinement fusion. Methods to improve the efficiency of the surface production of negative ions, without the use of low work function metals, are of interest for mitigating the complex engineering challenges these materials introduce. In this study we investigate the production of negative ions by doping diamond with nitrogen. Negatively biased (−20 V or −130 V), nitrogen doped micro-crystalline diamond films are introduced to a low pressure deuterium plasma (helicon source operated in capacitive mode, 2 Pa, 26 W) and negative ion energy distribution functions are measured via mass spectrometry with respect to the surface temperature (30 °C to 750 °C) and dopant concentration. The results suggest that nitrogen doping has little influence on the yield when the sample is biased at −130 V, but when a relatively small bias voltage of −20 V is applied the yield is increased by a factor of 2 above that of un-doped diamond when its temperature reaches 550 °C. The doping of diamond with nitrogen is a new method for controlling the surface production of negative ions, which continues to be of significant interest for a wide variety of practical applications.

Experimentally validated computations of simultaneous ion and fast neutral energy and angular distributions in a capacitively coupled plasma reactor

Accurate predictions of the ion energy and angular distribution functions (IEADFs) and fast neutral energy and angular distribution functions (FNEADFs), are essential for a range of critical applications in the plasma processing of thin film etching and deposition. Computationally efficient methods that can be applied to industrial reactor systems that are also validated across a range of operating conditions are essential for prediction of IEADFs and FNEADFs. In this work, we present a hybrid model where a capacitively coupled plasma (CCP) solution was computed using a fluid model and the IEADF/FNEADF was generated using a particle transport model with a multi-species Monte Carlo Collision model. We first compare the computed IEADFs across a range of pressures with experimental measurements for a CCP reactor. We predict FNEADFs that are typically difficult to measure experimentally but are believed to have a significant effect on etch/deposition process phenomena. Across a large pressure range, we observe significant fast neutral bombardment of the electrode surface with at least half the energy of the most energetic ions as well as an angular spread that is larger than that of the ions.

Application of a microwave cathode to a 200-W Hall thruster with comparison to a hollow cathode

A hollow cathode is an efficient electron source in the self-heating mode utilizing the discharge power. However, in sub-ampere currents, it needs keeper power to maintain the thermionic electron discharge, which could decrease the thrust efficiency. To address this problem, we propose using a microwave cathode, which is based on the flight model of a microwave ion thruster neutralizer cathode, as an alternative to a hollow cathode. First, we redesigned the magnetic field of a microwave cathode discharge chamber and tested it in the diode mode configuration. The electron emission current is doubled compared to the original performance. Next, we coupled the improved microwave cathode with a 200-W class Hall thruster and compared the characteristics and performance with a hollow cathode. We confirmed that the magnetic field polarity affects the ignition characteristics. We measured the thrust by an inverted thrust stand, the ion energy distribution functions by a retarding potential analyzer, and the beam profiles by an ion collector. The thrust and thrust efficiency are equivalent for both types of cathode. The specific impulse is 10% higher in the case of the microwave cathode. Since the potential difference between the microwave cathode and ground rapidly increased at currents above 600 mA, this could be taken to be the trade-off point against the hollow cathode.