Plasma uniformity and ion dynamics in Ar/He capacitively coupled plasmas

It is known that in very-high-frequency (VHF) capacitively coupled plasmas, the higher harmonics generated by nonlinear sheath motion can enhance the standing wave effect (SWE), which can lead to center-peaked plasma density profiles. In this work, an improved nonlinear electromagnetic model incorporating a transmission line model, an electron momentum balance model, a bulk plasma model, a collisionless nonlinear numerical sheath model, and an ion Monte-Carlo collision (MCC) model is developed to study the effects of low-frequency (LF) voltage VL on the nonlinear standing wave excitation, plasma uniformity, and ion energy and angular distribution functions (IEDFs and IADFs) in dual-frequency (DF) asymmetric capacitive argon discharges at relatively low pressure of 3 Pa. The plasma diffusion in the radial direction and ion dynamics within the LF oscillating sheath are self-consistently considered. The LF voltage VL at 2 MHz varies from 0 to 700 V while the HF voltage VH at 60 MHz is fixed at 100 V. Simulation results indicate that without the addition of an LF source (i.e. VL= 0 V), there are a considerable number of high-order harmonics with short wavelengths, leading to significant SWE and central peak in the radial plasma density profile. Nevertheless, the high-order harmonic excitations tend to be weakened and merely occur around the phase of the full LF sheath collapse due to a shorter characteristic damping time of the surface waves as VL increases. This, combined with increased surface wavelengths of both the driving frequency and the higher harmonics at a higher VL , leads to suppressed standing waves and improved plasma uniformity. Meanwhile, the simulations show that both the low and the high energy peaks of IEDF move towards higher energies, and the energy peak separation width ΔE becomes wider with the increase of VL . The IEDF at the radial center of the powered electrode exhibits a broader ΔE than that at the edge. For the IADF, an increased VL results in more ions incident on the electrode with a smaller deflection angle. Because of a thinner sheath and a higher sheath voltage at the electrode center, the peak value of IADF at the electrode center is greater than that at the edge.

A combined Monte Carlo (MC)/analytical surface model is developed to study the plasma processes occurring during the reactive sputter deposition of TiOx thin films. This model describes the important plasma species with a MC approach (i.e. electrons, Ar+ ions, ions, fast Ar atoms and sputtered Ti atoms). The deposition of the TiOx film is treated by an analytical surface model.The implementation of our so-called multi-species MC model is presented, and some typical calculation results are shown, such as densities, fluxes, energies and collision rates. The advantages and disadvantages of the multi-species MC model are illustrated by a comparison with a particle-in-cell/Monte Carlo collisions (PIC/MCC) model. Disadvantages include the fact that certain input values and assumptions are needed. However, when these are accounted for, the results are in good agreement with the PIC/MCC simulations, and the calculation time has drastically decreased, which enables us to simulate large and complicated reactor geometries.To illustrate this, the effect of larger target–substrate distances on the film properties is investigated. It is shown that a stoichiometric film is deposited at all investigated target–substrate distances (24, 40, 60 and 80 mm). Moreover, a larger target–substrate distance promotes film uniformity, but the deposition rate is much lower.

Microplasma discharges are of interest both in their fundamental understanding and in their applications – such as plasma sources, metasurfaces, and in emerging radiofrequency and microwave applications. One common topology for microplasma discharge formation is a split-ring resonator. Much work has investigated split-ring resonators as a platform for radiofrequency and microwave driven plasma [1] . Microwave circuit models for the behavior of such circuits have been developed, and electromagnetic simulations of the fields generated by these devices have provided an additional avenue of investigation. This foundation can be valuably extended by introducing particle-in-cell/Monte Carlo collision (PIC/MCC) modeling of the breakdown phenomena. We present the simulation and experimental validation of micro-plasma formation in split-ring resonator structures for frequencies in excess 5 gigahertz. Split-ring resonator devices with planar gap geometry were designed and fabricated at Purdue’s Scifres Nanofabrication Cleanroom. Nominal gap widths between 5 and 20 micrometers were considered as well as signal frequencies between 5 and 18 gigahertz. Breakdown potential was measured experimentally in an Argon environment over a range of ambient pressures less than 1 atmosphere. Finally, PIC/MCC simulations were created in XOOPIC to predict breakdown potential. Measurement-model correlation, and model predictive strength are discussed. Domain-specific modeling challenges and recommendation for future measurements are provided.

In this paper, a one-dimensional (1D) particle-in-cell Monte Carlo collision (PIC-MCC) model is developed to investigate the effects of anisotropic pressure and inertial terms due to non-Maxwellian velocity distribution functions on cross-field electron transport. The conservation of momentum is evaluated by taking the moments of the first-principles gas-kinetic equation. A steady-state discharge is obtained without any low-frequency ionization oscillations by considering an anomalous electron scattering profile. The results obtained from the 1D PIC-MCC model are compared with fluid models, including the quasi-neutral drift-diffusion (DD), non-neutral DD, and full fluid moment models. The discharge current obtained from the PIC-MCC model is in good agreement with the fluid models. The cross-field electron transport due to the inertial terms, i.e. the gradient of axial and azimuthal drift, is evaluated. Moreover, PIC-MCC simulation results show non-zero, anisotropic, off-diagonal pressure tensor terms due to asymmetric non-Maxwellian electron velocity distribution function, potentially contributing to cross-field electron transport.

Precise control of ion energy distribution functions (IEDFs) is crucial for selectivity as well as control over sputter rate and substrate damage in nanoscale plasma processes. In this work, a low frequency (100 kHz) tailored pulse-wave-shaped bias voltage waveform is applied to the substrate electrode of an inductively coupled plasma (ICP) and its effects on the IEDF, electron density, electron dynamics and the etch rates of silicon dioxide as well as amorphous silicon are investigated in a commercial 200 mm reactive ion etching reactor. While the tailored waveform substrate bias hardly affects the electron density above the substrate and the spatio-temporally resolved electron power absorption dynamics, it is found to affect the ion flux to the substrate at high ICP source powers. Monoenergetic IEDFs with a full width at half maximum below 10 eV are realized with mean ion energies ranging from 20 eV to 100 eV in both argon and SF 6 . Using a modified voltage allows generating two independently controllable peaks in the IEDF. The monoenergetic IEDFs are used to determine the Ar ion sputter threshold energies of amorphous silicon and silicon dioxide to be 23 eV and 37 eV, respectively. This enables selective etching of these two materials by Ar ion sputtering based on tailoring the IEDF to ensure that all incident ions are within this narrow ion energy selectivity window.

A Cartesian-coordinate two-dimensional electrostatic particle-in-cell/Monte Carlo collision (PIC/MCC) plasma simulation code is presented, including a new treatment of charge balance at dielectric boundaries. It is used to simulate an Ar plasma in a symmetric radiofrequency capacitively-coupled parallel-plate reactor with a thick (3.5 cm) dielectric side-wall. The reactor size (12 cm electrode width, 2.5 cm electrode spacing) and frequency (15 MHz) are such that electromagnetic effects can be ignored. The dielectric side-wall effectively shields the plasma from the enhanced electric field at the powered-grounded electrode junction, which has previously been shown to produce locally enhanced plasma density (Dalvie et al 1993 Appl. Phys. Lett. 62 3207–9; Overzet and Hopkins 1993 Appl. Phys. Lett. 63 2484–6; Boeuf and Pitchford 1995 Phys. Rev. E 51 1376–90). Nevertheless, enhanced electron heating is observed in a region adjacent to the dielectric boundary, leading to maxima in ionization rate, plasma density and ion flux to the electrodes in this region, and not at the reactor centre as would otherwise be expected. The axially-integrated electron power deposition peaks closer to the dielectric edge than the electron density. The electron heating components are derived from the PIC/MCC simulations and show that this enhanced electron heating results from increased Ohmic heating in the axial direction as the electron density decreases towards the side-wall. We investigated the validity of different analytical formulas to estimate the Ohmic heating by comparing them to the PIC results. The widespread assumption that a time-averaged momentum transfer frequency, vm, can be used to estimate the momentum change can cause large errors, since it neglects both phase and amplitude information. Furthermore, the classical relationship between the total electron current and the electric field must be used with caution, particularly close to the dielectric edge where the (neglected) pressure gradient term becomes significant.

Pulsed filtered cathodic arc deposition involves formation of energetic multiply charged metal ions, which help to form dense, adherent, and macroparticle-free thin films. Ions possess not only significant kinetic energy, but also potential energy primarily due to their charge, which for cathodic arc plasmas is usually greater than one. While the effects of kinetic ion energy on the growing film are well investigated, the effects of the ions’ potential energy are less known. In the present work, we make a step toward decoupling the contributions of kinetic and potential energies of ions on thin film formation. The potential energy is changed by enhancing the ion charge states via using an external magnetic field at the plasma source. The kinetic energy is adjusted by biasing the arc source (“plasma bias”), which allows us to approximately compensate the differences in kinetic energy, while the substrate and ion energy detector remain at ground. However, application of an external magnetic field also leads to an enhancement of the ion flux and hence the desired complete decoupling of the potential and kinetic energy effects will require further steps. Charge-state-resolved energy distribution functions of ions are measured at the substrate position for different arc source configurations, and thin films are deposited using exactly those configurations. Detailed characterization of the deposited thin films is performed to reveal the correlations of changes in structure with kinetic and potential energies of multiply charged ions. It is observed that the cathode composition (Al:V ratio) strongly affects the formation of the thermodynamically stable wurtzite or the metastable cubic phase. The external magnetic field applied at the arc source is found to greatly alter the plasma and, therefore, to be the primary, easily accessible “tuning knob” to enhance film crystallinity. The effect of “atomic scale heating” provided by the ions’ kinetic and potential energies on the film crystallinity is investigated, and the possibility to deposit crystalline (V,Al)N films without substrate heating is demonstrated. This study shows an approach toward distinguishing the contributions stemming from kinetic and potential energies of ions on the film growth, however, further research is needed to assess and distinguish the additional effect of ion flux intensity (current).

Particle-in-cell/Monte Carlo collision (PIC/MCC) simulations are performed to investigate the asymmetric secondary electron emission (SEE) effects when electrons strike two different material electrodes in low pressure capacitively coupled plasmas (CCPs). To describe the electron-surface interactions, a realistic model, considering the primary electron impact energy and angle, as well as the corresponding surface property-dependent secondary electron yields, is employed in PIC/MCC simulations. In this model, three kinds of electrons emitted from the surface are considered: (i) elastically reflected electrons, (ii) inelastically backscattered electrons, and (iii) electron induced secondary electrons (SEs, i.e., δ-electrons). Here, we examined the effects of electron-surface interactions on the ionization dynamics and plasma characteristics of an argon discharge. The discharge is driven by a voltage source of 13.56 MHz with amplitudes in the range of 200–2000 V. The grounded electrode material is copper (Cu) for all cases, while the powered electrode material is either Cu or silicon dioxide (SiO2). The simulations reveal that the electron impact-induced SEE is an essential process at low pressures, especially at high voltages. Different electrode materials result in an asymmetric response of SEE. Depending on the instantaneous local sheath potential and the phase of the SEE, these SEs either are reflected by the opposite sheath or strike the electrode surface, where they can induce δ-electrons upon their residual energies. It is shown that highly energetic δ-electrons contribute significantly to the ionization rate and a self-bias forms when the powered electrode material is assumed to be made of SiO2. Complex dynamics is observed due to the multiple electron-surface interaction processes and asymmetric yields of SEs in CCPs.

In direct-current (DC) discharge, it is well known that hysteresis is observed between the Townsend (gas breakdown) and glow regimes. Forward and backward voltage sweep is performed using a one-dimensional particle-in-cell Monte Carlo collision (PIC-MCC) model considering a ballast resistor. When increasing the applied voltage after reaching the breakdown voltage (Vb), transition from Townsend to glow discharges is observed. When decreasing the applied voltage from the glow regime, the discharge voltage (Vd) between the anode–cathode gap can be smaller than the breakdown voltage, resulting in a hysteresis, which is consistent with experimental observations. Next, the PIC-MCC model is used to investigate the self-sustaining voltage (Vs) in the presence of finite initial plasma densities between the anode and cathode gap. It is observed that the self-sustaining voltage coincides with the discharge voltage obtained from the backward voltage sweep. In addition, the self-sustaining voltage decreases with increased initial plasma density and saturates above a certain initial plasma density, which indicates a change in plasma resistivity. The decrease in self-sustaining voltage is associated with the electron heat loss at the anode for the low pd (rarefied) regime. In the high pd (collisional) regime, the ion energy loss toward the cathode due to the cathode fall and the inelastic collision loss of electrons in the bulk discharge balance out. Finally, it is demonstrated that the self-sustaining voltage collapses to a singular value, despite the presence of a initial plasma, for microgaps when field emission is dominant, which is also consistent with experimental observations.

High power impulse magnetron sputtering (HiPIMS) plasmas exhibit a high ionization fraction of the sputtered material and ions with high kinetic energies, which produce thin films with superior quality. These ion energy distribution functions (IEDF) contain energetic peaks, which are believed to be linked to a distinct electrical potential hump inside rotating localized ionization zones, so called spokes, at target power densities above 1 kW cm−2. Any direct measurement of this electrical potential structure is, however, very difficult due to the dynamic nature of the spokes and the very high local power density, which hampers the use of conventional emissive probes. Instead, we use a careful analysis of the IEDFs for singly and doubly charged titanium ions from a HiPIMS plasma at varying target power density. The energy peaks in the IEDFs measured at the substrate depend on the point of ionization and any charge exchange collisions on the path between ionization and impact at the substrate. Thereby, the IEDFs contain a convoluted information about the electrical potential structure inside the plasma. The analysis of these IEDFs reveal that higher ionization states originate at high target power densities from the central part of the plasma spoke, whereas singly charged ions originate from the perimeter of the plasma spoke. Consequently, we observe different absolute ion energies with the energy of Ti2+ being slightly higher than two times the energy of Ti+. Additional peaks are observed in the IEDFs of Ti+ originating from charge exchange reactions from Ti2+ and Ti3+ with titanium neutrals. Based on this analysis of the IEDFs, the structure of the electrical potential inside a spoke is inferred yielding = 25 V above the plasma potential, irrespective of target power density.

Results from a 3D self-consistent Particle-In-Cell Monte Carlo Collisions (PIC-MCC) model of a high power fusion-type negative ion source are presented for the first time <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> . The model is used to characterize the ITER prototype BATMAN ion source developed in IPP-Garching (Germany). The source is a tandem type device with a cylindrical antenna conferring to the background gas (either molecular hydrogen or deuterium) ~100kW of RF power. This produces high density plasmas of the order of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">18</sup> m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> . The expansion chamber, which is connected to the ICP discharge, has a larger volume and is magnetized. The magnetic field is generated by permanent magnets (maximum ~75G on the source symmetry axis).

A nanosecond atmospheric pressure plasma jet operated in pure nitrogen is studied by spatially and temporally resolved optical emission spectroscopy complementing the companion paper (Kuhfeld et al 2023 Plasma Sources Sci. Technol. 32 084001), where the discharge is investigated by means of Particle-in-Cell/Monte Carlo collisions (PIC/MCC) simulations and fluid models. Two temporal phases of the evolution of the discharge are identified: a fast breakdown and a quasi-DC phase. It is shown that during the breakdown phase several ionization waves develop, while after the breakdown the discharge has a structure similar to DC glow discharges, in agreement with the modeling predictions. The results of the measurements of the spatial-temporal dynamics of the light emission are compared with the distribution of densities of the and states reconstructed from the PIC/MCC simulations. A good agreement is demonstrated.

Radio-frequency-driven atmospheric pressure plasma jets (RF APPJs) play an essential role in many technological applications. This work studies the characteristics of these discharges in the so-called non-neutral regime where the conventional structure of a quasi-neutral bulk and an electron depleted sheath does not develop, and the electrons are instead organized in a drift-soliton-like structure that never reaches quasi-neutrality. A hybrid particle-in-cell/Monte Carlo collisions (PIC/MCC) simulation is set up, which combines a fully kinetic electron model via the PIC/MCC algorithm with a drift-diffusion model for the ions. In addition, an analytical model for the electron dynamics is formulated. The formation of the soliton-like structure and the connection between the soliton and the electron dynamics are investigated. The location of the electron group follows a drift equation, while the spatial shape can be described by Poisson–Boltzmann equilibrium in a co-moving frame. A stability analysis is conducted using the Lyapunov method and a linear stability analysis. A comparison of the numerical simulation with the analytical models yields a good agreement.

Measurements of hydrogen plasma density are made in a symmetric single frequency confined capacitively coupled plasma (C-CCP) RF system. Comparison is made between density measured by microwave interferometer (MWI) and electrode wall ion density gathered from Ion Energy Distribution Function (IEDF) responses. Ion number density at electrode wall is obtained by two methods as IEDF integration method and IEDF splitting method. Both methods were compared with MWI and a linear relation is obtained between both methods and MWI. It is demonstrated that electrode wall surface density obtained by IEDF splitting and IEDF integral methods are about 50,000 times less than the bulk plasma density, and integral method reads more data than splitting method. The three different measurement results are compared and they are in good qualitative agreement; the deviation in ratio of bulk plasma density measured by MWI to number density at the electrode wall resolved from ion energy distribution function is greatest at highest pressure or electrode voltages/powers. The reasons for deviations are explained by analysis of the potential drop across the presheath decreases with respect to increased applied power.

Non‐Maxwellian behaviour and plasma‐wall interaction are key processes in the physics of Hall thrusters. For this purpose, a 2D{r,z}‐3V axisymmetric fully kinetic Particle‐in‐Cell/Monte Carlo Collision (PIC‐MCC) model of the acceleration channel including the process of secondary electron emission (SEE) from the dielectric walls has been developed. In order to make the simulation possible with regard to the computational time, a reduction of the thruster dimension was done. This was derived from a new physics‐based scaling law. This model has demonstrated its outstanding capability in improving the physics insight into the processes in Stationary Plasma Thruster (SPT) and in reproducing accurately well experimental data.