Radio-frequency Plasma Sheath Research Articles

The effect of the electron κ-distribution on the dust particle charging in the radio-frequency thermal-sheaths

In order to investigate collisionless radiofrequency plasma sheaths containing dust particles, three models are utilized: the novel kinetic scheme Ensemble-in-Spacetime (EST) model for calculating sheath parameters, the Dust Particle Charging model, and the Single Dust Particle model. The EST model has been modified to account for κ-electron distributions. This model is applicable to radiofrequency plasma sheaths found in tokamaks equipped with an ion cyclotron radiofrequency (ICRF) wave heating system, such as JET, West(Tore Supra), EAST, ASDEX-U, and KSTAR. The calculated sheath parameters are utilized to determine the electron and ion currents of the dust particles. In the intermediate radio-frequency regime, when the ion plasma frequency is comparable to the ICRF, the flux and energy of the ions are modulated in time within the sheath. The ions are not inertialess, and the value of κ affects the electron and ion densities. As the value of κ increases, the time-averaged electron and ion densities, sheath edge position, and area of the sheath voltage-sheath charge hysteresis loop also increase. However, the ion energy distribution remains insensitive to the κ distribution. The dust particles are charged with different negative charges based on their radius, position within the sheath, κ-electron distribution, and sheath potential. These particles exhibit oscillatory motion due to their interactions with the plasma and gravitational fields and are accelerated toward the plasma core.

Characteristics of Vertical Spatial Distribution of Dust Particles in Radio Frequency-Plasma Sheath

The vertical spatial distribution of dust particles in radio frequency (RF) discharge plasma sheath is studied. The dust particles are levitated above the powered electrode in the discharge. From the distribution of the dust particles of different sizes generated by mixing of suitable gases, the effect of changing the RF power on the dust cloud behavior is studied. It is found that the distribution of the different sized dust particles in the sheath with variable bias differs significantly from that of single sized dust particles with fixed bias. As the RF power increases, the distribution range as well as the levitation height of the dust cloud above the powered electrode decrease. A theory for the observed results is also given. Based on the experimental and numerical results, we attribute the observed dependence to a combination of the enhanced sheath electric field and the ion drag force, but the decrease of the sheath thickness with increase of the discharge power has only minor contribution.

Intense boundary emission destroys normal radio-frequency plasma sheath.

The plasma sheath is the non-neutral space charge region that isolates bulk plasma from a boundary. Radio-frequency (RF) sheaths are formed when applying RF voltage to electrodes. Generally, applied bias is mainly consumed by a RF sheath, which shields an external field. Here we report evidence that an intense boundary emission destroys a normal RF sheath and establishes a type of RF plasma where external bias is consumed by bulk plasma instead of a sheath. Ions are naturally confined while plasma electrons are unobstructed, generating a strong RF current in the entire plasma, combined with a unique particle and energy balance. The proposed model offers the possibility for ion erosion mitigation of a plasma-facing component. It also inspires techniques for reaction rate control in plasma processing and wave mode conversion.

Dynamics of dust particles in a collisional radio-frequency plasma sheath

In this work, we have examined the dynamics of a single dust particle in a non-ionized radio-frequency plasma sheath. For this, we have used a steady state one-dimensional time-averaged model where the electrons are considered to be in thermal equilibrium, while the positive ions are described by cold fluid equations. The interactions between ions and neutrals are considered. Numerous forces acting on the dust particles, such as electric force, gravitational force, neutral drag force and ion drag force are taken into account. The numerical results show that the ion–neutral collisions have significant effects on the properties of the motion of the dust. The dust oscillation frequency increases and the equilibrium position of the dust particle drops when the coefficient of ion collision increases.

Numerical Study on Collision-Less Plasma Sheaths of RF-Glow Discharge

Abstract A self-consistent mathematic model for radio frequency (RF) glow discharge was proposed to investigate the spatiotemporal evolvement of collision-less plasma sheaths at different plasma characteristics, in which the influences of ion motion by instantaneous sheath electric field were considered and the present model would be suitable for describing the spatiotemporal characteristics plasma sheaths with wide RF-frequency ranges. The instantaneous relationship between the voltage on the RFbias electrode and the sheath thickness was determined by an equivalent circuit model coupled with a fluid model. The periodic distributions of voltage on RF-bias electrode, sheath thickness, sheath electric field, density of ion and electron in sheath were obtained by numerical methods based on the present model. It was found that the distribution of electrode voltage presents nonsinusoidal waveform which is different from the sinusoidal waveform assumptions of other researches. The numerical computation results show that β, the ratio of RF frequency and ion plasma frequency, is an important parameter that affects RF plasma sheath's features: the motion and density distribution of ion are mostly controlled by instantaneous sheath electric field if β 1, the ion motion could be determined by the average field intensity of plasma sheath, and the ion density could almost not be changed.

Temporally resolved ion velocity distribution measurements in a radio-frequency plasma sheath

The ion velocity distribution function (IVDF) above and within a radio-frequency (RF) biased plasma sheath is studied experimentally with a pulsed laser-induced fluorescence diagnostic in an industrial plasma etch tool. Temporally resolved measurements taken at eight different phases of the 2.2 MHz bias waveform show that the ion dynamics vary dramatically throughout the RF cycle (the ratio of the average ion transit time through the sheath to the RF period is τion/τRF = 0.3). The position of the presheath/sheath edge is constant throughout the RF cycle and the time-averaged ion flux is conserved within the sheath region. The characteristic bimodal structure of the time-averaged ion distributions found in previous experiments is observed to arise from the time-dependent ion dynamics, in accord with existing theory. The large temporal variation of the IVDF has implications for the plasma chemistry and etching quality.

Effect of neutral gas motion on the rotation of dust clusters in an axial magnetic field

Experiments are carried out to investigate the rotation of dust clusters in a radio-frequency plasma sheath with a vertical magnetic field. Our observations are in disagreement with the standard model, in which it was assumed that the neutral gas is at rest and that a steady rotation is attained when the ion-drag force is balanced by neutral friction. Here, we re-examine this basic assumption by carefully designed experiments. Our results suggest that the neutral gas is set into rotation by E×B induced ion flow through ion-neutral collisions and that the dust particles are advected by this flow. A hydrodynamic model is proposed to describe the rotation of the neutral gas and it can explain our observations.

Effect of external magnetic field on ion energy density of collisional radio-frequency sheath

A two-fluid model is proposed to describe the collisional radio-frequency plasma sheath in a magnetic field, and the ion energy distribution incident on the radio-frequency sheath biased electrode is numerically investigated. The simulation results reveal that the external magnetic field dominates the ion flux and energy distribution of the sheath. The ion energy can be transferred between the perpendicular direction and parallel direction under the action of magnetic field.

Collisionless electron power absorption in capacitive radio-frequency plasma sheaths

A capacitively coupled, rf biased electrode mounted in an inductively coupled plasma reactor is used to investigate rf power coupling through the resulting capacitive sheath. Carefully calibrated current and voltage probes provide the electrical measurements necessary for this investigation. An external negative dc bias enables control over the electron component of the total current arriving at the electrode through the capacitive sheath. Sheath models generally assume that electron loss at the end of the rf cycle is negligible but recent theoretical work indicates that there is a significant difference in power coupled through the sheath when electron loss is permitted. The experimental study presented here confirms this result. Retardation of electron loss to the electrode is accompanied with an increase in rf power absorbed by the electrons in the capacitive sheath. Comparing the current signals with and without electron loss establishes that the measured increase in power is associated with the electron loss phase of the rf cycle, which is consistent with predictions of the earlier theoretical work.

Characteristics of single and dual radio-frequency (RF) plasma sheaths

The characteristics of radio-frequency (RF) plasma sheaths have been topics of much scientific study for decades, and have also been of great importance in the manufacture of integrated circuits and fabricating microelectromechanical systems (MEMS), as well as in the study of physical phenomena in dusty plasmas. The sheaths behave special properties under various situations where they can be treated as collisionless or collisional, single-or dual-RF, one-or two-dimensional (1D or 2D) sheaths, etc. This paper reviews our recent progress on the dynamics of RF plasma sheaths using a fluid method that includes the fluid equations and Poission’s equation coupled with an equivalent circuit model and a hybrid method in which the fluid model is combined with the Monte-Carlo (MC) method. The structures of RF sheaths behave differently in various situations and plasma parameters such as the ion density, electron temperature, as well as the external parameters such as the applied frequency, power, gas pressure, magnetic field, are crucial for determining the characteristics of plasma sheaths.

Experiments with microrods in a radio-frequency plasma sheath

This paper presents an experimental analysis of the behavior of elongated particles suspended in an rf-enhanced plasma sheath and subjected to different forces. The linear motion of the particles through the chamber was tracked, and the forces acting on the particles were analyzed. Two different experiments shall be presented here, involving the balance of the Lorentz force or the electrostatic force with the neutral drag force on the microrods. In both experiments, the sheath electric field, charging of the particles, floating potential, as well as many other factors, were used to quantify the forces and interpret the experiments.

Simulations of ion transport in a collisional radio-frequency plasma sheath.

A hybrid theoretical model, capable of describing the characteristics of a collisional sheath driven by a sinusoidal current source and determining the energy and angular distributions of ions incident onto the substrate, is proposed. The model consists of one-dimensional time-dependent fluid equations coupled with the Poisson equation determining spatiotemporal evolution of the sheath and the Monte Carlo simulation predicting the energy and angular distributions of ions striking the electrode, in which charge-exchange collisions between ions and neutrals are included. Additionally, an equivalent circuit model in conjunction with the fluid equations is adopted to self-consistently determine the relationship between the instantaneous potential at a rf-biased electrode and the sheath thickness. It is found that the collisional effects would influence the height of the energy peaks in the ion energy distributions and the ion angular distributions.

Evolution of a dust void in a radio-frequency plasma sheath.

The onset and growth of a dust void are investigated in a radio-frequency (rf) sheath of a capacitively coupled argon plasma. A circularly symmetric void emerges and grows with increasing rf power and pressure in the central region of the dust cloud levitating in the sheath. Experimental measurements of the void diameter are compared with the predictions of a simple phenomenological theory, based on a balance of forces on dust grains.

Wake effects on vertical alignment of two dust particles in a rf plasma sheath

A theoretical method is proposed to study the motion of two dust particles in a radio-frequency plasma sheath with flowing ions. It is shown that, owing to the asymmetric wake force, the particles move in a coordinated way, remaining aligned in a direction perpendicular to an electrode, when a modulating laser beam hits the upper particle. These results imply that the wake effects may be responsible for formation of the vertically aligned Coulomb crystal structure.

Experimental tests of models of radio-frequency plasma sheaths

Experimental tests of models of radio-frequency plasma sheaths

Dynamic model of the radio-frequency plasma sheath in a highly asymmetric discharge cell

A self-consistent fluid model for the radio-frequency sheath at the powered electrode of a highly asymmetric discharge cell is developed and solved. The model assumes time-independent ion motion and inertialess electrons. The voltage on the powered electrode, assumed to be sinusoidal, is shared between the powered sheath and a series resistance that represents the remainder of the discharge. The model includes ion collisions, sheath conduction currents, and secondary electron emission from the electrode surface. Model results are compared with previous sheath models and with experiment. Current wave forms predicted by the model closely resemble the nonsinusoidal current wave forms measured in highly asymmetric cells. The model accurately predicts the shape of sheath voltage wave forms, but not their dc components. The magnitudes and phases of sheath impedances predicted by the model agree with experimental measurements performed in argon discharges at pressures of 4.0--133 Pa.

Experimental test of models of radio-frequency plasma sheaths

The ion current and sheath impedance were measured at the radio-frequency-powered electrode of an asymmetric, capacitively coupled plasma reactor, for discharges in argon at 1.33–133 Pa. The measurements were used to test the models of the radio frequency sheath derived by Lieberman [IEEE Trans. Plasma Sci. 17, 338 (1989)] and Godyak and Sternberg [Phys. Rev. A 42, 2299 (1990)], and establish the range of pressure and sheath voltage in which they are valid.

Collisionless electron heating by radio-frequency plasma sheaths

Collisionless rf sheaths have been investigated in a self-consistent particle simulation. The one-dimensional simulation is bounded by an rf driven electrode on one side and quasineutral plasma on the other so that the sheath can be examined in isolation from other discharge processes. The simulations indicate that electron velocity distributions arriving at the electrode are distorted when the ratio of the maximum velocity of the moving electron front in the rf sheath to the thermal velocity is greater than ∼0.5. Both electron heating and power loss to the electrode increases as this ratio is increased. At ratios greater than ∼0.8–1 a positive net energy flux returning from the rf sheath is observed. Electron inertia is not negligible in this regime.