Low-pressure Capacitive Discharges Research Articles

On the importance of excited state species in low pressure capacitively coupled plasma argon discharges

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 modeling of the low pressure radio frequency (rf) driven capacitive discharges. In this work, we report that the energetic electron-induced secondary electron emission (SEE) 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 lead to additional ionizing impacts and further increase of 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 SEE on the electrode surface. The PIC/MCC simulation results show good agreement with the recent experimental measurements in the low pressure range (1–10 Pa) that is commonly used for etching in the semiconductor industry. At the highest pressure (20 Pa) and driving voltage amplitudes 250 and 350 V explored here, the plasma densities from PIC/MCC simulations considering excited state neutrals and resonant photon-induced SEE are quantitatively higher than observed in the experiments, requiring further investigation on high pressure discharges.

Simultaneous existence of stochastic and ohmic heating in capacitive discharges

A one-dimensional particle-in-cell/Monte Carlo (PIC/MCC) model of low-pressure capacitive discharges with a large discharge gap is presented in the paper. The results from the model are for the dependence of the plasma parameters on the pressure and on the discharge radius. The study is directed to the heating mechanisms in the discharge. It is shown that the ohmic (Joule) heating in the plasma bulk could act simultaneously with the stochastic heating in the region of the plasma–sheath boundary. In confirmation of the results of the model, experimental results showing qualitatively the same behaviour are presented.

A nonlinear electromagnetics model of an asymmetrically-driven, low pressure capacitive discharge

It is well-known that standing waves having radially center-high voltage profiles exist in high frequency driven capacitive discharges. Capacitive sheaths can also nonlinearly excite driving frequency harmonics near the series resonance that can be spatially near-resonant, and therefore enhance the on-axis power deposition. The powered-electrode/plasma/grounded-electrode sandwich structure of an asymmetrically excited cylindrical discharge forms a three electrode system in which both z-symmetric and z-antisymmetric radially propagating wave modes can exist. We develop a nonlinear electromagnetics model for this system with radially- and time-varying sheath widths, incorporating both symmetric and antisymmetric modes, and the plasma skin effect. Waves generated in the electrostatic wave limit are also treated. The discharge is modeled as a uniform density bulk plasma with either homogeneous or Child law sheaths at the electrodes, incorporating their nonlinear voltage versus charge relations. The model includes a finite power source resistance and a self-consistent calculation of the dc bias voltages. The resulting set of nonlinear partial differential equations is solved numerically to determine the symmetric and antisymmetric mode amplitudes and the nonlinearly-excited radially-varying harmonics. Two examples driven at lower frequency (30 MHz) or at higher frequency (60 MHz) are examined. The first case displays the excited dominant ninth harmonic near the series resonance frequency with the fundamental frequency having a weak standing wave. The higher frequency case shows a more obvious standing wave effect, enhanced by the nonlinear harmonics. The symmetric and antisymmetric modes are of similar amplitudes over the driving electrode, summing to give a larger bottom sheath.

Escape factors for Paschen 2p–1s emission lines in low-temperature Ar, Kr, and Xe plasmas

Radiation trapping phenomenon is often observed when investigating low-temperature plasmas. Photons emitted from the upper excited states may be reabsorbed by the lower states before they leave the plasmas. In order to account for this effect in the modelling and optical diagnostics of plasmas, either an ‘escape factor’ of a function of the optical depth or a strict solution of the radiation transfer equation can be employed. However, the former is more convenient in comparison and thus is widely adopted.Previous literatures have provided several simple expressions of the escape factor for the uniform plasmas. The emission line profiles are assumed to be dominated by the Doppler broadening, and the line splitting due to the hyperfine structure is not considered. This kind of expression is only valid for small atoms, e.g. Ar in low-pressure uniform discharges.Actually, the excited state density in many of the low-temperature plasmas is non-uniform and the emission line profile can be significantly influenced by the collisional broadening at medium and high pressures. In these cases, a new escape factor equation should be calculated. In this work, we study the escape factor equations for the often used 2p–1s transitions (Paschen’s notation) of the Ar, Kr, and Xe atoms. Possible non-uniform density profiles are considered. In addition, we include the line splitting due to the hyperfine structure for Kr and Xe. For the low-pressure plasmas, an escape factor expression mainly based on the Gaussian line profile is given and particularly verified by an experiment in a low-pressure capacitive discharge. For the high-pressure plasmas, an equation based on the Voigt line profile is also calculated. In this way, the new escape factor expression is ready for use in the modelling of the Ar, Kr, and Xe plasmas from low to atmospheric pressure.

Linear electromagnetic excitation of an asymmetric low pressure capacitive discharge with unequal sheath widths

It is well-known that standing waves having radially center-high radio frequency (rf) voltage profiles exist in high frequency capacitive discharges. In this work, we determine the symmetric and antisymmetric radially propagating waves in a cylindrical capacitive discharge that is asymmetrically driven at the lower electrode by an rf voltage source. The discharge is modeled as a uniform bulk plasma which at lower frequencies has a thicker sheath at the smaller area powered electrode and a thinner sheath at the larger area grounded electrode. These are self-consistently determined at a specified density using the Child law to calculate sheath widths and the electron power balance to calculate the rf voltage. The fields and the system resonant frequencies are determined. The center-to-edge voltage ratio on the powered electrode is calculated versus frequency, and central highs are found near the resonances. The results are compared with simulations in a similar geometry using a two-dimensional hybrid fluid-analytical code, giving mainly a reasonable agreement. The analytic model may be useful for finding good operating frequencies for a given discharge geometry and power.

Nonlinear standing wave excitation by series resonance-enhanced harmonics in low pressure capacitive discharges

It is well-known that standing waves having radially center-high rf voltage profiles exist in high frequency capacitive discharges. It is also known that in radially uniform discharges, the capacitive sheath nonlinearities excite strong nonlinear series resonance harmonics that enhance the electron power deposition. In this work, we consider the coupling of the series resonance-enhanced harmonics to the standing waves. A one-dimensional, asymmetric radial transmission line model is developed incorporating the wave and nonlinear sheath physics and a self-consistent dc potential, for both conducting and insulating electrode surfaces. The resulting coupled pde equation set is solved numerically to determine the discharge voltages and currents. A 10 mTorr argon plasma is chosen with density m−3, gap width 2 cm and conducting electrode radius 15 cm, driven by a 500 V rf source with resistance 0.5 . We examine a set of frequencies from near 30 MHz up to frequencies more than three times as high. For most frequencies, no harmonics correspond exactly with the series or spatial resonances, which is the generic situation. Nevertheless, nearby resonances lead to a significantly enhanced ratio of the electron power per unit area on axis, compared to the average. Nearly similar results are found for insulating electrodes. Strong effects are seen for varying source resistance: high (50 ) resistance damps out most of the harmonic activity, while zero source resistance leads to a non-steady discharge with bias voltage relaxation oscillations. Stronger harmonic effects are seen for an increased radius of 30 cm, as lower harmonics become spatially resonant at lower frequencies. The radial dependence of electron power with frequency showed significant variations, with the central enhancement and sharpness of the spatial resonances depending in a complicated way on the amplitudes of the nearby series resonance current harmonics and the phase relations among the voltage harmonics driving these current harmonics. Significant center/average electron power per unit area enhancement is found even at the lowest frequencies for both high and low densities: 4.5 at 30 MHz and m−3, and 2.2 at m−3.

The effect of the driving frequency on the confinement of beam electrons and plasma density in low-pressure capacitive discharges

The effect of changing the driving frequency on the plasma density and the electron dynamics in a capacitive radio-frequency argon plasma operated at low pressures of a few Pa is investigated by particle-in-cell/Monte-Carlo collision simulations and analytical modeling. In contrast to previous assumptions, the plasma density does not follow a quadratic dependence on the driving frequency in this non-local collisionless regime. Instead, a step-like increase at a distinct driving frequency is observed. Based on an analytical power balance model, in combination with a detailed analysis of the electron kinetics, the density jump is found to be caused by an electron heating mode transition from the classical α-mode into a low-density resonant heating mode characterized by the generation of two energetic electron beams at each electrode per sheath expansion phase. These electron beams propagate through the bulk without collisions and interact with the opposing sheath. In the low-density mode, the second beam is found to hit the opposing sheath during its collapse. Consequently, a large number of energetic electrons is lost at the electrodes resulting in a poor confinement of beam electrons in contrast to the classical α-mode observed at higher driving frequencies. Based on the analytical model this modulated confinement quality and the related modulation of the energy lost per electron lost at the electrodes is demonstrated to cause the step-like change of the plasma density. The effects of a variation of the electrode gap, the neutral gas pressure, the electron sticking and secondary electron emission coefficients of the electrodes on this step-like increase of the plasma density are analyzed based on the simulation results.

Electron heating in low pressure capacitive discharges revisited

The electrons in capacitively coupled plasmas (CCPs) absorb energy via ohmic heating due to electron-neutral collisions and stochastic heating due to momentum transfer from high voltage moving sheaths. We use Particle-in-Cell (PIC) simulations to explore these heating mechanisms and to compare the PIC results with available theories on ohmic and stochastic heating. The PIC results for ohmic heating show good agreement with the ohmic heating calculation of Lafleur et al. [Phys. Plasmas 20, 124503 (2013)]. The PIC results for stochastic heating in low pressure CCPs with collisionless sheaths show good agreement with the stochastic heating model of Kaganovich et al. [IEEE Trans. Plasma Sci. 34, 696 (2006)], which revises the hard wall asymptotic model of Lieberman [IEEE Trans. Plasma Sci. 16, 638 (1988)] by taking current continuity and bulk oscillation into account.

Carbon Nanotubes Functionalized in Oxygen and Water Low Pressure Discharges used as Reinforcement of Polyurethane Composites

AbstractThe functionalization of multi‐walled CNTs in O2/Ar and H2O/Ar low pressure capacitive discharges was studied by XPS and FT‐IR. The pristine and functionalized CNTs were used as fillers in polyurethane paints. Successful plasma functionalization was confirmed by changes in atomic composition and chemical shift of the XPS atomic signals. The functionalization was indicated also by the shift of IR absorption peaks corresponding to the motion of carbon skeleton, especially the peak at about 1 560 cm−1. The presence of carbonyl was confirmed by IR absorption peak at 1 723 cm−1 only for O2/Ar plasma. The plasma functionalized CNTs increased significantly the universal and plastic hardness of the CNTs reinforced polyurethane as compared to the composites with pristine CNTs.

Feature of electron energy distribution in a low-pressure capacitive discharge

The evolution of the electron energy distribution function is investigated in the low-pressure capacitive discharge under the collisionless electron heating regime, where the electron mean-free path is comparable to or larger than the system length. As the gas pressure decreases from 50 to 10 mTorr, a different feature of electron energy distribution with a plateau in the low-energy electron range, indicating the strong electron heating in that energy range, is found. This observed result can be explained in terms of collisionless heating from the interaction between the electron bouncing motion and the oscillating sheath [Y. M. Aliev, I. D. Kaganovich, and H. Schuter, Phys. Plasmas 4, 2413 (1997)]. A simple calculation of the electron energy distribution with the energy diffusion coefficient, including the electron bounce effect, is in good agreement with the experiment.

Energy balance in a low pressure capacitive discharge driven by a double-saddle antenna

A radio frequency (rf) plasma is created at low pressure (∼1 mTorr) in the source tube of a “helicon” excited diffusion system in the absence of a dc magnetic field. The coupling is capacitive for the low source power of 160 W at 13.56 MHz considered here. Temperature measurements of the glass source tube yield a plasma power deposition of ∼35 W. The plasma parameters (density, potential, electron temperature) were measured using a retarding field energy analyzer. An analytical model based on the measured plasma parameters and on additional external parameters measured in the matching box (rf voltages and phase, rf current) is developed. The model takes into account the geometry of the double saddle rf antenna. It is found that the inside of the glass wall adjacent to the antenna wire charges negatively. Ion acceleration into the glass along the antenna and fast electrons escaping the plasma account for most of the power deposition to the walls (∼16.8 W). Secondary electrons liberated by ions impinging onto the glass along the antenna contribute a power of ∼4.6 W. Adding the power of 3.7 W deposited to the part of the tube not affected by the antenna, the total power deposition responsible for the temperature rise of the tube is found to be about 25 W. The model shows that the power deposition is strongly nonuniform along the tube as a result of the antenna geometry. An estimate of the power deposited into the electrons by stochastic heating yields ∼1.4 W, compared to an estimate of 5.8 W for the measured power loss from electrons.