Demetre J. Economou

Fluid simulations of glow discharges : effect of metastable atoms in argon

A one‐dimensional fluid simulation of a 13.56 MHz argon glow discharge including metastable species was performed as an example of a coupled glow‐discharge/neutral‐transport‐reaction system. Due to the slow response time of metastables (∼10 ms) direct time integration of the coupled system requires ∼105 rf cycles to converge. This translates to prohibitively long computation time. An ‘‘acceleration’’ scheme was employed using the Newton–Raphson method to speed up convergence, thereby reducing the computation time by orders of magnitude. For a pressure of 1 Torr, metastables were found to play a major role in the discharge despite the fact that their mole fraction was less than 10−5. In particular, metastable (two‐step) ionization was the main mechanism for electron production to sustain the discharge. Bulk electric field and electron energy were lower, and a smaller fraction of power was dissipated in the bulk plasma when compared to the case without metastables. These results suggest that neutral transport and reaction must be considered in a self‐consistent manner in glow discharge simulations, even in noble gas discharges.

Simulation of a direct current microplasma discharge in helium at atmospheric pressure

A numerical simulation of a dc microplasma discharge in helium at atmospheric pressure was performed based on a one-dimensional fluid model. The microdischarge was found to resemble a macroscopic low pressure dc glow discharge in many respects. The simulation predicted the existence of electric field reversals in the negative glow under operating conditions that favor a high electron diffusion flux emanating from the cathode sheath. The electric field adjusts to satisfy continuity of the total current. Also, the electric field in the anode layer is self adjusted to be positive or negative to satisfy the “global” particle balance in the plasma. Gas heating was found to play an important role in shaping the electric field profiles both in the negative glow and the anode layer. Basic plasma properties such as electron temperature, electron density, gas temperature, and electric field were studied. Simulation results were in good agreement with experimental observations.

Realization of atomic layer etching of silicon

An experimental system and methodology were developed to realize dry etching of single crystal silicon with monolayer accuracy. Atomic layer etching of silicon is a cyclic process composed of four consecutive steps: reactant adsorption, excess reactant evacuation, ion irradiation, and product evacuation. When successful, completion of one cycle results in removal of one monolayer of silicon. The process was self‐limiting with respect to both reactant and ion dose. Control of the ion energy was the most important factor in realizing etching of one monolayer per cycle.

PLASMA SHEATH MODEL AND ION ENERGY DISTRIBUTION FOR ALL RADIO FREQUENCIES

The spatiotemporal structure of the sheath and the ion energy distribution (IED) at the electrode of a collisionless electropositive glow discharge were studied with a model that is valid for arbitrary radio frequencies (rf). The model is based on the work of P. A. Miller and M. E. Riley [J. Appl. Phys. 82, 3689 (1997)] and uses an effective electric field to which the heavy ions respond. Given the plasma density and electron temperature at the sheath edge, and the waveform of either the potential or total current across the sheath, the spatial and/or temporal profiles of the following quantities were obtained: sheath thickness and capacitance, electron and ion densities, potential, and individual components of the current. An analytic expression for the energy split of the IED function was also obtained. The product ωτi of applied radian frequency ω and ion transit time τi is a critical parameter for describing the sheath dynamics.

Spatially resolved diagnostics of an atmospheric pressure direct current helium microplasma

Optical emission spectroscopy measurements were performed with added trace probe gases in an atmospheric pressure direct current helium microplasma. Spatially resolved measurements (resolution ~6 µm) were taken across a 200 µm slot-type discharge. Gas temperature profiles were determined from N2 emission rotational spectroscopy. Stark splitting of the hydrogen Balmer-β line was used to investigate the electric field distribution in the cathode sheath region. Electron densities were evaluated from the analysis of the spectral line broadening of Hβ emission. The gas temperature was between 350 and 550 K, peaking nearer the cathode and increasing with power. The electron density in the bulk plasma was in the range (4–7) × 1013 cm−3. The electric field peaked at the cathode (~60 kV cm−1) and decayed to small values over a distance of ~50 µm (sheath edge) from the cathode. These experimental data were generally in good agreement with a self-consistent one-dimensional model of the discharge.

Two-Dimensional Self-Consistent Radio Frequency Plasma Simulations Relevant to the Gaseous Electronics Conference RF Reference Cell

Over the past few years multidimensional self-consistent plasma simulations including complex chemistry have been developed which are promising tools for furthering our understanding of reactive gas plasmas and for reactor design and optimization. These simulations must be benchmarked against experimental data obtained in well-characterized systems such as the Gaseous Electronics Conference (GEC) reference cell. Two-dimensional simulations relevant to the GEC Cell are reviewed in this paper with emphasis on fluid simulations. Important features observed experimentally, such as off-axis maxima in the charge density and hot spots of metastable species density near the electrode edges in capacitively-coupled GEC cells, have been captured by these simulations.

Analysis of low pressure rf glow discharges using a continuum model

A continuum model was used to analyze charged particle transport and potential distribution in low‐pressure radio frequency (rf) glow discharges. The method of lines with orthogonal collocation on finite elements for the spatial discretization was found to be an effective numerical technique for solving the model equations. An argonlike (electropositive) discharge was compared to a pure chlorine (electronegative) discharge. The electronegative discharge was found to have much thinner sheaths, much greater potential drop and electric field strength in the bulk plasma, and severe modulation by the applied rf (10 MHz frequency) of the electron temperature, ionization, and excitation rate, even in the bulk. The effect of varying excitation frequency was also examined. The results showed that continuum models can capture the essential features of both kinds of discharges. Integration of these models with neutral species transport and reaction can result in powerful tools for the modeling and design of plasma r...

Molecular dynamics simulation of atomic layer etching of silicon

A molecular dynamics study of 50 eV Ar+ ion bombardment of a Si(100) crystal with a monolayer of adsorbed chlorine was conducted to simulate atomic layer etching (ALET) of Si. The total reaction yield (Si atoms removed per ion) was 0.172; 84% of silicon was removed as SiCl, 8% as elemental Si and 8% as SiCl2. Based on the total yield, an ion dose of 1.16×1016 ions/cm2 is necessary to remove one monolayer of silicon. Reaction occurs during the ps time scale of the ion–solid interaction. Long time‐scale chemistry (100s of ms) which is possible in ion‐assisted etching with simultaneous exposure to neutral and ion beams does not happen in ALET. It was further found that 93% of Si originated from the top silicon layer and 7% from the layer underneath. In addition, some structural ‘‘damage’’ was induced to the top three silicon layers. It appears that perfect ALET of silicon is not possible for an ion energy of 50 eV.

Anisotropic etching of polymer films by high energy (∼100s of eV) oxygen atom neutral beams

An inductively coupled high density plasma source was used to generate an energetic (100s of eV), high flux (equivalent of ∼10s mA/cm2) oxygen atom neutral beam. Positive ions were extracted from the plasma and neutralized by a metal grid with high aspect ratio holes. High rate (up to 0.6 μm/min), microloading-free, high aspect ratio (up to 5:1) etching of polymer with straight sidewalls of sub-0.25 μm features was demonstrated. The polymer etch rate increased with power and showed a shallow maximum with plasma gas pressure. The etch rate increased roughly as the square root of the boundary voltage (which controls neutral beam energy), and was independent of substrate temperature. The latter observation suggests that spontaneous etching did not occur. The degree of neutralization of the extracted ions was estimated to be greater than 99% at the base case conditions used in this work.

Dynamics of ion-ion plasmas under radio frequency bias

A time-dependent one-dimensional fluid model was developed to study the dynamics of a positive ion-negative ion (ion-ion) plasma under the influence of a rf bias voltage. The full ion momentum and continuity equations were coupled to the Poisson equation for the electrostatic field. Special emphasis was placed on the effect of applied bias frequency. Due to the lower temperature and greater mass of negative ions compared to electrons, the sheath structure in ion-ion plasmas differs significantly from that of conventional electron-ion plasmas, and shows profound structure changes as the bias frequency is varied. For low bias frequencies (100 kHz), the charge distribution in the sheath is monotonic (switching from positive to negative) during each half cycle. For intermediate frequencies (10 MHz), when the bias period approaches the ion transit time through the sheath, double layers form with both positive and negative charges coexisting in the sheath. For high frequencies (60 MHz), beyond the plasma freque...