T. E. Sheridan

Collisional plasma sheath model

The effects of ion collisionality on the plasma sheath are revealed by a two‐fluid model. In contrast to previous work, the ion–neutral collision cross section is modeled using a power law dependence on ion energy. Exact numerical solutions of the model are used to determine the collisional dependence of the sheath width and the ion impact energy at the wall. Approximate analytical solutions appropriate for the collisionless and collisionally dominated regimes are derived. These approximate solutions are used to find the amount of collisionality at the center of the transition regime separating the collisionless and collisional regimes. For the constant ion mean‐free‐path case, the center of the transition regime for the sheath width is at a sheath width of five mean‐free paths. The center of the transition regime for the ion impact energy is at a sheath width of about one‐half of a mean‐free path.

Model of energetic electron transport in magnetron discharges

A particle model of energetic electron transport in sputtering magnetron discharges is presented. The model assumes time‐independent magnetic and electric fields and supposes that scattering by neutral atoms is the dominant transport mechanism. Without scattering, we find that some orbits are confined indefinitely. Using the differential cross sections for elastic, excitation, and ionization collisions in argon, we perform a Monte Carlo simulation of the electrons emitted by ion bombardment of a planar magnetron cathode to predict the spatial distribution of ionization. We find good agreement with experimental measurements of the radial profile of ion flux to the cathode and of the axial profile of optical emission.

Positive ion flux from a low-pressure electronegative discharge

We compute the flux of positive ions exiting a low-pressure, planar, electronegative discharge as a function of the negative ion concentration and temperature. The positive ions are modelled as a cold, collisionless fluid, while both the electron and negative ion densities obey Boltzmann relations. For the plasma approximation, the plasma edge potential is double-valued when the negative ions are sufficiently cold. When strict charge neutrality is relaxed, spatial space-charge oscillations are observed at the edge of the plasma when the flux associated with the low (in absolute value) potential solution is less than that of the high potential solution. However, the flux is always well defined and varies continuously with the negative ion concentration. We demonstrate that the correct solution for the plasma approximation is that having the greater flux.

Observation of two‐temperature electrons in a sputtering magnetron plasma

We experimentally find that there are hot and cold electron components present in a sputtering magnetron plasma. The density of the hot component is greatest in the magnetic trap and decreases with the distance from the cathode. The cold electron density is negligible inside the trap and is approximately constant outside. The largest cold electron density is nearly as great as the hot electron density inside the magnetic trap.

Absolute measurements and modeling of radio frequency electric fields using a retarding field energy analyzer

Measurements of the rf electric field have been made along the z axis of a helicon reactor using a retarding field energy analyzer. A fluid code and a simple analytical model have been developed to analyze the ion energy distribution functions, especially in the case of bimodal distributions where the ion transit time through the sheath in front of the analyzer is comparable to the rf period. A generalized curve (and an analytical approximation to that curve) has been developed from the analytical model and confirmed by the self-consistent fluid model for high, low, and intermediate ion transit time, which can be used by experimenters to quickly convert the experimental results (energy peak separation, plasma potential and density, electron temperature), which are related to rf sheath oscillations, to absolute values of the rf electric field. An analysis of the errors involved in the derivation of the field is given. The results agree qualitatively with rf pickup measured with a floating Langmuir probe.

How big is a small Langmuir probe

The area of the sheath around a thin, disk-shaped electrode that is biased below the plasma potential has been computed using a hybrid simulation with cold, collisionless ions and Boltzmann electrons. That is, the “collecting area” of a double-sided, planar Langmuir probe has been determined for the ion saturation current regime. Sheath areas are calculated for probe radii from 10 to 45 electron Debye lengths and for probe biases from −5 to −30 times the electron temperature. The dependence of the sheath area on probe radius and bias is parameterized using simple empirical formulas.

Monte Carlo simulation of ions in a magnetron plasma

A simulation of ion dynamics in a planar magnetron discharge is performed using separate three-dimensional Monte Carlo codes for the electrons and ions. First, to predict the ionization sites, the orbits of energetic electrons are simulated for prescribed DC electric and magnetic fields, subject to collision with neutrals at random intervals. In the second code the predicted sites are used as the starting positions of ion trajectories. The ion trajectories are followed taking into account collisions with neutrals, turbulent electric fields, and the DC field. The authors report results for ion impact on the cathode and substrate anode surfaces (energy, angle, and spatial distribution) and ion parameters in the plasma (density, drift velocity, random energy, and transit time). To test these results they compare them to several previously reported experiments, and in most cases find good agreement. These simulation methods not only are useful for gaining an understanding of the magnetron plasma operation, but may also aid in designing magnetrons. >

Ion‐matrix sheath in a cylindrical bore

The potential structure, electric field, and sheath width for the ion‐matrix sheath in a cylindrical bore are calculated. The appropriate scaling length for this problem is found to be √2 times larger than the planar ion matrix sheath width. If the radius of the bore is less than this scaling length, then the sheaths from ‘‘opposite’’ sides of the bore overlap, and the potential drop from the axis to the sidewalls decreases with the square of the bore radius. This limits the maximum energy of ions impacting the target. For bores larger than this scaling length, the asymptotic planar solutions are rapidly approached.

Ion focusing by an expanding, two‐dimensional plasma sheath

The temporal evolution of the collisionless, pulsed plasma sheath around a square bar is studied using a two‐dimensional particle‐in‐cell code. It is found that the incident ion dose is peaked near to, but not on, the corner. This effect is explained physically by considering ion trajectories across the sheath, yielding an estimate for the dose in good agreement with the simulation results. The present results are compared to those from a fluid simulation [T. E. Sheridan and M. J. Alport, Appl. Phys. Lett. 64, 1783 (1994)], and it is found that the fluid simulation erroneously underestimates the ion dose near the corner of the bar.

Observation of ion-cyclotron turbulence at small values of magnetic-field-aligned current

Fluctuations in plasma density are observed in the ion-cyclotron frequency range in a Q-machine plasma column at values of magnetic-field-aligned current significantly below the critical value for current-driven electrostatic ion-cyclotron (CDEIC) waves. These fluctuations arise from the inhomogeneous energy-density driven (IEDD) instability, are relatively broadband, and can have large amplitude compared to CDEIC fluctuations. These results impact the interpretation of ion heating and acceleration in the ionosphere, especially at low-altitude where magnetic- field-aligned current densities estimated to be large enough to be supercritical to current-driven or beam-driven electrostatic ion-cyclotron waves are rarely detected.