Hollow neutral pressure profiles, with significant on-axis reductions in neutral pressure (up to 40%), are observed across the face of an inert wafer in discharges with uniform plasma density. These results show that significant neutral depletion, which may cause the nonuniform plasma process results, can occur in large-area high-density plasma sources with a wafer present. The neutral depletion is explained by the ion pumping effect, wherein electron impact ionization of neutral particles is followed by their rapid movement from the plasma to the chamber wall by the presheath electric field. Cooling of plasma electrons via inelastic neutral collisions is also observed at elevated fill pressure, and results in a reduction of the magnitude of neutral depletion, thus demonstrating the linkage between plasma equilibrium and neutral equilibrium conditions. Initial experiments have also been performed in O2 discharges. Similar hollow neutral pressure profiles are observed, suggesting that similar effects occur in chemically reactive discharges.

Measurement of radial neutral pressure and plasma density profiles in various plasma conditions in large-area high-density plasma sources

Plasma uniformity has been recognized as a significant parameter in large-sized high density plasma processing tools, but neutral uniformity issues have received less attention. In this article we show experimental and modeling results which indicate that significant neutral uniformity variations can occur in high density plasma processing tools. The experiments are carried out in both inductively coupled plasma and helicon plasma sources. A movable static pressure gauge is used to obtain the static radial neutral pressure distribution both with and without a discharge present. Without a wafer present in the reactor, significant (∼20%–40%) reductions in neutral pressure are observed in these sources during steady-state plasma operations. This spatially averaged neutral depletion is accompanied by hollow neutral pressure profiles. The degree of on-axis neutral depletion depends upon both plasma density and neutral fill pressure. We show that the “plasma pumping” effect, wherein electron impact ionization of neutral particles is followed by their rapid removal from the plasma by the pre-sheath electric field, can reproduce the experimental results. This effect has the potential to result in large (∼50%) neutral density variation across 300 mm wafers in high density plasma sources.

Neutral depletion and transport mechanisms in large-area high density plasma sources

Spectral line broadening due to the Coulomb interaction in plasma

A hydrodynamic description of the positive column is used to study the radial variation of particle densities, drift velocities, temperatures and heat fluxes of electrons, singly-charged ions and neutral atoms and the radial electric field. Elastic collisions between the plasma particles and neutrals as well as Coulomb collisions between ions and electrons are taken into account. The relevant equations to solve are the balance equations of particle densities, momentum, energy and the equations for the heat fluxes for each of the three studied particle types; the Poisson equation has to be added for closure. They form a system of 13 nonlinear differential equations with critical points. One singularity occurs when the ions reach the ion sound velocity which is the case inside the positive column. Therefore, a numerical method for multipoint boundary value problems was used which can also successfully handle removable singular points. The applied relaxation method is an iterative method which demands some preliminary knowl­ edge of the solution looked for. The necessary knowledge can be retrieved from the quasineutral model and from a simplified two-fluid model.

/pdf/numerical-modeling-of-the-non-isothermal-positive-column-of-1fiiptkzv7.pdf

Numerical modeling of the non-isothermal positive column of an Ar+-laser

The transverse distribution of neutral and charged species in mixed gas plasma is calculated within a simplified model. The fluid equations for densities, velocities and self-consistent field are derived and solved numerically. The appearance of a dip in the centre of the heavy-species profile is found and interpreted. The depletion of ions near the centre occurs when the ionization length of the heavy impurity is less than the plasma dimension, while the length remains large for the main gas.

Transverse inhomogeneity of the low-pressure discharge in a gas mixture

A hydrodynamic description of a low-pressure discharge with singly and doubly-charged positive ions in the high ionization regime is given. Modified hydrodynamic equations are used to include the neutral gas depletion by ionization processes under free-flight conditions. Analytical formulas for the concentrations of the two species of ions at the discharge axis are derived.



Numerical results for the radial drift velocities, the radial distributions of the densities and the neutral gas temperature are presented. The nature of the dip in the density profile of the singly-charged ions and the decrease in their radial drift velocity near the axis with increasing degree of ionization are discussed.

Hydrodynamic theory of low-pressure multi-component discharges with neutral gas depletion

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Hydrodynamic theory of low-pressure multi-component discharges with neutral gas depletion