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Ion Transport Modeling in Non-Collisional RF Sheaths

A reactor scale ICP plasma model does not adequately resolve the submillimeter scale rf sheaths due to severe disparities in length and times scales. These non-collisional sheaths determine the spread in the ion bombardment energy distribution on the wafer. Analytical models based on "damped potential" has been used by various authors to simplify sheath modeling. However, inherent in these models are some assumptions that may be invalid. In this work we show that simplifying assumptions such as a uniform ion flux may be in error by as much as 200% at 13.56MHz. This work involves solving ion transport in non-collisional rf sheaths. A comprehensive study of the dependence of ion flux and energy on uncertainties in the sheath-presheath (i.e. sheath thickness) boundary will also be done.

Meyyappan, M.↗

A Coupled Plasma-Sheath Model for High Density Sources

High density, low pressure plasmas are used for etching and deposition in microelectronics fabrication processes. The process characteristics are strongly determined by the ion energy distribution (IED) and the ion flux arriving at the substrate that are responsible for desorption of etch products and neutral dissociation at the surface. The ion flux and energy are determined by a self- consistent modeling of the bulk plasma, where the ions and the neutral radicals are produced, and the sheath, where the ions are accelerated. Due to their widely different time scales, it is a formidable task to self-consistently resolve non-collisional sheath in a high density bulk plasma model. In this work, we first describe a coupled plasma-sheath model that attempts to resolve the non-collisional sheath in a reactor scale model. Second, we propose a semianalytical radio frequency (RF) sheath model to improve ion dynamics.

Bose, Deepak↗

A Self-Consistent Plasma-Sheath Model for the Inductively Coupled Plasma Reactor

Accurate determination of ion flux on a wafer requires a self-consistent, multidimensional modeling of plasma reactor that adequately resolves the sheath region adjoining the wafer. This level of modeling is difficult to achieve since non-collisional sheath lengths are usually 3-4 orders of magnitude smaller than the reactor scale. Also, the drift-diffusion equations used for ion transport becomes invalid in the sheath since the ion frictional force is no longer in equilibrium with drift and diffusion forces. The alternative is to use a full momentum equation for each ionic species. In this work we will present results from a self-consistent reactor scale-sheath scale model for 2D inductively coupled plasmas. The goal of this study is to improve the modeling capabilities and assess the importance of additional physics in determining important reactor performance features, such as the ion flux uniformity, coil frequency and configuration effects, etc. Effect of numerical dissipation on the solution quality will also be discussed.

Bose, Deepak↗

Modeling of Sheath Ion-Molecule Reactions in Plasma Enhanced Chemical Vapor Deposition of Carbon Nanotubes

In many plasma simulations, ion-molecule reactions are modeled using ion energy independent reaction rate coefficients that are taken from low temperature selected-ion flow tube experiments. Only exothermic or nearly thermoneutral reactions are considered. This is appropriate for plasma applications such as high-density plasma sources in which sheaths are collisionless and ion temperatures 111 the bulk p!asma do not deviate significantly from the gas temperature. However, for applications at high pressure and large sheath voltages, this assumption does not hold as the sheaths are collisional and ions gain significant energy in the sheaths from Joule heating. Ion temperatures and thus reaction rates vary significantly across the discharge, and endothermic reactions become important in the sheaths. One such application is plasma enhanced chemical vapor deposition of carbon nanotubes in which dc discharges are struck at pressures between 1-20 Torr with applied voltages in the range of 500-700 V. The present work investigates The importance of the inclusion of ion energy dependent ion-molecule reaction rates and the role of collision induced dissociation in generating radicals from the feedstock used in carbon nanotube growth.

Hash, David B.↗