Scaling laws for oxygen plasmas

Abstract

Summary form only given. Electronegative gases are widely used in modern plasma technologies. Scaling laws enable one to simply estimate and predict plasma characteristics based of external discharge parameters. The presence of negative ions drastically changes the transport processes that define the spatial distributions of plasma components and other properties of the plasma. That is why the existing scaling laws for electropositive gases are not directly applicable to electronegative plasmas. The scaling laws can be derived using a global model of a plasma reactor that assumes certain spatial distributions of charged species. The developed global models of electronegative plasmas assumed that the spatial distributions of negatively charged species are governed by the Boltzmann equilibrium with different ion and electron temperatures. However, it has been recently shown that this assumption is not valid in the general case. Moreover, the relative importance of the ion-ion recombination and detachment has not been properly accounted for even for the most extensively studied oxygen plasmas requiring revision of the previously published results. The goal of this work is to derive scaling laws for electronegative plasmas using the approach described by Rozhansky and Tsendin (2001). This approach accounts for proper spatial distributions of charged species in the plasma and finds the ionization rate as an eigenvalue problem. The principal feature of electronegative plasmas is separation of the plasma onto a core with abundance of negative ions and a shell where the negative ions are practically absent. We restrict ourselves to the low pressure case when the positive ion loss to the wall due to diffusion dominates over volume recombination. The dependencies of plasma properties upon input parameters pL (the product of gas pressure p and characteristic size of the plasma L), and power density W adsorbed in the plasma have been obtained for oxygen plasma for the parameters range most important for microelectronics applications To verify scaling laws, 2-D simulations of an Inductively Coupled Plasma in Oxygen have been performed in the pressure range ==20-1000 mTorr and power densities W= 10/sup 3/-3.6/spl times/10/sup 4/ W/m/sup 3/ in a cylindrical reactor of radius R=15.42 cm and height H=7.62 cm. A fluid model of plasma has been used taking into account O/sub 2/, O, O/sub 2/*, O/sup -/ and O/sub 2/*. Three types of spatial distributions of the charged species have been observed in the simulations. At low pressures, a parabolic ion density profile and a flat electron distribution has been obtained. With increasing gas pressure, top-flat profiles of ions and electrons have been observed. Finally, nonmonotonic profiles with a minimum in the center and a maximum on the periphery of the discharge have been obtained similar to those experimentally observed by Buddemeier (1997).