Global model for high pressure electronegative radio-frequency discharges

Abstract

We develop a global model for high pressure (0.1–1 Torr) electronegative rf discharges and apply it to model a capacitively driven plasma etcher. The molecular gases considered consist of either pure chlorine species or a mixture of chlorine and helium species. The charged and neutral heavy particle densities together with the electron density and electron temperature are calculated by using the equations of particle balance and power balance for the input discharge parameters rf power or rf current, inlet pressure, gas flow rates, reactor diameter, and gap spacing. The power is deposited in the electrons via ohmic heating and in those ions accelerated across the dc sheath potential. The voltage across the sheath is calculated self-consistently with the densities and the electron temperature by using a collisional Child law sheath model. Analytic scaling laws for the dependence of charged and neutral particle densities, electron temperature, rf voltage and current, sheath width, and plasma impedance on pressure and absorbed rf power are presented and used to explain the numerical results obtained from the global model. The model results are compared to recent experimental measurements in a chlorine discharge over a range of absorbed power Pabs=20–180 W at an inlet pressure pin=0.4 Torr and a range of pressure 0.1–1.6 Torr with a fixed input power of 100 W. We obtain reasonable agreement for Pabs<200 W and for 0.2 Torr<pin<1 Torr.

Modeling of the plasma chemistry and plasma–surface interactions in reactive plasmas

“…We try to obtain this insight by computer simulations. Several modeling approaches exist for plasmas, such as analytical models [1,2], fluid models [3,4], the Boltzmann equation [5], Monte Carlo (MC) [6,7], and particle-in-cell MC simulations [8,9], collisional-radiative (CR) models [10,11], as well as hybrid models, which are a combination of the above models [12][13][14]. For describing the plasma chemistry, fluid modeling is, however, the most suitable approach, because a large number of plasma species and chemical reactions can be taken into ac-In these equations, n, j, and R stand for the species number density, flux, and production or loss rate.…”

The parameters of plasma and the kinetics of generation and loss of active particles under conditions of discharge in HCl

“…The probe diagnostics of plasma produced data on the axial intensity of electric field E in the zone of positive column of the discharge (double Langmuir probe) and on the density of ion flux to the wall Γ + (plane wall probe). In determining the reduced field intensity (E/N) and in simulating the discharge, the temperature and concentration of particles were averaged assuming that the profiles of radial distribution of these parameters were preassigned [10,11].…”

“…The output parameters of the model included the electron energy distribution function (EEDF), the integral characteristics of electron gas (mean energy, drift velocity, reduced diffusion coefficient, and mobility), the rates of elementary processes, the plasma bulk average concentrations of particles, and their fluxes to the surface. In realizing the self-consistent algorithm of discharge modeling, the criterion of termination of calculation by the parameter E/N was the validity of the condition R F = = R D + ν D n e , where R F and R D are the plasma bulk average rates of generation and loss of electrons in bulk processes, respectively, and ν D is the rate of diffusion loss of electrons: ν D = D/Λ 2 , Λ ≈ r/2.405 is the diffusion length [10], r is the reactor radius. The effective diffusion coefficient was determined as [10] ,…”

“…In realizing the self-consistent algorithm of discharge modeling, the criterion of termination of calculation by the parameter E/N was the validity of the condition R F = = R D + ν D n e , where R F and R D are the plasma bulk average rates of generation and loss of electrons in bulk processes, respectively, and ν D is the rate of diffusion loss of electrons: ν D = D/Λ 2 , Λ ≈ r/2.405 is the diffusion length [10], r is the reactor radius. The effective diffusion coefficient was determined as [10] ,…”

Computer Simulations for Processing Plasmas

“…In the literature, there exist different modeling approaches for processing plasmas. In analytical models ,1 analytical formulas describe the dependency of certain plasma quantities from macroscopic parameters (e.g., voltage, current). This method can quickly predict the plasma behavior, but it is only an approximation, valid for a limited range of conditions.…”