Computer calculation of neutral–radical densities in a CF4 electron cyclotron resonance plasma processing system

Abstract

The steady-state densities of neutral–radical species in a CF4 electron-cyclotron-resonance (ECR) plasma were calculated based on the following drift-diffusion equation: Kni(r,t)/∂t=−ℏ⋅(uin)+Di∇2ni+ ∑jnkijnj +∑j,mnjkijmnm− ni(∑jnekji +∑j,mkj imnm), where ni is the density, ui is the drift velocity, and Di is the diffusion coefficient of species i, and ne is the electron density, and k’s are the chemical rate coefficients. The above equation was solved in cylindrical coordinates using finite differences assuming symmetry in the azimuthal direction. The densities of the radical species were obtained for pressures between 1.0 and 2.5 mTorr in increments of 0.5 mTorr and the ECR power in a range between 500 and 900 W. The chemical rate coefficients were calculated directly from the convolution of electron-impact cross sections with the electron energy distribution function, and experimental plasma parameters, otherwise the best available chemical reaction rates were taken from the literature. Diffusion coefficients were calculated from the Lennard–Jones parameters of intermolecular potential. The boundary conditions at the walls were based on available heterogeneous reactions and sticking coefficients. The electron densities entered the drift-diffusion equation directly. Results for the chemically dominant radical species such as F, CF3, and CF2 were obtained and compared with experimental measurements. The absolute magnitudes of the radical densities as predicted by the code are within an order of magnitude of the experimental measurements and in almost all cases follow the same trends as parameters are varied.