Dependence of electric potentials at trench surfaces on ion angular distribution in plasma etching processes

Abstract

Ion-stimulated etching of dielectrics in radio frequency plasma results in positive charging of a trench bottom because of the significant difference in the angular distribution functions of ions and electrons. They are anisotropic for ions and quasi-isotropic for electrons. The charging leads to a decrease in the energy of the ions bombarding the trench bottom and to undesirable sputtering of the walls near the trench bottom because of the curving of the ion trajectories. This process is normally investigated by Monte Carlo methods in the absence of experimental data. In this paper the analytical dependence of the ion flux bombarding the trench bottom on a trench aspect ratio and ion angular distribution function is obtained. Numerical calculations of the electric potential on the trench bottom for a set of trench aspect ratios and angles of the ion angular distribution function were performed based on a Monte Carlo method to demonstrate the ion flux and electric potential correlated well with each other. The proposed formula for an ion flux is suggested to be helpful for analyzing charging the trenches with different aspect ratios in plasma with an arbitrary angular ion distribution function.