Ion flux's pressure dependence in an asymmetric capacitively coupled rf discharge in NF₃

Abstract

Starting from an analytical macroscopic/phenomenological model yielding the self-bias voltage as a function of the absorbed radio-frequency (rf) power of an asymmetric capacitively coupled discharge in NF₃ this paper studies the dependence of the ion flux onto the powered electrode on the gas pressure. An essential feature of the model is the assumption that the ions' drift velocity in the sheath near the powered electrode is proportional to E ^α, where E=−ΔU (U being the self-bias potential), and α is a coefficient depending on the gas pressure and cross section of elastic ion-neutral collisions. The model also considers the role of γ-electrons, stochastic heating as well as the contribution of the active electron current to the global discharge power balance. Numerically solving the model's basic equations one can extract the magnitude of the ion flux (at three different gas pressures) in a technological etching device (Alcatel GIR 220) by using easily measurable quantities, notably the self-bias voltage and absorbed rf power.