Calculation of Ion Bombarding Energy and Its Distribution in rf Sputtering

Abstract

The energy distribution of bombarding ions in typical rf sputtering conditions has been calculated. The Mathieu-type equations of motion of ions and electrons in the cathode-fall region are numerically integrated by a computer with various initial and boundary conditions. The self-biased dc component $V_{\mathrm{dc}}$ is found to be 0.999928 of one-half the peak-to-peak rf potential applied across the cathode dark space, which is in agreement with the value obtained from mobility considerations. The ion energy distribution is found to depend on rf voltage and frequency, dark-space distance, and $\frac{e}{\left(\mathrm{ion}\mathrm{mass}\right)}$ ratio. Physical explanations are provided for the fact that a large percentage of the ions possess energies greater than $e{V}_{\mathrm{dc}}$. The effect of high electron temperature on the ion-energy distribution has been studied and found to be very small. Trajectories of both the ion and electron in the cathode-fall region have also been calculated.