Modeling and parameter analysis of plasma cleaning

A simple mathematical model based on Berg's original work for reactive sputtering is introduced to study the plasma cleaning process. The governing equations are formulated by overall mass balance for the gases inside the chamber and compounds on the substrate surface. Several non-dimensional parameters were identified along with their physical meanings to non-dimensionalize the governing equations. Solutions were obtained analytically and studied parametrically. Results show that the existence of reactive gas in a chamber could prevent the compound fraction being reduced to zero by ion sputtering. Increasing the reactive gas flux would increase the compound fraction and sputtering rate but lower the reactive gas concentration. At steady state, when the reactive gas flux is dominant, asymptotic values for compound fraction, reactive gas concentration and sputtering rate can be derived. A minimum value for the inflow rate at steady state is also identified as the starting threshold of a cleaning process.