Integrated framework for the flux calculation of neutral species inside trenches and holes during plasma etching

Abstract

An integrated framework for the neutral flux calculation inside trenches and holes during plasma etching is described, and a comparison between the two types of structure in a number of applications is presented. First, a detailed and functional set of equations for the neutral and ion flux calculations inside long trenches and holes with cylindrical symmetry is explicitly formulated. This set is based on early works [T. S. Cale and G. B. Raupp, J. Vac. Sci. Technol. B 8, 1242 (1990); V. K. Singh et al., J. Vac. Sci. Technol. B 10, 1091 (1992)], and includes new equations for the case of holes with cylindrical symmetry. Second, a method for the solution of the respective numerical task, i.e., one or a set of linear or nonlinear integral equations, is described. This method includes a coupling algorithm with a surface chemistry model and resolves the singularity problem of the integral equations. Third, the fluxes inside trenches and holes are compared. The flux from reemission is the major portion of the local flux at the bottom of both types of structure. The framework is applied in SiO2 etching by fluorocarbon plasmas to predict the increased intensity of reactive ion etching lag in SiO2 holes compared to trenches. It is also applied in deep Si etching: By calculating the flux of F atoms at the bottom of very high aspect ratio (up to 150) Si trenches and holes during the gas chopping process, the aspect ratio at which the flux of F atoms is eliminated and etching practically stops is estimated.