Effective thermo-electric-mechanical modeling of capacitively coupled plasma in low-pressure conditions: Modeling and application in dry etching

Abstract

In semiconductor dry etching process, capacitively coupled plasma (CCP) is widely used in low-pressure environments. However, the kinetics of species particles in low-pressure conditions are different from the general environments. Traditional continuum models are popular in industry due to their simplicity, but they struggle to account for the kinetics of particles in low-pressure conditions. Although particle-in-cell (PIC) modeling is suitable for simulating the behavior of a single particle, it is difficult to perform such industrial simulations due to the high computational cost. To account for both kinetics and engineering applicability, this study presents an effective thermo-electric-mechanical modeling structure of CCP at low-pressure conditions. This modeling structure includes balance laws of continua derived from the global energy equilibrium containing thermal, electric and mechanical energies. The ion momentum, which is ignored in traditional plasma continuum models, is considered in the balance laws, and electron energy distributions are obtained by solving the Boltzmann equation to obtain the properties of electron transport. In addition, the model variables are calculated based on mixed kinetic theory accounting for the fraction of each species. The results of the proposed modeling are compared to those of a PIC model to validate its ability to describe the distribution of electrons with respect to pressure conditions. Based on the proposed numerical formulations, this study built a MATLAB-based program to guide the design of a screen baffle in dry etching equipment. This program captures the critical aspects of the practical application of screen baffle design in the context of the dry etching process. The results of this paper showed that the proposed model can be applied to engineering applications under low-pressure conditions.