To Describe Non Maxwellian Electrons by Maxwellian Distributions

Summary form only given. To numerically simulate a radio-frequency (RF) coupled discharged plasma, we can use the particle-in-cell (PIC) approach. The ion and electron motions are simulated by an ensemble of PIC particles. The external driving force from the RF source will be obtained by solving Poisson´s equation. To successfully resolve the electron motion, the finite difference cell length must be less than the electron Debye length and the time step must be less than the inverse of electron plasma frequency. For a typical RF coupled partially discharged plasma, it will take a long time to carry out a simulation. An alternative is to describe the electron density by Boltzmann´s relation. It is well known that in a low pressure partially ionized plasma at room temperature, the ions are rarely in thermal equilibrium but the electrons are generally in near-thermal equilibrium. Taking the bulk plasma density as a reference point, the Boltzmann´s relation has been used extensively in simulating plasma immersion ion implantation process with great success. However, in RF coupled discharge plasma, the space potential at the bulk plasma will vary with the RF signal. A lack of a referencing potential make it hard to apply Boltzmann´s relation in simulating RF coupled discharged plasma. In this work, we extend the use of Boltzmann´s relation in simulating RF coupled discharged plasma. A reference electron density is calculated and the related reference potential is estimated by bisection method. We will apply our method to simulate bi-Maxwellian electrons by introducing two Boltzmann´s relations to describe the cold and hot thermal electrons in low pressure RF coupled discharge plasma