A Phasor and Particle Model for Coupling between an Auto-Matching Network and Electrical Plasma

Abstract

Summary form given only. In most of the semiconductor fabrication processes such as plasma doping, plasma-enhanced chemical vapor deposition, and plasma etching, electrical plasma (ions and electrons) are involved. To generate the plasma, it is common to use radio-frequency (RF) coupled inductive or capacitive discharge with an external matching network. Verboncoeur et. al. developed a simultaneous potential and circuit solution for ID bounded plasma particle simulation. Gauss' law was applied to the plasma system and the second order finite difference equation was derived for the second order Kirchoff's voltage law for a general voltage-driven RLC circuit. However, an external matching network is more complicated than a simple RLC circuit. In plasma processes such as plasma doping, several matching networks with different frequencies may be applied to the electrodes. Solving the second order Kirchoff's voltage equations pertinent to these complicated matching networks is very difficult. An RF signal going through a general matching network can be described by its absolute amplitude and phase. Based on the phasor analysis, any complicated circuits can be described by several linear equations that can be solved directly. On model combining the plasma particle model and electrical phasor model is developed, so that the coupling of the plasma with any external matching network can be effectively simulated. Using this model, the amplitude and phase of the voltage/current of the external matching network are numerically estimated', an auto-matching network is simulated; the negative DC offset voltage generated with a blocking capacitor is observed. By treating the blocking capacitor as a phasor element, the model can handle quasi-matching condition. It is shown that the model can simulate non-linear effect.