A unified global model accompanied with a voltage and current sensor for low-pressure capacitively coupled RF discharge

Abstract A global model (GM) assumes ion energy ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>ε</mml:mi> </mml:math> ) on the electrode equals the time-averaged sheath voltage ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mfenced close="〉" open="〈"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>V</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">sh</mml:mi> </mml:mrow> </mml:msub> <mml:mrow> <mml:mfenced close=")" open="("> <mml:mrow> <mml:mi>t</mml:mi> </mml:mrow> </mml:mfenced> </mml:mrow> </mml:mrow> </mml:mfenced> </mml:mrow> <mml:mrow> <mml:mi>t</mml:mi> </mml:mrow> </mml:msub> </mml:math> ). However, using particle-in-cell simulation, we found that <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>ε</mml:mi> </mml:math> differs from <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mfenced close="〉" open="〈"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>V</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">sh</mml:mi> </mml:mrow> </mml:msub> <mml:mrow> <mml:mfenced close=")" open="("> <mml:mrow> <mml:mi>t</mml:mi> </mml:mrow> </mml:mfenced> </mml:mrow> </mml:mrow> </mml:mfenced> </mml:mrow> <mml:mrow> <mml:mi>t</mml:mi> </mml:mrow> </mml:msub> <mml:mo>.</mml:mo> </mml:math> We propose a unified global model (UGM) that calculates <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>ε</mml:mi> </mml:math> and collisional energy losses of ions by employing plasma circuit and sheath models, accompanied by a voltage and current sensor. We compared the results of the UGM with the experimental measurements and the results revealed that UGM is closer to the experiment than GM. UGM shows a linear relationship with the experiment, indicating that the UGM is applicable for plasma monitoring.