2D electromagnetic fluid simulations of the Alpha/Gamma transition in large area collisional nitrogen capacitive discharges

Abstract Intermediate pressure (0.2 to 6 Torr) capacitive discharges with feedstock mixtures containing N 2 are commonly used for thin film processing. Using previous one-dimensional (1D) particle-in-cell (PIC) simulations of an intermediate pressure capacitive N 2 discharge, (Kawamura et al 2021 Plasma Sources Sci. Technol. 30 035001) we develop a 2D electromagnetic (EM) fluid model including secondary emission to study the effect of the α to γ transition on plasma uniformity in a large area 1.6 Torr N 2 reactor with radius R = 1.8 m and gap size l = 2.5 cm. In the α -mode, the hot γ electrons due to ion-induced secondary emission from the electrodes play a minimal role in the discharge while, in the γ -mode, they are essential for its maintenance. The 1D PIC simulations of a 2.5 cm gap, 1.6 Torr N 2 capacitive discharge showed an α to γ transition, characterized by a rise in density and a collapse of the sheath widths when the rf sheath voltage amplitude V 1 exceeded a breakdown voltage <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>V</mml:mi> <mml:mtext>B</mml:mtext> </mml:msub> </mml:mrow> </mml:math> . Smaller sheath widths enhance EM effects which may negatively affect plasma uniformity and stability. In the 2D EM fluid simulations at lower powers, the discharge is fully in the α -mode with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>V</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>&lt;</mml:mo> <mml:msub> <mml:mi>V</mml:mi> <mml:mtext>B</mml:mtext> </mml:msub> </mml:mrow> </mml:math> for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mn>0</mml:mn> <mml:mtext>⩽</mml:mtext> <mml:mi>r</mml:mi> <mml:mtext>⩽</mml:mtext> <mml:mi>R</mml:mi> </mml:mrow> </mml:math> . As power is raised, the enhanced finite wavelength effect causes <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>V</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>&gt;</mml:mo> <mml:msub> <mml:mi>V</mml:mi> <mml:mtext>B</mml:mtext> </mml:msub> </mml:mrow> </mml:math> ( γ -mode) toward the radial center, and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>V</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>&lt;</mml:mo> <mml:msub> <mml:mi>V</mml:mi> <mml:mtext>B</mml:mtext> </mml:msub> </mml:mrow> </mml:math> ( α -mode) toward the radial edge with the transition point <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>r</mml:mi> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>r</mml:mi> <mml:mtext>B</mml:mtext> </mml:msub> </mml:mrow> </mml:math> approaching R . A fully γ -mode discharge where <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>V</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>&gt;</mml:mo> <mml:msub> <mml:mi>V</mml:mi> <mml:mtext>B</mml:mtext> </mml:msub> </mml:mrow> </mml:math> for all r is obtainable at 6.78 MHz but not at 13.56 MHz due to the enhanced EM effect at the higher frequency.