Gas pressure effects on the instabilities in direct current magnetron discharges

Abstract Instabilities in direct current magnetron discharges under different gas pressures are explored by means of two dimensional axial-azimuthal ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>z</mml:mi> <mml:mo>−</mml:mo> <mml:mi>θ</mml:mi> </mml:mrow> </mml:math> ) particle-in-cell/Monte Carlo collision method. As the gas pressure increases, four distinct regimes of the instability are identified: the rotating spoke-electron cyclotron drift instability (ECDI) regime, the spoke dominated regime, the lower hybrid drift instability regime and the drift dissipative instability regime. These fluctuations are found to occur in the vicinity of the sheath-plasma transition region, and are hereby driven by the evident <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mtext mathvariant="bold">E</mml:mtext> <mml:mo>×</mml:mo> <mml:mtext mathvariant="bold">B</mml:mtext> </mml:mrow> </mml:math> drift (except for the drift dissipative instability). Under typical pressures of magnetron discharges <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>∼</mml:mo> <mml:mstyle scriptlevel="0"/> <mml:mstyle scriptlevel="0"/> <mml:mn>1</mml:mn> <mml:mstyle scriptlevel="0"/> <mml:mtext>Pa</mml:mtext> </mml:mrow> </mml:math> , the spoke is found to rotate in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mo>−</mml:mo> <mml:mtext mathvariant="bold">E</mml:mtext> <mml:mo>×</mml:mo> <mml:mtext mathvariant="bold">B</mml:mtext> </mml:mrow> </mml:math> direction and originates from the generalized Simon–Hoh instability (SHI) with the magnetic field non-uniformity accounted for. The kinetic simulations clearly show that the spoke mode number increases with the gas pressure, in good agreement with the available experimental data. The spoke dominant mode keeps almost unchanged during the linear-nonlinear evolution, suggesting that the spoke mode number can be determined by the plasma equilibrium in the linear stage of generalized SHI. The coexistence of spoke and ECDI is detected in the low pressures, consistent with the previous experimental observations. The transition from spoke to lower hybrid drift instability that propagates in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mo>+</mml:mo> <mml:mtext mathvariant="bold">E</mml:mtext> <mml:mo>×</mml:mo> <mml:mtext mathvariant="bold">B</mml:mtext> </mml:mrow> </mml:math> direction occurs in the medium pressures <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>∼</mml:mo> <mml:mstyle scriptlevel="0"/> <mml:mstyle scriptlevel="0"/> <mml:mn>15</mml:mn> <mml:mstyle scriptlevel="0"/> <mml:mtext>Pa</mml:mtext> </mml:mrow> </mml:math> . With gas pressure further increasing beyond <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>∼</mml:mo> <mml:mstyle scriptlevel="0"/> <mml:mstyle scriptlevel="0"/> <mml:mn>40</mml:mn> <mml:mstyle scriptlevel="0"/> <mml:mtext>Pa</mml:mtext> </mml:mrow> </mml:math> , collisional effect is appreciable and the local axial electric field becomes negligible, resulting in the drift dissipative instability.