Electron density measurements and calculations in a helium capacitively-coupled radio-frequency plasma

Abstract We report a comparison of inferred electron density ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>n</mml:mi> <mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">e</mml:mi> </mml:mrow> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> ) in a He capacitively-coupled plasma, deduced from laser-collision induced fluorescence measurements, with values computed using a hybrid simulation framework based on particle-in-cell/Monte Carlo collisions simulations and a fluid model for excited He atoms. The studies were carried out for gas pressures between 50 mTorr and 1000 mTorr and peak-to-peak radio-frequency (13.56 MHz) voltages between 150 V and 350 V, in a highly symmetric source equipped with plane-parallel electrodes. A good agreement is found between the experimental and modeling results for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>n</mml:mi> <mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">e</mml:mi> </mml:mrow> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> except at the lowest operating voltages and gas pressures. The (effective) electron temperature ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>T</mml:mi> <mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">e</mml:mi> </mml:mrow> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> ) values derived by the two methods agree as well reasonably within the plasma bulk. The simulation results are used to compare the density distributions of He + and various He excited levels and their major populating and de-populating channels at 100 mTorr and 1000 mTorr.