Novel Methodology for Characterizing Non-Linear Harmonics in Radio Frequency Discharges

Abstract

This paper presents an accurate, non-invasive diagnostic technique for analyzing the harmonics generated by plasma <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1, 2</sup> in parallel plate radio frequency (RF) discharges utilizing a broadband Dual Directional Coupler (DDC) that can measure accurately both the forward and reflected voltage signals in a transmission line. For monitoring signals containing the harmonics, the DDC is placed in close proximity of the powered electrode in an asymmetric, parallel plate RF discharge at 13.56 MHz, with 10–50 W (cw) power at 200 mTorr of argon gas pressure. The voltage signals obtained from the DDC data are a superposition of the fundamental and its harmonics that are produced by the plasma. These are separated using Fast Fourier Transform (FFT) technique carefully to avoid aliasing errors. A careful and complete analysis not only determines the harmonics present in plasma, but also yields accurately the power content in the forward and reflected waves of the fundamental along with other harmonics generated in the plasma. One can also estimate the complex plasma impedance, reflection coefficient, VSWR etc. at the plasma end which also makes it a valuable diagnostic tool <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> . In present experiment, the harmonic spectrum shows that the 3 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rd</sup> harmonic is the dominant harmonic, followed by the 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nd</sup> and 4 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> . Typically, one has for the 3 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rd</sup> harmonic ≈ 4.87 mW to 72.31 mW from 10 to 50 W of input RF power. Furthermore, using a simplified RF equivalent circuit model that includes the internal plasma source impedance Zg and the sheath impedance ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathrm{Z}_{\text{sh}}$</tex> ), one can estimate the strength of lumped RF voltage source <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\left\vert V_{rf}^{pl}\right\vert$</tex> for all harmonics induced in RF discharge.