Electrical and Optical Diagnostics to Measure the Electron Plasma Frequency

The electron plasma frequency is a fundamental parameter of plasmas. As the governing equation of the electron plasma frequency (ω_pe) is ω_pe=[(n_ee²)/(ε₀m)]^0.5 , one can obtain the absolute electron density from the measured ω_pe. In this invited talk, we will introduce electrical and optical methods of measuring the electron plasma frequency for non-invasive, non-perturbing, and precise plasma monitoring. The electrical method is based on the microwave cutoff probe [1], but it is modified to a flat-type sensor that can be imbedded into the substrate chuck or chamber wall. We focus on a bar-type flat-cutoff sensor, called BCP, owing to its simple structure, absence of unwanted resonance signals, and high signal-to-noise ratio, as well as the precise measurement of ω_pe [2-4]. The optical method for obtaining ω_pe is to measure the time interval between multiple electron beams generated during a single phase of sheath expansion at one of the electrodes by phase resolved optical emission spectroscopy. A previous study [5] clearly showed experimental evidence of such multiple electron beam generation at frequencies corresponding to the local electron plasma frequency in a radio-frequency (RF) capacitive discharge, caused by the plasma perturbation through the electron beam propagation. Thus, we propose a new method for measuring the electron plasma frequency by using the time interval between the electron beam optical emission maxima in the presence of an oscillating RF sheath. The electron plasma frequency and density measured by this optical diagnostic coincides with those obtained from the electrical method.