Active Compensation in RF-Driven Plasmas by Means of Differential Evolution

Abstract

In this section two different stochastic optimization methods are discussed and compared. They were applied to the deduction of 14 Fourier terms in a radio-frequency (RF) waveform to tune a Langmuir probe. Langmuir probes are diagnostic tools used to analyze the electron energy distribution in plasma processes. RF plasmas are inherently nonlinear, and many harmonics of the driving fundamental are generated in the plasma. RF components across the probe sheath distort the measurements made by the probes. To improve the quality of the measurements, these RF components must be removed. In this research, this was achieved by applying an RF signal to the probe tip that matches both the phase and amplitude of the driving RF signal. It also had to match the waveform of the plasma, which is determined by the nonlinearity of the plasma. Here, seven harmonics are used to generate the waveform. Therefore, 14 mutually interacting parameters (seven phases and seven amplitudes) had to be tuned on-line. In this work, two stochastic optimization algorithms were used for automated tuning of the probe — simulated annealing (SA) and differential evolution (DE). SA was previously used for this problem, whereas DE was chosen and compared with SA because of its reported global optimization performance.