Data processing techniques for ion and electron-energy distribution functions

Retarding field energy analyzers and Langmuir probes are routinely used to obtain ion and electron-energy distribution functions (IEDF and EEDF). These typically require knowledge of the first and second derivatives of the current-voltage characteristics, both of which can be obtained using analog and numerical techniques. A frequent problem with electric-probe plasma diagnostics is the noise from the plasma environment and measurement circuits. This poses challenges inherent to differentiating noisy signals, which often require prior filtering of the raw current-voltage data before evaluating the distribution functions. A review of commonly used filtering and differentiation techniques is presented. It covers analog differentiator circuits, polynomial fitting (Savitzky-Golay filter and B-spline fitting), window filtering (Gaussian and Blackman windows) methods as well as the AC superimposition and Gaussian deconvolution routines. The application of each method on experimental datasets with signal-to-noise ratios ranging from 44 to 66 dB is evaluated with regard to the dynamic range, energy resolution, and signal distortion of the obtained IEDF and EEDF as well as to the deduced plasma parameters.