Electron Energy Distribution Function Extraction Using Integrated Step Function Response and Regularization Methods

Recently, electron energy distribution function (EEDF) extraction techniques have been evaluated using regularized solutions to the integral problem. These techniques do not assume any mathematical representation of the EEDF and solve the integral problem for any function that best represents the EEDF. Also, unlike the more widely used point-by-point extraction of the second-derivative relationship, the integrated relationship between electron current and the EEDF is used, instead of a relatively small fraction of the integrated data in the point-by-point method. In this paper, the electron current for an arbitrary distribution function is derived, assuming that the distribution is a sum of step functions representing such a function. This technique for EEDF extraction is validated by adding noise to numerically generated data and using a regularized least squares (RLS) method to calculate the original function by solving for the individual step function contribution to the total electron current. Comparisons are then made between the expected and the reconstructed solution to evaluate its accuracy with respect to EEDF reconstruction and integrated normalization of the electron density.