Lock-in technique for precise measurement of ion distribution functions

Retarding field energy analyzers are commonly used for the experimental determination of the distribution of ions. Measurements require taking the first derivative of the measured current with respect to the retarding voltage, which limits the accuracy of the results. Here a commercial energy analyzer is combined with a lock-in detection and AC modulation technique to obtain ion distribution functions with an improved dynamic range. The technical realization of the method together with its theoretical motivation are presented. The various challenges for implementing the technique and ways to address them are given. The energy resolution of the method is discussed based on the concept of transfer functions, and the influence of the various adjustable parameters (grid bias voltages, frequency and amplitude of the modulation signal) on the obtained results are studied. The application of the method to an inductive discharge readily shows a dynamic range of more than three orders of magnitude. This dynamic range provides information on additional plasma parameters, such as the potential and the plasma density at the sheath edge and in the center of the discharge. Possibilities for further improvement of the technique are discussed.