Floating double probe in non-Maxwellian plasmas: Determination of the electron density and mean electron energy

A theoretical study of the floating double probe based on the Druyvesteyn theory is developed in the case of non-Maxwellian electron energy distribution functions (EEDFs). It is used to calculate the EEDF in the electron energy range larger than -e(V-f - V-p) from the I-V double probe characteristics. V-f and V-p are the floating and plasma potential, respectively. The analytical distribution function corresponding to the best fit of EEDF in the energy range larger than e(V-f - V-p) allows the determination of the total electron density (n(e)) and the mean electron energy (). The method is detailed and tested in the case of a theoretical Maxwell-Boltzmann distribution function. It is applied for experiments that are performed in expanding microwave plasmas sustained in argon. Analytical EEDFs determined by this method are compared with those measured by means of single probes under the same experimental conditions. A good agreement is observed between single and double probe measurements. Results obtained under different experimental conditions are used to define the best conditions to obtain reliable results by means of the double probe technique.