Effect of the electron energy distribution function in plasma on the Bohm criterion and on the drop voltage through the sheath: Case of microwave expanding plasma

Abstract

This work is devoted to the study of the sheath expansion above a charged species collector immersed into the plasma in the general case of the electron energy distribution function (EEDF) (not necessarily a Boltzmann distributed function). In the first part, considering the general form of the electron kinetic energy distribution function (EEDF) in the plasma and assuming a one dimensional system, we propose an equation describing the limit value of the ion velocity at the sheath edge. Then, we extend this equation to the three dimensional problem. These results are discussed assuming Boltzmann distribution for the one dimensional system and Maxwell–Boltzmann distribution in the case of the three dimensional system. Both one and two temperature distributions are considered. Then, the method is applied to experimental results obtained in expanding microwave discharge sustained in argon. In the second part, we study the drop voltage through the sheath that is produced around a cylindrical collector biased at the floating potential. A theoretical model is given, and results are compared with experimental values measured by means of a cylindrical Langmuir probe immersed in microwave expanding plasma. The model agrees with experiments and points out the role of the EEDF profile on the ion velocity at the sheath edge and, consequently, on the drop voltage through the sheath.