Plasma parameters deduced from cylindrical probe measurements: determination of the electron density at the ion saturation current

Abstract

This work is devoted to the study of the electron density measured by means of a Langmuir probe at the ion saturation current. Investigations are performed in a microwave expanding plasma in an Ar-N 2 gas mixture. We show that in such a plasma the electron energy distribution function (EEDF) is not a Maxwell-Boltzmann distribution function and we study the ion velocity at the sheath edge and the sheath thickness around the probe in that case. On the basis of previous works given in the literature and by considering a general expression for the EEDF (no assumption concerning the distribution function), we develop a model describing the ion motion in the sheath around the probe by considering both the sheath expansion and the effect of ion-neutral collision processes. This model is tested in Ar-N 2 gas mixtures using different experimental conditions. Results show a good agreement between the electron density values measured in ion saturation current conditions using this model and values measured using other classical methods. These investigations mainly show the efficiency of the method.

Comments on the Bohm Criterion and on the Determination of the Ion Velocity at the Sheath Edge in Non‐Maxwellian Plasma

“…We show that the conditions on the ions velocity defined at the sheath edge in the case of a Maxwellian distribution cannot be used in the case of other distributions like a Druyvesteyn distribution. According to the plasma parameters, we discuss the collisionless condition used in the model, then the condition n i (χ) ≥ n e (χ) in the sheath, used to determine the ion velocity at the sheath edge [3,4,5]. All these results are correlated to previous works [3,4,6,7].…”

“…This condition can be used to determine the ion velocity at the sheath edge. This value is necessary to calculate the electron density at ion saturation of a negative biased Langmuir probe [3,4,5].…”

“…The ion probe current collected decreases with k increasing because the ion velocity at the sheath edge is decreasing, depending on the distribution shape. As expected, the ion energy value at the sheath edge is an important parameter to determine the ion density by means of a Langmuir probe at the ion saturation [3]. In experimental conditions, Poisson equation cannot be resolved so easily because the equation of the electron distribution function is unknown.…”

“…Nowadays the criterion in its initial form defined for Maxwellian electrons, is largely used to describe the sheath produced in the various kinds of cold plasmas, including also non-Maxwellian plasmas. In recent publications [2,3,4,5], authors have pointed out problems due to this error. For example, wrong results have been obtained in the case of the measurements of the electron density by means of Langmuir probe at the ion saturation in non-Maxwellian plasmas.…”

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

“…Then, it is applied in the particular case of the microwave expanding plasma. In this case, we use plasma parameter values previously measured by means of a Langmuir probe in a microwave discharge working in pure argon; 6 we study the sheath expansion around the cylindrical collector ͑Langmuir probe͒. Then, a model is developed in order to determine the drop voltage through the sheath, assuming the collector biased at the floating potential.…”