Validating experimental and theoretical Langmuir probe analyses

Abstract

Analysis of Langmuir probe characteristics contains a paradox in that it is unknown a priori which theory is applicable before it is applied. Often theories are assumed to be correct when certain criteria are met although they may not validate the approach used. We have analysed the Langmuir probe data from cylindrical double and single probes acquired from a dc discharge plasma over a wide variety of conditions. This discharge contains a dual-temperature distribution and hence fitting a theoretically generated curve is impractical. To determine the densities, an examination of the current theories was necessary. For the conditions where the probe radius is the same order of magnitude as the Debye length, the gradient expected for orbital-motion limited (OML) is approximately the same as the radial-motion gradients. An analysis of the 'gradients' from the radial-motion theory was able to resolve the differences from the OML gradient value of two. The method was also able to determine whether radial or OML theories applied without knowledge of the electron temperature, or separation of the ion and electron contributions. Only the value of the space potential is necessary to determine the applicable theory.

Short- and long-term plasma phenomena in a HiPIMS discharge

“…Ion density: The Orbital Motion Limited theory (OML) is used to interpret ion current and ion density. For OML theory to be valid, the sheath surrounding the probe should be collision-less, which is generally valid for the condition ξ = (r p /λ De ) < 1 [66].…”

“…Using an appropriate model for charged particle collection in collisionless conditions, the ion and electron density can be determined directly from the saturation regions of the I-V characteristic without the knowledge of electron temperature. To be able to assume collision-less sheath conditions and therefore a simple probe analysis, the probe radius and the Debye screening length, λ De = ( 0 T e /en e ) 1/2 , should be less than both the electron-neutral λ en and ion-neutral λ in mean-free-paths [66,67]. In HiPIMS discharges, with plasma densities varying typically between 10 9 to 10 12 cm −3 , one calculates that λ De ∼ 0.010 -0.19 mm, λ en ∼ 20 -117 mm, λ in ∼ 9 -27 mm for electron energies typically between 5 and 100 eV and therefore the conditions…”

Plasma parameters controlled by remote electron shower in a double plasma device

“…From the application of the semi log plot method to the Langmuir probe data taken in the source sec tion, the dual electron temperatures are obtained after the removal of ion current component [11]. This is shown in Fig.…”

Influence of the Ion Mass in the Radial to Orbital Transition in Weakly Collisional Low-Pressure Plasmas Using Cylindrical Langmuir Probes

“…When the values of the plasma parameters deduced from these theories are compared to the values of the plasma parameters obtained using the much higher electron current in the electron saturation zone, depending on the plasma conditions, it is found that either the radial or the orbital theories are consistent with the well-established electron saturation zone theory. This implies a paradox when the ion current is used in plasma diagnosis, given that the appropriate theory that should be used is not known a priori before it is used in plasma diagnosis [1,4,25]. Actually, in many situations which depend on the plasma discharge power and the pressure, values for the ion current collected by the probe between the two theories are measured in experiments [5,[26][27][28].…”

“…25 [1,2,4,26,28], which accounts for V p values in the rangeV p (V) ∈ [2.15, 9.48]for the given range of electron temperatures T e (K) ∈ [1000, 4400]. A single point in the Sonin plot is obtained for each set of plasma conditions-that is, for each set of experimental values for I + V p , n…”