Calibration of Langmuir probes against microwaves and plasma oscillation probes

Abstract

The use of Langmuir probes for measuring plasma density is subject to uncertainty because the theories commonly used to interpret the data give widely differing results. This is especially troublesome in partially ionized plasmas used, for instance, in the semiconductor industry, since no existing theory adequately treats the case when there are a few collisions between ions and neutral atoms. In this work, plasma densities measured by microwave interferometry and plasma-oscillation probes are compared with those from probe data analyzed with Langmuir's orbital motion limited (OML) theory, the Allen-Boyd-Reynolds (ABR) theory and the Bernstein-Rabinowitz-Laframboise (BRL) theory. It is found that ABR underestimates and BRL overestimates the density, the problems being the neglect of ion orbiting in ABR and the effect of ion-neutral collisions in BRL. The best theory is either OML or the geometric mean between the ABR and BRL results. For thicker probes, other methods are suggested.

Millimeter-Wave Beam Scattering by Field-Aligned Blobs in Simple Magnetized Toroidal Plasmas

“…4(c) and 4(d). Consistent with the expected systematic uncertainties in n e calculated from ion-saturation data [39,40], we estimate uncertainties of the model by bounding the outcome with results obtained using 0.5n e and 2n e . The shaded areas in Figs.…”

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

“…This change of the ion saturation current arises from the change in the sheath thickness with increasing voltage across the sheath. [2] As previously mentioned, the ion saturation current depends on the square root of the probe potential [8,9] in OML theory, whereas it changes linearly with the probe potential in the Swift approximation. [7] In the case shown in Figure 6, the comparison between the ion current calculated from the OML theory and the Swift approximation gives a relative change of about 5% at a probe voltage V a = 0.…”

“…Maxwell-Boltzmann EEDF [2,7] Figure 3 shows the variation of ΔV 1 /ΔV a calculated versus G for different values of F, using Equation (9). ΔV 1 /ΔV a increases with increasing G. The larger the F value, the larger the value of ΔV 1 /ΔV a .…”

“…It agrees with the previous values obtained for a Maxwell-Boltzmann distribution. [7] Thus, starting from a well-defined EEDF, we calculated the I-V probe characteristics using Equations (16) and (9). Then, we calculated EEDF in the energy range e > f , using Equation (8).…”

“…This hypothesis is convenient to simplify the method proposed by the author (classical method). However, according to orbital motion limited (OML) theory, [8,9] the ion current should be proportional to the square root of the applied voltage and not to the applied voltage like in the Swift approximation. OML theory is rigorous only in the case of FIGURE 1 Double probe apparatus and the scale for the characteristic voltage values a collisionless ion sheath around the probes, that is, when the Debye length is much smaller than the ion mean free path.…”