Inferring plasma parameters from the sheath characteristics of a dc biased hairpin probe

Abstract

In this paper, the cylindrical sheath around a hairpin resonator probe has been varied by applying a dc potential to the hairpin to infer different plasma parameters in an argon and oxygen discharge. As the sheath width increases due to negative bias, the resonance frequency of the hairpin correspondingly shifts toward a lower value. An analytical model based on fluid approximation has been developed to estimate the sheath width variation as a function of the applied voltage on the probe. The analytical result is then compared with the well-known capacitance model that assumes a conjugate dielectric region around the hairpin consisting of a pair of cylindrical sheaths and the plasma. Using this method, a wide range of plasma parameters, including the electron temperature T , e plasma potential V , p and electronegativity parameter a s , have been obtained in an electronegative oxygen discharge. The advantage of this method over the conventional floating hairpin resonator probe has been qualitatively discussed.

Addressing the anomalies in determining negative ion parameters using electrostatic probes

“…This increase in current is caused due to an expansion in the sheath around the cylindrical wire. Pandey et al [12] applied a resonance hairpin probe to estimate the sheath width expansion around a cylindrical wire probe of same diameter. With the knowledge of the sheath width due to negative bias on the probe, it is possible to remove the expansion of the ion saturation current as shown by plotting the revised ion saturation current.…”

“…To benchmark the electron density obtained using LP, additionally a DC biased hairpin probe (HP) has been applied. The details about the DC biased HP technique can be found in our earlier work [12]. The objective of applying DC bias on the HP is to make the sheath around the cylindrical pins to zero, such that the HP measures the absolute value of electron density.…”

“…The DC biased HP can also provide the information about the sheath width variation around the cylindrical wire as a function of the applied bias to the HP. The methodology to extract sheath using DC biased HP is described in our earlier work [12]. The sheath width and electron density obtained as a function of negative bias voltage on the HP for the case of argon is shown in figure-13.…”

“…To find the true value of ion saturation current, the probe sheath area correction factor k is determined from HP. The parameter γ v which is a ratio of electron to negative ion temperature is calculated by assuming a constant negative ion temperature value which is typically in the range of 0.05 eV as found in the literature [13,12]; and the electron temperature is determined from LP. Then equations-4 and 5 are combined to obtain a relation between α and η s .…”

Equilibrium properties of inhomogeneous partially-magnetized plasma containing negative ions

“…Though this concept is simple, the saturation currents for a cylindrical probe can be highly error-prone due to a number of factors such as contamination on the probe surface, uncertainty in the current collection area, and external factors such as magnetic fields, which can drastically reduce the electron saturation current to the probe. Recently, a few novel concepts to determine the negative ion parameters have been introduced, which are based on DC and pulsed-bias hairpin probes [38][39][40][41][42]. The DC bias hairpin has been used to estimate the sheath radius with the application of negative bias applied to the cylindrical pins [39,42].…”