Measurement of localized plasma perturbation with hairpin resonator probes

Abstract

In situ plasma diagnostics present the classical problem of the scientific measurement: how does one accurately measure a system without also perturbing it? The uncertainty in the degree of perturbation then reflects an inherent uncertainty in the diagnostic results. Microwave probes are no exception. This work discusses an experimental methodology for quantifying the local perturbation in hairpin resonator probe measurements. By pulsing the delivered power to a plasma, an electron density hairpin spike (HS) is readily detected at generator shutoff. The phenomenon is understood to arise from an apparent density rise as the plasma sheath collapses, thus raising the spatially averaged density measured between the hairpin tines. Other explanations for the density rise are eliminated, and the utility of the HS is presented. Under the conditions investigated, the HS provides an experimental comparison to a previous sheath correction factor developed by Sands et al.

Electron temperature measurements with a hairpin resonator probe in a pulsed low pressure capacitively coupled plasma

“…At power-off, n e exhibits a slow decay (relative to T e ) with τ n = 150-250 μs, as one would expect from literature [11,12,[31][32][33][34]. A spike in n e occurs within 5 μs of power off, previously explained as probe sheath collapse manifesting as an observed increase in n e [35]. A dip in n e corresponding to sheath expansion can also be observed immediately after power on.…”

“…The sensitivity to the assumption in k has been noted previously, motivating additional investigation [7]. Sheath collapse at the beginning of the power-off cycle permits the estimation of k by matching steady state n e to the peak value after sheath collapse [35]. Using this approach, k = 1.3 can be estimated for steady state for a 2 μs linear decrease to k = 1 after power-off.…”

Radiofrequency phase resolved electron density measurements with the hairpin resonator probe

“…An electron temperature T e = 2 eV is assumed for the sheath corrections, which is a source of uncertainty. One Debye length is chosen based on previous work in which floating probe sheath thickness is estimated [28]. Hairpin probes exhibit Lorentzian resonance profiles because the resonance is resistive-inductive-capacitive (RLC) in nature [25,29].…”

Effect of an inhomogeneous electron density profile on the transmission microwave frequency spectrum of the cutoff probe

“…Various microwave diagnostics have been developed such as the plasma absorption probe [13,14], the multipole resonance probe [15,16], the hairpin probe [8,17,18], and the cutoff probe (CP) [10][11][12]. Related principles and recent progress are well explained elsewhere [10,19].…”