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

PETERSON, DAVID JOHN. Characterization of Intermediate Pressure Plasmas with Advanced Microwave Resonator Diagnostics. (Under the direction of Steven C. Shannon.) Intermediate pressure plasmas (1-100 Torr) are an area of growing academic and industrial interest for a number of different applications. Accurate measurement of plasma parameters is often challenging at these conditions. Most plasma diagnostics rely on interactions with either charged particles or excited species present in a discharge. As pressure increases, collisions with neutral gas particles can act to distort many measurements in a manner that is difficult to recover from. Microwave diagnostics offer a complementary approach to the suite of diagnostics necessary to fully characterize a plasma, one that is particularly well suited to making measurements at intermediate pressures. Specifically, the similarity of a microwave period and mean time between electron-neutral collisions allows microwave diagnostics to obtain additional information from a measurement that would otherwise be either unobtainable or deleterious to the measurement itself. This work uses an array of diagnostics to characterize both radiofrequency capacitively coupled plasmas and microwave surface-wave plasmas at low and intermediate pressures. The primary focus is developing an understanding of the general characteristics of these discharges and also to develop the measurement capabilities of a microwave diagnostic known as the hairpin resonator probe. In particular, mean electron energy can be measured by the probe through the complex plasma permittivity. This work aims to demonstrate the usefulness of the technique and understand the associated experimental limitations. Experiments are performed in radiofrequency capacitively coupled plasmas for pressures ranging from 0.01 Torr to 4.5 Torr and electron densities (ne ) spanning 1×108-2×1010 cm−3 in argon, helium, nitrogen, argon-helium mixtures, and argon-oxygen mixtures. Measurements are primarily made with the hairpin resonator probe. Results are compared to fluid and hybrid simulations and generally show good agreement with a number of notable discrepancies. Potential sources of simulation-model disagreement are discussed and in some cases quantified. Experiments are also performed in a microwave surface-wave discharge using an array of diagnostics, including a hairpin resonator probe, Langmuir probe, laser absorption spectroscopy, and optical emission spectroscopy. Conditions span pressures ranging from 0.2-6 Torr and ne spanning 1×108-2×1011 cm−3 in argon. All results are compared to at least one other diagnostic, all showing good qualitative agreement and in most cases decent quantitative agreement. © Copyright 2020 by David John Peterson

Characterization of Intermediate Pressure Plasmas with Advanced Microwave Resonator Diagnostics.

https://robots.iopscience.iop.org/article/10.1088/1361-6463/ab6944/pdf

Radiofrequency phase resolved electron density measurements with the hairpin resonator probe

Hairpin probes are used to determine electron densities via measuring the shift of the resonant frequency of the probe structure when immersed in a plasma. This manuscript presents new developments in hairpin probe hardware and theory that have enabled measurements in a high electron density plasma, up to approximately 1012 cm−3, corresponding to a plasma frequency of about 9 GHz. Hardware developments include the use of both quarter-wavelength and three-quarter-wavelength partially covered hairpin probes in a transmission mode together with an easily reproducible implementation of the associated microwave electronics using commercial off-the-shelf components. The three-quarter-wavelength structure is operated at its second harmonic with the purpose of measuring higher electron densities. New theory developments for interpreting the probe measurements include the use of a transmission line model to find an accurate relationship between the resonant frequency of the probe and the electron density, including effects of partially covering the probes with epoxy. Measurements are taken in an inductively coupled plasma sustained in argon at pressures below 50 mTorr. Results are compared with Langmuir probe and interferometry measurements.

Electron density measurement using a partially covered hairpin resonator in an inductively coupled plasma.

Inductively coupled plasmas driven by pulsed RF power have been used by the semiconductor industry for decades as they offer numerous advantages compared to continuous mode discharges. Current state-of-the-art global models characterize the plasma under conditions where power delivery is user defined and typically constant. This work details the development of an integrated global plasma-circuit model, which couples a transient plasma model with a broader circuit model that captures the behavior of the power delivery system. The transient response of electron density ne and the magnitude of the delivered and reflected power is captured for the duration of a pulse event. The plasma model incorporates negative feedback mechanisms that enhance the magnitude of reflected power in the early ON-cycle. These feedback mechanisms include a skin depth-dependent derivation of plasma impedance and a generalized electron energy distribution function. These mechanisms decrease the rate of power delivery and dnedt in the early power on cycle. Data taken in the global plasma-circuit model was benchmarked to hairpin probe measurements that were taken on the NC state’s inductively coupled argon oxygen system. Experimental data were taken using a working gas of high purity argon at pressures ranging from 2.67 to 6.67 Pa, and center point electron densities were measured in the range of 109– 1010cm−3.

Modulating power delivery in a pulsed ICP discharge via the incorporation of negative feedback mechanisms

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.

Measurement of localized plasma perturbation with hairpin resonator probes

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Measurement of localized plasma perturbation with hairpin resonator probes