Hairpin Resonance Probe Research Articles

Determining sheath edge electric field around cylindrical pins of a DC-biased hairpin resonator probe

The sheath-edge electric field ( Es ) is an important parameter to patch the quasi-neutral pre-sheath and non-neutral sheath regions. The choice of Es significantly influences the theoretically estimated values of the sheath width, potential, and ion density distribution inside the sheath, as determined by the Poisson equation. The precise nature of Es has been a persistent subject of investigation, giving rise to the question of whether it should be zero or possess a finite value, as proposed by various authors. In this study, we determine the values of Es by solving Poisson’s equation as a boundary-value problem, utilizing experimentally determined values of sheath radius from a DC-biased hairpin probe. The obtained values of Es are found to be finite and closely align with the analytical expressions presented by Riemann (1991 J. Phys. D: Appl. Phys. 24 493) and Kaganovich (2002 Phys. Plasmas 9 4788). Additionally, the impact of electron-penetrating sheaths and interacting sheaths on the applicability of the hairpin probe in low-pressure plasmas is briefly discussed.

Hairpin probe assisted saturation current ratio method to determine plasma electronegativity

The saturation current ratio (SCR) method is considered to be one of the simplest methods to determine plasma electronegativity in electronegative discharges using a Langmuir probe (LP). However, its accuracy is susceptible to errors incurred in the estimation of electron and positive ion saturation currents from the ampere–voltage characteristics obtained by a cylindrical LP and partly due to errors in estimating the positive ion flux at the sheath boundary. In spite of its wide use, these underlying limitations and their remedies have not been adequately investigated. In this paper, we address the above problems by involving a DC biased hairpin resonator probe to determine the plasma potential and sheath area correction factor for a cylindrical LP. These measurements are further integrated with the standard SCR method to deduce the plasma electronegativity in an oxygen plasma.

Thomson microwave scattering for diagnostics of small plasma objects enclosed within glass tubes.

In this work, coherent microwave scattering in the Thomson regime was demonstrated for small-scale plasmas enclosed within a glass tube and validated using a well-known hairpin resonator probe technique. The experiments were conducted in a DC discharge tube with a diameter of 1.5cm and a length of 7cm. Thomson microwave scattering (TMS) diagnostics yielded electron number densities of about 5.9 × 1010 cm-3, 2.8 × 1010 cm-3, and 1.8 × 1010 cm-3 for air pressures in the discharge tube of 0.2, 0.5, and 2.5 Torr, respectively. Measurements using the TMS technique were consistent across the tested microwave frequencies of 3-3.9GHz within the margin of error associated with non-idealities of the IQ mixer utilized in the circuit. The corresponding densities measured with the hairpin resonator probe were 4.8 × 1010, 3.8 × 1010, and 2.6 × 1010 cm-3. Discrepancies between the two techniques were within 30% and can be attributed to inaccuracies in the sheath thickness estimation required for correct interpretation of the hairpin resonator probe results.

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

Electron temperature is measured from time resolved hairpin resonator probe measurements in a pulsed capacitively coupled argon plasma at 400 mTorr. Effective collision frequency is related to the electron energy distribution via the effective conductivity and closes a system of equations that allow electron temperature to be determined. Results generally show good agreement with expected behavior and unfiltered time-resolved optical emission measurements.

Radiofrequency phase resolved electron density measurements with the hairpin resonator probe

A floating hairpin resonator probe is used to measure electron density within the radiofrequency cycle of a parallel plate capacitively coupled plasma at steady state. A time resolution capable of detecting electron density oscillations within the radiofrequency cycle is demonstrated. Electron density oscillations are observed at the drive frequency over a range of operating conditions including 10–250 mTorr (1.3–33 Pa) in argon driven at 13.56 or 27.12 MHz. Localized electron density oscillation amplitudes show moderate agreement with literature and fluid simulations near the powered electrode and disagreement in the plasma bulk. The technique is useful for studying electron heating mechanisms in radiofrequency discharges due to its high time resolution.

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

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 plasma potential and electronegativity parameter , have been obtained in an electronegative oxygen discharge. The advantage of this method over the conventional floating hairpin resonator probe has been qualitatively discussed.

Measurement of localized plasma perturbation with hairpin resonator probes

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.

Observation of the standing wave effect in large-area, very-high-frequency capacitively coupled plasmas by using a fiber Bragg grating sensor

The large-area capacitive discharges driven at very high frequencies have been attracting much attention due to their wide applications in material etching and thin film deposition. However, in the regime, the standing wave effect (SWE) becomes a major limitation for plasma material processing uniformity. In this work, a fiber Bragg grating sensor was utilized for the observation of the SWE in a large-area capacitive discharge reactor by measuring the radial distribution of the neutral gas temperature Tg. The influences of the RF power and the working pressure on the radial profiles of Tg were studied. At a higher frequency (100 MHz) and a lower pressure (5 Pa), Tg presents a center-peaked radial distribution, indicating a significant SWE. As the RF power increases, the central peak of Tg becomes more evident due to the enhanced SWE. By contrast, at 100 MHz and a higher pressure (40 Pa), the radial distribution of Tg shows an evident peak at the electrode edge and Tg decays dramatically towards the discharge center because the electromagnetic waves are strongly damped as they are propagating from the edge to the center. At a lower frequency (27 MHz), only edge-high profiles of Tg are observed for various pressures. For the sake of a comparison, a hairpin resonance probe was used to measure the radial distributions of the plasma density np under the same condition. The radial profiles of Tg are found to generally resemble those of np under various conditions. Based on the experimental results, the neutral gas heating mechanism was analyzed.

Electron neutral collision frequency measurement with the hairpin resonator probe

Electron neutral collision frequency is measured using both grounded and floating hairpin resonator probes in a 27 MHz parallel plate capacitively coupled plasma. Operating conditions are 0.1–2 Torr (13.3–267 Pa) in Ar, He, and Ar–He gas mixtures. The method treats the hairpin probe as a two wire transmission line immersed in a dielectric medium. Measurements are obtained using a pressure and sheath correction process by sweeping over assumed collision frequencies in order to obtain the measured collision frequency. Results are compared to hybrid plasma equipment module simulations and show good agreement.

Real-time control of electron density in a capacitively coupled plasma

Reactive ion etching (RIE) is sensitive to changes in chamber conditions, such as wall seasoning, which have a deleterious effect on process reproducibility. The application of real time, closed loop control to RIE may reduce this sensitivity and facilitate production with tighter tolerances. The real-time, closed loop control of plasma density with RF power in a capacitively coupled argon plasma using a hairpin resonance probe as a sensor is described. Elementary control analysis shows that an integral controller provides stable and effective set point tracking and disturbance attenuation. The trade off between performance and robustness may be quantified in terms of one parameter, namely the position of the closed loop pole. Experimental results are presented, which are consistent with the theoretical analysis.

Electron Density and Optical Emission Measurements of SF6/O2 Plasmas for Silicon Etch Processes

This work investigates internal plasma process parameters using a hairpin resonance probe and optical emission spectroscopy. The dependence of electron density and atomic fluorine on the percentage of oxygen in an SF6/O2 discharge was measured using these methods. An RIE Oxford Instruments 80 plus chamber was used for the experiments. Two different process powers (100 W and 300 W) at a constant pressure (100 mTorr) were used, and it was found that the optical emission intensity of the 703.7 nm and 685.6 nm lines of atomic fluorine increased rapidly as oxygen was added to the SF6 discharge, reached their maximum at an O2 fraction of 20% and then decreased with further addition of oxygen. The plasma electron density was also strongly influenced by the addition of O2.

PI Controller for Electron Density Control in Low Pressure Plasma

This paper reports a PID control application for real-time feedback control of electron density, ne, in a low pressure, capacitively coupled plasma chamber. Experimental results are presented which demonstrate that a PI controller enables effective control of electron density when radio frequency power is used as an actuator. A hairpin resonator probe is used to measure the electron density, when the resonator is placed in plasma, its characteristic resonance frequency in vacuum shifts to a higher value. From the frequency shifts, electron density can be easily determined. Actuation and data acquisition are briefly outlined.

Advanced high-pressure plasma diagnostics with hairpin resonator probe surrounded by film and sheath

The hairpin probe using microwave resonance in plasma is applicable to high pressure 1.33 × 103–1.01 × 105 Pa)) as developed recently. In this work, an analytic model of the hairpin resonator probe surrounded by a thin dielectric layer and a sheath layer is proposed. The correction factor due to these surroundings is analytically found and confirmed by electromagnetic field finite difference time domain simulation, thus enabling the accurate measurement of electron density in a high-pressure non-equilibrium uniform discharge.

Hairpin-resonator probe design and measurement considerations

A hairpin-resonator probe is designed to measure the spatial distribution of the electron density in RF plasmas. An effective simulation procedure with the commercial software simulator Ansoft(®) High Frequency Structure Simulator 8 in eigen-mode option was applied to evaluate the influence of the resonator structures on the resonance frequency (fv)00pand unloaded Q-factor (Qv)00p of the resonance modes. Many geometrical constructions were examined and finally, an optimal modification is proposed.

Method for Estimation of Electron Density in a Pulse Plasma Source

The time-dependent spatial electron density distribution in a constricted, pulsed plasma source is measured using a floating hairpin resonance probe, and an extrapolation method is described for determining peak electron density from experimental data. Using these techniques, a detailed characterization of the spatio-temporal evolution of electron density, outside the constricted region above the anode of the pulsed plasma source is presented. Electron density increases sharply during the creation phase, and the rate of increase is found to decrease with the distance from the axis of the constricted channel. By modeling the plasma creation characteristics vs position, the electron density along the axis of the constricted pulsed plasma sources can be determined.

Direct measurement of spatial electron density oscillations in a dual frequency capacitive plasma

The spatio-temporal electron density oscillation in a narrow gap dual frequency (27.12 and 1.937 MHz) capacitive discharge has been measured for the first time by using a floating microwave hairpin resonance probe. By measuring the probe’s resonance frequency in a space and phase-resolved manner, we observe significant oscillation in electron density at both drive frequencies throughout the region between the parallel plate electrodes. The observed phenomenon is attributed to the influence of presheath electric fields of the opposing electrodes in alternate fashion.

Measurement of electron density in a laser produced plasma using a hairpin resonance probe

A floating hairpin resonance probe has been used for the first time to measure the spatial and time evolution of local electron density in a laser produced plasma expanding in vacuum. The measured variation in electron density agrees closely with the variation of ion charge density as measured with a time-of-flight planar Langmuir ion probe confirming the reliability of Langmuir probe in the laser produced plasma.

Electron density modulation in an asymmetric bipolar pulsed dc magnetron discharge

This paper investigates the spatial and temporal variation in plasma electron density over a region between 5 and 10cm above the race-track region of a pulsed magnetron sputtering target. The pulse operation is performed using an asymmetric bipolar pulsed dc power supply, which provides a sequence of large negative “on-phase” voltage (−350V) and a small positive “reverse-phase” voltage (+10V) for 55% of the pulse duration (10μs). The electron density is measured using a floating microwave hairpin resonance probe. The results show electron expulsion from the target in the initial on phase, which propagates with a characteristic speed exceeding the ion thermal speed. In the steady state on phase, a consistent higher density is observed. A quantitative model has been developed to explain the resultant density drops in the initial on phase. While in the reverse phase, we observed an anomalous growth in density at a specific location from the target (d>7cm). The mechanism behind the increase in electron density has been attributed to the modulation in spatial plasma potential, which was measured earlier in the same apparatus using a floating emissive probe [J. W. Bradley et al., Plasma Sources Sci. Technol. 13, 189 (2004)].

Design and measurement considerations of hairpin resonator probes for determining electron number density in collisional plasmas

The hairpin resonator probe has been developed in recent years into a sophisticated diagnostic technique capable of measuring spatially resolved electron number densities in sub-Torr discharges. In this paper, we extend the use of this technique to discharges at pressures greater than 1 Torr. In this regime, the effects of electron–neutral collisions become significant and a suitable correction is applied in conjunction with the sheath correction. We also describe elements of hairpin design and coupling that need to be more carefully controlled in order to maximize the range of electron densities that can be detected at higher pressures. Finally, we discuss limitations to the transmission-line model used routinely to interpret hairpin data as they apply to measurements in a nonuniform plasma.

A floating hairpin resonance probe technique for measuring time-resolved electron density in pulse discharge

We present an automated hairpin resonance probe for obtaining time-varying plasma electron density in a pulsed-magnetron discharge, operated with a 13.56 MHz radio-frequency source. When the resonator is placed in plasma, its characteristic resonance frequency in vacuum shifts to a higher value. From the frequency shifts, electron density is easily determined. By applying a fixed microwave frequency, the probe immersed in plasma resonates only at a specific time of the pulse waveform. At a different time of the pulse, the probe resonates at a different frequency. The procedure is automated using a Labview™ program, which increments the applied microwave frequency in small steps of the prescribed value and reads the corresponding resonance peak from an oscilloscope. The spatial and temporal electron density measured using this technique shows a sharp drop in density during the first few microseconds in the on-phase, followed by an increase in density as the discharge develops in the steady-state on-phase. The off-phase shows that decay in electron density at different rates is faster in the region where the magnetic field lines intersect the target. A quantitative model is described to explain different features observed in the experiment.