Session LW3: Plasma Boundaries, Sheaths and Diagnostics

A Comparison of Emissive Probe Techniques for Electric Potential Measurements in a Complex Plasma

Accurate measurements of the plasma potential is a critical challenge especially for complex plasmas such as magnetized and flowing. We compare emissive probe techniques for measurements of the plasma potential in a low-pressure magnetized discharge of the Hall thruster. The thruster was operated with xenon gas in subkilowatt power range and the discharge voltage range of 200-450 V. The probe was placed at the channel exit where, the electron temperature is in the range of 10 to 60 eV and the plasma potential is in the range of 50 to 250 V. The floating point method is expected to give a value $\sim T_e/e$ below the plasma potential. The experimental results are consistent with these expectations. Specifically, it is shown that the floating potential of the emissive probe is $\sim 2T_e/e$ below the plasma potential. It is observed that the separation technique varies wildly and does not give a good measure of the plasma potential.   

Particle-in-Cell Simulations of Collisional RF Sheaths

Simulations of a high voltage argon rf capacitive discharge have been performed in the collisional sheath regime, with sheath width about eight ion mean free paths. Ion and neutral energy and angular distributions are determined, both within the sheath and at the electrode. The ion energy spread at a position within the sheath is proportional to the distance from the position to the electrode. Multiple low energy peaks due to charge transfer collisions, combined with the sheath oscillations, are seen to form. The ion angular distribution remains highly directed. The neutral energy distribution is relatively constant within the sheath. The neutral angular distribution has both isotropic and highly directed components. Comparisons are made to experimental results. A collisional sheath model is being developed.   

Semi-analytical sheath model for electronegative radio frequency plasmas

In plasma etching processes, the ion energy distributions (IEDs) arriving at substrates strongly affect the etching rates. In order to accurately determine the IEDs, various analytic and numerical models have been developed. However, over the past few decades, very few studies have been conducted on sheath model for electronegative radio frequency plasmas. Therefore, in this work, an equivalent circuit model is presented for electronegative radio frequency plasmas.   

Ar$^+$ and Xe$^+$ Velocities near the Presheath-Sheath Boundary in an Ar-Xe Discharge

The velocities of Ar$^+$ and Xe$^+$ ions near the presheath-sheath boundary in an Ar-Xe discharge are studied by particle-in-cell/Monte Carlo simulation [1]. For a pure argon discharge the argon ion has almost the same velocity profile as it does in the mixture of argon and xenon. Similarly, for a xenon discharge the xenon ion has almost the same velocity profile as it does in the mixture of argon and xenon. The ion speed at the sheath-presheath boundary is the same for an ion in a pure argon or xenon discharge and for the same ion in a mixture of argon and xenon. We conclude that, in our simulation, each ion reaches its own Bohm speed at the presheath-sheath interface. These findings contradict the experimental findings of Lee et al. [2] where the ion velocities near the presheath-sheath boundary approach the common ion sound speed for both argon and xenon ions in the Ar-Xe discharge. The simulation results are evaluated by calculating the ion-ion instability condition from kinetic theory. We find no evidence of unstable waves in our simulation, which is the proposed mechanism [3] for a common system speed. [1] J. T. Gudmundsson and M. A. Lieberman, Phys. Rev. Lett. accepted July 2011 [2] D. Lee, N. Hershkowitz, and G. D. Severn, Appl. Phys. Lett. {\bf 91} 041505 (2007) [3] S. D. Baalrud and C. C. Hegna, Phys. Plasmas {\bf 18} 023505 (2011)   

Anomalous Ion Kinetic Effects in RF Plasma Sheaths

An ion PIC code (1d2v) has been written to examine anomalous ion kinetic effects in rf sheaths. These phenomena are more pronounced in low pressure, plasma processing, capacitive applicators, where rf frequencies are typically less than the ion plasma frequency. For computational stability, a Newton Krylov solver was used to solve the Poisson Boltzmann equation. Using this code, the average ion velocity in the pre-sheath can be shown to have dramatic effects on the ion kinetics in sheath and pre-sheath regions when it exceeds the ion sound speed, Cs. As previously shown [Sternberg \& Godyak, IEEE Trans. Plasma Sci., 35(5), 2007], the ion average velocity can be $\sim$2.5 Cs at the pre-sheath/sheath interface - thereby creating a region where the ions in the pre-sheath have a Mach number greater than unity, giving rise to a wave-train of ion acoustic shock waves in a limited region. These waves are critically damped as they enter the sheath and give rise to additional structure in the ion velocity distribution function, particularly at lower sheath voltages. The nature of the dual peaked ion velocity distribution function will also be discussed in terms of ion resonance with the sheath electric field that derives from the motion of the electron sheath.   

Ion Energy Distributions in Pulsed Inductively-Coupled Plasmas Having a Pulsed Boundary Electrode

In applications requiring energetic ions, such as plasma etching, the time averaged ion energy distribution (IED) to surfaces is most important. In these situations, pulsed plasmas can be used to piece together the desired IED from different times during the power pulse. Such control of IEDs in inductively coupled plasmas (ICPs) can be obtained using a boundary electrode with a continuous or pulsed dc bias. The resulting shift in the plasma potential modifies the IEDs without significant changes in the bulk plasma. Pulsing the ICP provides additional control. In this paper we discuss results from a computational investigation of IEDs to surfaces in low pressure ICPs sustained in argon and Ar/H$_{2}$. The investigation was conducted using the Hybrid Plasma Equipment Model with which electron energy distributions and the IEDs are obtained using Monte Carlo simulations. ICP power and boundary voltage are applied in continuous and pulsed formats. Results for EEDs and IEADs are compared to experimental data. We find the IEDs have two peaks that can be controlled with the duration of the pulsing and relative magnitude of the boundary bias.   

Optical Emission Measurements of Electron Temperatures and Metastable Number Densities in a DC/RF Magnetically Confined Xe Plasma

We report optical emission studies of a Penning type RF/DC discharge in 0.27 mTorr Xe plus traces of other rare gases. Emissions from selected Paschen 2p levels of Xe and trace Ne, Ar, and Kr were used to determine electron temperature\footnote{V. M. Donnelly, J. Phys. D.: Appl. Phys. \textbf{37}, R217 (2004).} ($T_{e})$ and metastable number densities. Measurements were made as a function of distance from the center of the discharge chamber at several magnetic field strengths. Emission was viewed along a line-of-sight axis parallel or perpendicular to the axis of the magnets and 2 MHz RF inductively-coupled plasma source. $T_{e}$ values were 1- 3 eV, depending on the magnetic field, and were generally in good agreement with Langmuir probe measurements at 35 and 150 Gauss. Rare gas metastable number densities were derived from emission intensities from levels that were excited largely by electron impact from the ground state (e.g. Xe 2p$_{3})$, 1s$_{5}$ (e.g. Xe 2p$_{6})$ or 1s$_{3}$ (e.g. Xe 2p$_{4})$. The peak fraction of Xe 1s$_{5}$ varied from 0.005 at 435 Gauss to 0.001 at 35 Gauss. Intense Xe$^{+}$ emission down the center of the discharge at high magnetic fields indicates a second population of high energy electrons.   

An approximate method for analysis of double probe characteristic in the absence of ion saturation

Ion current to a double probe (DP) with cylindrical leads is subject to sheath expansion effects, so probe's volt-ampere characteristic (VAC) differs significantly from a simple \textit{tanh}-like shape, which is valid only in the limit of an infinitely large ratio of probe radius, $r_{p}$, to Debye length, \textit{$\lambda $}$_{D}$: \textit{$\xi $}$_{p}=r_{p}$/\textit{$\lambda $}$_{D}$. Thus, a commonly employed simple method, in which straight lines are fitted to VAC at zero and large positive (or negative) bias voltages, and the ordinate of the intersection point is used as $I_{sat}$\textit{ = 2$\pi $ r}$_{p }L_{p} e^{-1/2 }N_{is}^{ }$\textit{$\surd $T}$_{e}/M_{i}^{+}$, often results in overestimation of the calculated ion density, $N_{is}$, by a factor \textit{$\eta $}$_{i}^{-1}=N_{is}$ / $N_{i}^{+ }\sim $ 2 -- 3, where $N_{i}^{+}$ is the true positive ion density. The shape of the VAC and therefore value of \textit{$\eta $}$_{i}$ are also strongly affected by plasma's electronegativity, \textit{$\beta $} = $N_{neg}$ / $N_{e}$. In this work, for the first time, we present an approximate analytical expression for \textit{$\eta $}$_{i }$as a function of \textit{$\beta $} and\textit{ $\xi $}$_{ps}=r_{p}$\textit{ / $\lambda $}$_{D}$ ($N_{is})$, which is valid in the wide range of parameters: \textit{$\beta $} = 0 -- 40, and \textit{$\xi $}$_{pi}=r_{p}$\textit{ / $\lambda $}$_{D}$ ($N_{i}^{+})$ = 0.1 -- 10. We obtained this expression in O$_{2}$ and CF$_{4}$, for $T_{e}/T_{neg}$ = 30, by solving ``radial motion'' equation in the presence of singly-charged electronegative ions [H. Amemiya et al., Plasma Sources Sci. Technol. \textbf{8}, 179 (1999)], and numerically calculating a family of DP VAC. We also obtained a formula for \textit{$\eta $}$_{i}$ ($M_{i}^{+}$, \textit{$\xi $}$_{ps})$ in electropositive plasma for \textit{$\xi $}$_{pi}$ = 0.1 -- 50 and a wide range of ions, from H to Xe.   

Experimental Study of the Impedance Characteristics of the Plasma Absorption Probe

The plasma absorption probe (PAP) is a diagnostic which permits the determination of the spatially resolved electron density in a plasma. The simple structure of the probe allows us a robust measurement; however, the mechanism of the absorption is complicated and several papers report that there is still some uncertainty. Basically, the PAP detects the plasma density by determining the absorption peak frequency in the frequency characteristics of the reflection coefficient. We have shown, by an electromagnetic field simulation (GT3-0003, GEC2009) that the frequency characteristics of the PAP impedance reflect the plasma resonance more directly than the frequency characteristics of the reflection coefficient. This time, we will report the experimental observation of the resonance in the frequency characteristics of impedance.   

Cut-off probe analysis and improvement

This study investigates the mechanism of microwave frequency transmitted spectrum of cut-off probe and improves the probe based on the results. Simplified circuit modeling reproduces the overall N-shape spectrum and establishes the exact frequency of cut-off peak taking account with the plasma frequency and the collision frequency on the spectrum and it enables diagnostics of the plasma density from low pressure to high pressure. E/M wave simulation (CST microwave studio) reveals that origin of cut-off like peaks and plasma density is acquired from one of them, a probe holder $\lambda/4$ resonance peak applying the hairpin relation. Furthermore, phase difference method for diagnostics of the plasma density is conducted. This method uses a single frequency microwave source and it is low-priced.   

Resistance and capacitance measurements of the films deposited on a planar Langmuir probe

The beneficial use of DC-pulsing instead of RF for biasing a capacitively coupled planar Langmuir probe mounted in industrial CCP etcher is demonstrated. The ion flux is determined from the discharging of a DC-biased capacitor for Ar, O$_{2}$, and C$_{2}$H$_{4}$-based plasmas taking into account the RC constant of the films grown on the probe. A comparison is made between the clean probe after Ar sputter-cleaning and the probe coated with a polymer film. A new fitting procedure is proposed including both the capacitance and resistance of the film. The experimental validation is done with a C$_{2}$H$_{4}$-based polymer film, which resistance and capacitance are measured. Finally, it is shown that, together with the measurement of intrinsic plasma parameters like T$_{e}$ and ion flux, one can monitor deposition on the chamber walls that can possibly be extrapolated to the etched wafer.