Session BT1: Plasma Sources I

Electron beam-generated ion-ion plasmas: Etching and diagnostics

Positive ion-negative ion (ion-ion) plasmas are those where negative ions are the primary negative charge carrier and in the absence of any significant electron density, these negative ions are not confined to the bulk plasma. Thus, a nearly equal and anisotropic flux of positive and negative ions can be delivered to surfaces located adjacent to the plasma and eliminate electron-induced damage to substrates in etching applications. A requirement for the formation of ion-ion plasmas in low pressure, halogen-based gas backgrounds is a low electron energy so that the attachment rate is comparable to the ionization rate and the plasma electrons can be rapidly converted to negative ions. Electron beam-generated plasmas provide an opportunity to investigate ion-ion plasmas and their potential applications because of their uniquely low electron temperature compared to conventional discharges. In this presentation, we discuss recent investigations of ion-ion plasmas formed in pulsed, electron beam-generated plasmas produced in mixtures of SF$_{6 }$and their use in silicon etching. In this system, positive and negative ions were extracted using a low frequency (10-50 kHz), low voltage (0-300 V) bias. The results of Si etching experiments and plasma diagnostics will be presented with the goal of understanding the optimum system configuration and operating conditions.   

Automated method for creating arbitrary substrate voltage wave forms for manipulating energy distribution of bombarding ions during plasma processing

Accurate and reproducible control of ion bombardment energy during plasma processing is a means to better understand the nature of plasma-surface interaction and to control process outcomes. Ion energy distribution (IED) control can be achieved by tailoring the wave form shape of an rf bias applied to the substrate during processing, through the use of a programmable wave form generator in combination with a power amplifier. Due to the frequency dependence of the amplifier gain and the impedance of the plasma in contact with the substrate, however, it is not practical to predict the shape of wave form needed at the generator to produce a desired result at the substrate. Introduced here is a systematic approach using feedback control in the frequency domain to produce arbitrary wave form shapes at the substrate. Specifically, a fast Fourier Transform (FFT) of the substrate wave form is compared, one frequency at a time, with the FFT of a desired “target” wave form, to determine adjustments needed at the generator. This iterative procedure, which is fully automated and tested for several target wave form shapes, is repeated until the substrate wave form converges to the targeted shape, providing a quick systematic method for producing an arbitrary IED at the substrate.   

Scaling laws in dc micro discharges

In order to establish the operation regime of micro discharges we should start from the low pressure discharges and employ the standard scaling laws. Discharges should scale according to the reduced electric field $E/N$ and $p$d - product proportional to the number of collisions. Finally, the scaling should be made in accordance with the $jd^2 $ - describing the space charge effects [1]. We have calculated the Paschen curves and Volt- Ampere characteristic by using a PIC code and appropriate data for argon in order to establish whether the standard micro discharges operate in Townsend regime or in Glow Regime. \newline [1] A.V.Phelps, Z.Lj.Petrovi\'{c} and B.M.Jelenkovi\'{c}, Phys. Rev. E \textbf{47} 2825 (1993)   

Hydrodynamic models for the positive column with neutral gas depletion.

In the classical low-temperature plasma equilibrium, the ionization degree is sufficiently small that neutral density is considered constant. However, in many contemporary plasma reactors, such as helicons, the ionized fraction can be significant. This fraction may even reach 100\% in plasma thrusters. In such circumstances, neutral dynamics has to be included in order to solve the plasma equilibrium. We have revisited the plasma equilibrium models, from low-pressure (Tonks-Langmuir) to high pressure (ambipolar diffusion) regime, including the neutral dynamics. The results show that neutrals are pushed towards the wall by the electronic pressure, creating a neutral depletion at the center of the discharge. The effect is significant when the electronic pressure becomes comparable to the neutral pressure. The electron temperature becomes a function of the electron density, so that particle and power balance are not decoupled. Finally, we derived a new expression for the edge-to-center electron density ratio which accounts for neutral density depletion.   

Numerical Simulation of the DC Discharge Using CFD-ACE+

A low pressure DC discharge is simulated using the CFD-ACE+. The electron kinetics is obtained from the kinetic module. The local and non-local approaches are used separately for solving the kinetic equation. The results are compared at different locations in the discharge. It is shown that although the local approximation gives a good description of the electron energy distribution function (EEDF) in the bulk plasma, it fails to give accurate information of the EEDF near the wall, which is highly non-Maxwellian. As a result, the non-local approach is more appropriate for the kinetic treatment of plasma electrons in a low pressure DC discharge. The ion number density and momentum are obtained from a fluid model. For comparison, the electron continuity equations are also included. Based on the simulation model, the species' density profile, the power balance and the influence of the electron-electron coulomb collisions on the EEDF and discharge physics are investigated. The simulation results are also compared with results from pure fluid model without kinetic description.   

Simulation of moving striations in rare gas plasmas

Ionization waves (moving striations) have been observed in classical DC discharges of rare gases in a wide range of gas pressures and discharge currents. Recently, striations have been also observed in plasma display cells and other micro-discharges. We have obtained moving striations in computer experiments using self-consistent discharge model. The model includes Boltzmann solver for electron kinetics, fluid model for ion transport, Poisson equation for the electric field and (optionally) an external circuit model. Simulations are performed from cathode to anode in 1d or 2d settings. Striations appear initially near the cathode and propagate towards the anode as observed in experiments. The model allows studies of nonlinear waves and effects of external circuit on the wave properties. We will discuss the mechanism of striations for different operating conditions and present results of simulations for a DC discharge in Argon gas for a typical pressure of 1 Torr, tube radius R=1 cm, for different discharge currents. High sensitivity of striations to the state of electron gas and ionization kinetics makes them an ideal tool for testing discharge models and advanced plasma diagnostics.   

Session BT2: Plasma Boundaries: Sheaths and Boundary Layers

Electron Sheaths and Non-ambipolar Diffusion in Laboratory Plasma

Electron sheaths were first predicted by Langmuir in 1929 when he stated that, ``with a large area, A, an anode sheath is a positive ion sheath, but that as A decreases, a point is reached where the positive ion sheath disappears and it is replaced by an electron sheath.''\footnote{I. Langmuir, Physical Review. \textbf{33}, 954 (1929).} We show that electron sheath formation near a positive anode depends on the anode area, A$_{a}$, as well as the area available for ion loss, A$_{i}$. When A$_{a}$/A$_{i} \quad <$ (m$_{e}$/m$_{i})^{1/2}$, the electron sheath potential monotonically decreases from the anode to the bulk plasma. When the anode is larger than this, a potential dip forms in the electron sheath to reduce the electron current lost to the anode. This potential dip is necessary to preserve global current balance and when it is present, total non-ambipolar diffusion can occur where all electrons are lost from the plasma through an electron sheath and all positive ions are lost elsewhere. Additional measurements were carried out to identify the transition from positive (ion) to negative (electron) sheaths. Data were taken in low-pressure argon plasma generated by hot filaments and confined in a multidipole chamber.   

Total Non-Ambipolar RF Electron Source -- Better than a Hollow Cathode

A Radio Frequency (RF) plasma based electron source has been developed based on results of our electron sheath studies in weakly collisional DC plasmas. In total non-ambipolar flow, all of the electrons leaving the plasma are lost through an electron sheath at the aperture. This occurs if the ratio of the ion loss area to the extraction aperture area is approximately equal to the square root of the ratio of the ion mass to the electron mass, and the ion sheath potential drop at the chamber walls is much larger than T$_{e}$/e. Gridless extraction of electrons is achieved by using an axial expanding magnetic field of (maximum value of 100 Gauss) that makes it possible to achieve a uniform plasma potential across the exit aperture. An electron current of 15 A was achieved with 15 sccm Ar and 1200 W.   

Arc cathode spots and normal spots on glow cathodes: self-organization phenomena

Current transfer from high-pressure DC arc plasmas to thermionic cathodes may occur in the diffuse mode, where the current is distributed over the front surface of the cathode in a more or less uniform way, or in a spot mode, where most of the current is localized in one or more small areas. The diffuse mode occurs at high values of the discharge current, spot modes occur at low currents. A similar phenomenon is observed on cold cathodes of DC glow discharges: current transfer can occur in the abnormal mode, where the current is more or less uniformly distributed over the cathode, or in the normal mode, where only part of the cathode is active; the abnormal mode occurs at high discharge currents and the normal mode occurs at low currents. Although physical mechanisms are very different, the overall patterns of the two phenomena are similar: the mode with a uniform current distribution operates on the falling branch of the current-voltage characteristic and is unstable due to a positive feedback; the spot mode operates on the growing section and is stable. In fact, both phenomena represent examples of self-organization. Mathematical descriptions also have important features in common. This allows one to develop a unified treatment of both phenomena, which is a subject of the present work.   

Revisiting the capacitive sheath

Traditional theory of the capacitive sheath assumes that the large negative charge at the electrode is screened by the ion space charge and the transition to the small rf electric field in the plasma occurs abruptly within the narrow transition region of the Debye length. However, careful self-consistent kinetic treatment of the problem reveals existence of additional transition layer of length $V_T /\omega $, where $V_T $ is the electron thermal velocity and $\omega $ is the discharge frequency [1,2,3]. Electrons interacting with the capacitive sheath acquire velocity modulations. As a result, the electron density bunches appear in the region adjacent to the sheath. These electron density perturbations decay due to phase mixing over a length of order $V_T /\omega $. The electron density perturbations polarize the plasma and produce an electric field in the plasma bulk. This electric field, in turn, changes the velocity modulations and total power deposition. Recent particle-in-cell simulations [4,5] confirm the prediction of analytic theory. [1] L. D. Landau, J. Phys. (USSR) \textbf{10}, 25 (1946). [2] Igor D. Kaganovich, Phys. Rev. Lett. \textbf{89}, 265006 (2002). [3] I. D. Kaganovich, O. V. Polomarov, and C. E. Theodosiou, ``Revisiting the anomalous rf field penetration into a warm plasma,'' to be published in IEEE Trans. Plasma Sci. (2006). [4] H. C. Kim,{\_} G. Y. Park, and J. K. Lee, \textbf{13}, 023501 (2006). [5] E. Kawamura, M. A. Lieberman, and A. J. Lichtenberg, Phys. of Plasmas \textbf{13}, 053506 (2006).   

Influence of a micro-scale wafer structure upon sheath profile in 2f-CCP in SF$_6$/O$_2$

MEMS-dry processes have been developed on the basis of plasma technologies in microelectronic device fabrications. Deep Si etching for MEMS requires a high speed, selective and anisotropic process having several tens or hundreds $\mu$m in width and depth as compared with that of ULSI elements. During the MEMS process at hundreds mTorr, the sheath thickness in front of the surface to be etched will be comparable to or smaller than the trench/hole width, and a distorted sheath field will have a strong influence on the incident ion flux and velocity distribution (i.e., plasma molding). In the present study, we will estimate the local characteristics of the plasma molding, i.e., the ion velocity distribution incident on a micro scale patterned wafer by using a series of repetitive calculation of the structure from cm to $\mu$m in 2f-CCP in SF$_6$/O$_2$ at 300 mTorr. Further investigation will be given for the feature profile of a Si-MEMS by plasma etching in the 2f-CCP system.   

Ion Energy Distribution Measured in Pulsed Boron Trifluoride Glow Discharge

Pulsed plasma doping has emerged as an efficient technology for low energy implantation. The cathode sheath in the pulsed glow discharge plays a key role in defining the ion energy distribution of ions reaching the wafer. Understanding the structure, dynamics and collisional properties of the sheath is critical for successful application of these discharges to low energy plasma implantation. In this study, the ion energy distributions in the cathode sheath of a boron trifluoride discharge are discussed. Measured ion energy distributions are analyzed in the collisionless and collisional sheath regime. Based on the experimental ion energy distributions, the dopant depth profile is calculated. The optimal shallow dopant depth distribution in silicon can therefore be obtained by proper tuning of the plasma parameters.