### Session BT2: Plasma Boundaries: Sheaths and Boundary Layers

Chair: M.A. Lieberman, University of California, Berkeley
Room: Holiday Inn Salon B

 Tuesday, October 10, 2006 8:00AM - 8:15AM BT2.00001: Electron Sheaths and Non-ambipolar Diffusion in Laboratory Plasma Scott Baalrud , Noah Hershkowitz 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. Tuesday, October 10, 2006 8:15AM - 8:30AM BT2.00002: Total Non-Ambipolar RF Electron Source -- Better than a Hollow Cathode Noah Hershkowitz , Ben Longmier , Scott Baalrud 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. Tuesday, October 10, 2006 8:30AM - 8:45AM BT2.00003: Arc cathode spots and normal spots on glow cathodes: self-organization phenomena Mikhail Benilov 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. Tuesday, October 10, 2006 8:45AM - 9:00AM BT2.00004: Revisiting the capacitive sheath Igor Kaganovich 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). Tuesday, October 10, 2006 9:00AM - 9:15AM BT2.00005: Influence of a micro-scale wafer structure upon sheath profile in 2f-CCP in SF$_6$/O$_2$ Fukutaro Hamaoka , Takashi Yagisawa , Toshiaki Makabe 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. Tuesday, October 10, 2006 9:15AM - 9:30AM BT2.00006: Ion Energy Distribution Measured in Pulsed Boron Trifluoride Glow Discharge Ludovic Godet , Svetlana Radovanov , Jay Scheuer , Christophe Cardinaud , Gilles Cartry 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.