AVS2001 Session PS2-WeM: Modeling

Wednesday, October 31, 2001 8:20 AM in Room 104

Wednesday Morning

Start	Invited?	Item
8:20 AM		PS2-WeM-1 Time-Dependent Electron Impact Source Functions in Inductive and Capacitive Plasma Sources Obtained Using an "On-The-Fly" Monte-Carlo Technique¹ A. Sankaran, M.J. Kushner (University of Illinois) Electron temperatures in low-pressure inductively and capacitively coupled plasma reactors do not significantly vary during the rf cycle. There can be, however, considerable modulation of rate coefficients and source functions for electron impact reactions having high threshold due to modulation in the tail of the electron energy distribution at energies which are less collisional. Since the character of this modulation requires that the electron energy distribution (EED) be resolved, we developed a new "On-the-Fly" (OTF) Monte-Carlo technique to compute the time dependent properties of EEDs. Using this method, Fourier frequency coefficients of the moments of the EEDs are obtained as a function of position in the reactor. The time dependence of the resulting electron impact processes are then reconstructed as a time series. The OTF method was incorporated into the Electron Monte Carlo module of a 2-dimensional plasma equipment model. The time and spatial variation of low and high threshold processes in rare gas/molecular gas mixtures will be discussed, comparing systematic trends in ICP, capacitive and helicon plasma sources. In ICPs, we found that time dependence of high threshold events such as ionization are dominated by even harmonics, whereas in asymmetric CCPs, odd harmonics are also important. The harmonic content of sources increases with increasing threshold energy and pressure. ¹ ¹Work supported by NSF, SRC and Applied Materials
8:40 AM		PS2-WeM-2 Global Neutral Modeling of Fluorine Plasma Etching for MEMS Applications R.L. Jarecki, M.G. Blain, R.J. Shul (Sandia National Laboratories) The advent of time-sequenced processes featuring alternating fluorocarbon (i.e. C₄F₈) deposition and fluorine-based (i.e. SF₆) etching steps for very deep (≥100 µm) and mask-selective (≥100:1) etching of silicon¹ has made fabrication of advanced bulk MEMS (micro-electro-mechanical systems) devices much more feasible. This intriguing new application suddenly makes the fundamental process of ion-assisted etching of silicon by atomic fluorine of much greater research interest. In this work, a simple continuous stirred tank reactor (CSTR) framework has been used to model representative neutral species in an inductively-coupled etch tool during SF₆/Ar plasma etching. The well-established technique of actinometry has been employed to assess the mean relative fluorine concentration by ratioing the F I (703.7 nm) and Ar I (750.4 nm) atomic line emission collected by an optical multichannel analyzer (OMA). A strong correlation of the pressure rise upon discharge, at fixed throttle valve position, to actinometric fluorine concentration has been observed, in agreement with the CSTR model. Silicon etch rates have also been measured. By testing a range of source powers, throttle valve positions, and flowrates, the fluorine losses for a particular reactor can be characterized to complete the CSTR model. Such a model makes possible reasonable extrapolations of fluorine concentration, and hence silicon etch rate, and can potentially speed evaluation of ultimate process limits for a given hardware configuration, as well as facilitate etch process development.² ¹U.S. Patent 5,501,893, Laermer, et al., March 26, 1996. ²Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy under contract DE-AC04-94AL85000.
9:00 AM		PS2-WeM-3 Instabilities in Low-Pressure Electronegative Inductive Discharges P. Chabert (Ecole Polytechnique, France); A.J. Lichtenberg, M.A. Lieberman, A.M. Marakhtanov, H.B. Smith (University of California, Berkeley); M. Tuszewski (Los Alamos National Laboratory) Plasma instabilities are sometimes seen in commercial inductive processing tools with attaching gas feedstocks. We have studied these instabilities experimentally in low-pressure inductive discharges with Ar/SF6 mixtures using optical emission, Langmuir probes, microwave diagnostics, neutral and ion mass spectrometry, a fast video camera, and voltage-current sensors. The onset of instability as a function of pressure and driving power was explored for gas pressures between 2.5 and 100 mTorr and absorbed powers between 150 and 1200 W. The frequency of the oscillations increases with pressure and lies between 1 and 100 kHz. At a given pressure, there is a power window at the transition from capacitive to inductive modes where oscillations are seen in charged particle density, electron temperature and plasma potential (the unstable region). The instability window gets smaller as the argon partial pressure increases. The settings of the matching network influence the frequency of the instability. We have improved a previously developed volume-averaged (global) model to describe the instability. We consider a cylindrical discharge containing time varying densities of electrons, positive ions, negative ions, and time invariant excited states. The driving power is applied to the discharge through a conventional L-type capacitive matching network, and we use realistic models for the inductive and capacitive energy deposition and the particle losses. The particle and energy balance equations are integrated, considering quasi-neutrality in the plasma volume and charge balance at the walls, to produce the dynamical behavior. As pressure or power is varied to cross a threshold, the instability is born at a Hopf bifurcation, with relaxation oscillations between higher and lower density states. The model qualitatively agrees with experimental observations, and phase plane portraits of the dynamics found experimentally and theoretically are in good agreement.
9:20 AM		PS2-WeM-4 3-Dimensional Modeling of Asymmetric Gas Heating in Plasma Processing Reactors¹ P. Subramonium, M.J. Kushner (University of Illinois) As wafer sizes increase, obtaining uniform processing conditions becomes more problematic particularly with respect to side-to-side asymmetries. Side pumping or gas injection produces asymmetries not only in the gas density but also in ion temperatures and fluxes. As a major source of gas heating is momentum transfer from ions, small asymmetries in ion temperatures are amplified through asymmetries in gas pressure. To investigate the consequences and prevalence of asymmetric gas heating and gas temperatures, a 3-dimensional plasma equipment model was improved by adding multi-fluid modules for gas and ion temperatures. A temperature is computed for each neutral and heavy particle species, while accounting for convective transport, conduction, compressive heating, sources, momentum exchange between species and temperature jumps at surfaces. As ion heating occurs dominantly in the presheath, we found that asymmetries which perturb the presheath produce gradients in ion temperature which in turn produce gas heating. Somewhat counter-intuitive, we therefore find higher gas temperatures near ports due to there being higher ion temperatures in the presheath. We will also discuss the consequences of 3-dimensional coil structures on gas heating. ¹ ¹Work supported by NSF, SRC and Applied Materials.
9:40 AM	Invited	PS2-WeM-5 Electron-Molecule Collisions in Processing Plasmas¹ V. McKoy (California Institute of Technology) In the plasmas that are widely used in semiconductor fabrication, inelastic collisions between low-energy electrons and polyatomic gases are the principal mechanism for the production of the reactive species responsible for etching and other processes at wafer surfaces. An understanding of the behavior of these plasmas thus depends on knowledge of the relevant electron-molecule collision cross sections. However, such cross sections, particularly those for the production of neutral fragments, are difficult to measure or to calculate and are often unknown for gases of interest. Over the past several years we have been exploiting large-scale parallel computers to calculate electron-collision cross sections for numerous flurocarbon feed gases and their radicals. In this talk, I will give an overview of these calculations and examples of the results we have obtained. ¹Work supported by Sematech, Inc. and Intel Corp. and done in collaboration with Carl Winstead and M. H. F. Bettega.
10:20 AM		PS2-WeM-7 Ionization Mechanism in ICPs F.F. Chen (UCLA) Inductively coupled plasmas with antennas wrapped around the radial surface of a cylinder are known to produce uniform plasma density profiles even though the skin depth is smaller than the discharge radius. The penetration of rf energy into interior regions has been attributed to the anomalous skin effect, in which thermal motions carry ionizing electrons past the skin layer,¹ or to the nonlinear generation of 2nd harmonic currents.² We have computed the orbits of electrons starting at arbitrary positions as they are accelerated and decelerated at different rf phases. Elastic and inelastic collisions are taken into account, and electrons are reflected when they strike the wall sheath unless they have sufficient energy to penetrate it, in which case they are lost and replaced by a slow electron elsewhere. The nonlinear Lorentz force preferentially pushes fast current-carrying electrons toward the axis. This effect, coupled with reflections from the curved wall, generates a population of fast, ionizing electrons distributed throughout the discharge. This dominant mechanism eliminates the need to place antenna elements at small radii. ¹V.A. Godyak and V.I. Kolobov, Phys. Rev. Lett. 81, 369 (1998). ²R.B. Piejak and V.A. Godyak, Appl. Phys. Lett. 76, 2188 (2000).
10:40 AM		PS2-WeM-8 A 3-dimensional Model for Wave Propagation and Plasma Properties in Magnetically Enhanced ICP Reactors¹ R.L. Kinder, M.J. Kushner (University of Illinois) Electromagnetic wave propagation in magnetically enhanced inductively coupled plasmas (MEICPs) enables power deposition to occur remotely from the coils and at locations beyond the classical skin depth. 3-dimensional, azimuthally symmetric components of the electric field can be produced by an azimuthally symmetric (m=0) antenna in flaring solenoidal static magnetic fields. Asymmetric antennas (m=+1,-1) produce 3-d components of the electric field lacking any significant symmetries, and so must be fully resolved in 3-dimensions. To investigate these processes, a 3-dimensional plasma equipment model was improved to resolve 3-d components of the electric field produced by m=+1,-1 antennas in flaring magnetic fields. A tensor conductivity was used to couple the components while solving the wave equation in the frequency domain using an iterative, sparse matrix technique. For gas pressures of 2-20 mTorr, magnetic fields of 10-300 G, we observe rotation of the electric field downstream of the antenna where significant power deposition also occurs. Feedback from the plasma which produces local extrema in conductivity (e.g., ionization rates and electron temperatures peak where fields are largest) result in the electric field patterns not having pure modal content. Comparisons for electron density and temperature will be made to probe measurements made in a MEICP having a helicon source. ¹ ¹Work supported by NSF, SRC and Applied Materials
11:00 AM		PS2-WeM-9 Modeling of Fundamental Processes in a Capacitively Coupled Helium Atmospheric-Pressure Glow Discharges X. Yuan, L.L. Raja (Colorado School of Mines) Stable, large-volume, non-equilibrium plasmas, called Atmospheric-Pressure Glow Discharges (APGD), are emerging as an important new class of glow discharges with several potential applications in materials processing. These discharges operate in a previously inaccessible regime of the plasma parameter space, where properties resemble low-pressure glow plasmas but at significantly higher (atmospheric) pressures. Recently, several investigators have reported the generation of large-volume APGD and uses of APGD in the processing of materials. However, there exists no clear explanation of the structure of these discharges and the reasons for their stability. This paper reports detailed one-dimensional model-based investigation of a capacitively coupled APGD. The paper will discuss the structure of these highly collisional, non-equilibrium plasmas and the chemical nature of these discharges. Model predictions of the stability boundaries of the discharge will be reported. Results show that for certain operating conditions and working gas compositions, stable operating regimes between breakdown and arcing are obtained. Model predictions for discharge V-I characteristics and the stability boundaries are compared to experimental results reported in the literature. This work is supported by a NSF-CAREER Award.
11:20 AM		PS2-WeM-10 A Novel Approach for Control of High-Density Plasma Process Parameters through Optimal Pulse Shaping T.L. Vincent, L.L. Raja (Colorado School of Mines) Increasingly stringent requirements in the manufacture of Integrated Circuits (IC) are demanding new approaches for the design and operation of semiconductor process equipment and plasma process equipment in particular. Indeed, several novel plasma process techniques have been proposed recently, one of which is the operation of plasma reactors in a pulsed mode. In this approach, the main ICP power to a High-Density Plasma (HDP) reactor is deliberately modulated using square-wave pulses to provide control of plasma process characteristics. Square-wave pulsed operation has been demonstrated to improve etch/deposition rates of thin films, etch selectivity, and process uniformity. In this study, we propose a completely general technique, called "pulse shaping", for the dynamic operation of plasma reactors. Pulse shaping uses a numerical optimal control methodology for the systematic design of power modulation waveforms to achieve user-specified plasma process conditions. In the work discussed here, a time-dependent global model for an argon HDP reactor is used in conjunction with an optimal control algorithm to demonstrate that optimal design of pulse shapes can be achieved to simultaneously control time-averaged bulk plasma electron temperature and active species composition. Results are presented to illustrate the potential for significantly improved control of plasma characteristics over simple square-wave modulation of reactor power.