Bulletin of the American Physical Society
61st Annual Gaseous Electronics Conference
Volume 53, Number 10
Monday–Friday, October 13–17, 2008; Dallas, Texas
Session WF3: Computational Methods for Plasmas |
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Chair: J.P. Boeuf, LAPLACE, CNRS - University of Toulouse Room: Addison Room |
Friday, October 17, 2008 10:00AM - 10:30AM |
WF3.00001: Numerical Simulation on the Profile of Plasma and Radicals in Plasma Chambers Invited Speaker: With the dimensions of integrated circuit devices approaching less than 45nm regime, the control of uniformity of plasma and radicals in etching chamber becomes more and more important. In spite of many studies on the capacitively coupled plasma, there had been no matured one which can predict the plasma and radical profiles in a plasma chamber reasonably. Recently, I. Lee et al. [1] proposed a new model to predict the non-uniformity of radial power deposition caused by electromagnetic effects such as standing wave and skin effects. Y. Yang et al. [2] has proposed a coupled solution method between plasma fluid eqs. and Maxwell eqs. to consider both EM and electrostatic effects. In this report, we present some results on our methodology-mix to predict the profile of plasma and radicals comparing with the measured data. The non-uniformity of plasma and radicals are governed by many process and tool parameters like as pressure, gas species, gas flow-rate, frequency and power of RF, configuration of electrodes and wall, solid materials surrounding plasma and so on. From a physical standpoint of view, these parameters change the impedances of plasma or boundary materials and affect some non-linear phenomena among plasma, sheath and boundary materials. Considering these aspects, we developed a several kind of models and methods. One of them is the introduction of a new dimensionless parameter to predict the uniformity of plasma. One of the other is the hybrid method to predict the plasma and radicals profiles by using the two-dimensional numerical simulation models described above. Based on the chemical reaction database either developed by ourselves or obtained in the published papers, we've calculated the profiles of plasma and radicals and compared the calculated electron density profile with the measured one in a mass-production chamber in case of some gases to confirm the good accuracy of the calculation. [1] I. Lee et al. : Plasma Sources Sci. Technol. (17) 2008, p16 [2] Y.Yang et al. : Proceeding of IITC 2008 [Preview Abstract] |
Friday, October 17, 2008 10:30AM - 10:45AM |
WF3.00002: ABSTRACT WITHDRAWN |
Friday, October 17, 2008 10:45AM - 11:00AM |
WF3.00003: Quantitative improvement in MD-based plasma etching simulator: Si etching by halogen-including plasmas Hiroaki Ohta, Tatsuya Nagaoka, Akira Iwakawa, Koji Eriguchi, Kouichi Ono Classical molecular dynamics (MD) is widely used as a numerical technique to simulate interactions between chemically reactive plasmas and solid materials. Although many MD studies have been published, discussions on the accuracy, capability, and validly are still lacking. Here we focus on simulations of Si etch by HBr/Cl$_{2}$ plasmas because this is used in the state-of-art fabrication of gate structures or shallow trench isolators included in SRAMs. In this conference, recent progresses in our simulation technique are reported. First, a Stillinger-Weber-type interatomic potential for Si/H/Br systems was newly developed. Second, we modify its potential form adding a new term partially including multibody interactions, which enabled us to predict thicknesses of reaction layers more accurately. From the analysis of obtained etch yields for cases of Si etch by various ions such as Cl$^{+}$, Cl$_{2}^{+}$, Br, Br$_{2}^{+}$, HBr$^{+}$, and H$^{+}$, a new scaling law, which is an extension of Steinbruchel's scaling, were derived. Third, simulations including both high-energy ions and low-energy neutral radicals with high neutral-to-ion flux ratio were performed. The distinct characteristics (monotonically decreasing yield curve as a function of incident angle) in realistic plasma conditions could be reproduced. [Preview Abstract] |
Friday, October 17, 2008 11:00AM - 11:15AM |
WF3.00004: Finite volume formulation of low-temperature plasma equations and numerical solution in one dimension Mirko Vukovic Differential transport equations for plasma are most commonly discretized using the finite difference formalism. More recently, discretizations based on the finite element method have also been used. An alternate method is the finite volume method which discretizes the integral conservation equations.\footnote{Numerical Heat Transfer and Fluid Flow, Suhas V. Patankar, McGraw-Hill, 1980} This method conserves flux across the grid cell interfaces. In this presentation, we present the discretization of plasma transport equations based on the finite volume formalism. We will discuss the discretization of the drift-diffusion, momentum, and electron kinetic equations based on this formalism. A one-dimensional problem will be solved for several DC and time-dependent cases. [Preview Abstract] |
Friday, October 17, 2008 11:15AM - 11:45AM |
WF3.00005: 3-Dimensional Modeling of Capacitively and Inductively Coupled Plasma Etching Systems Invited Speaker: Low temperature plasmas are widely used for thin film etching during micro and nano-electronic device fabrication. Fluid and hybrid plasma models were developed 15-20 years ago to understand the fundamentals of these plasmas and plasma etching. These models have significantly evolved since then, and are now a major tool used for new plasma hardware design and problem resolution. Plasma etching is a complex physical phenomenon, where inter-coupled plasma, electromagnetic, fluid dynamics, and thermal effects all have a major influence. The next frontier in the evolution of fluid-based plasma models is where these models are able to self-consistently treat the inter-coupling of plasma physics with fluid dynamics, electromagnetics, heat transfer and magnetostatics. We describe one such model in this paper and illustrate its use in solving engineering problems of interest for next generation plasma etcher design. Our 3-dimensional plasma model includes the full set of Maxwell equations, transport equations for all charged and neutral species in the plasma, the Navier-Stokes equation for fluid flow, and Kirchhoff's equations for the lumped external circuit. This model also includes Monte Carlo based kinetic models for secondary electrons and stochastic heating, and can take account of plasma chemistry. This modeling formalism allows us to self-consistently treat the dynamics in commercial inductively and capacitively coupled plasma etching reactors with realistic plasma chemistries, magnetic fields, and reactor geometries. We are also able to investigate the influence of the distributed electromagnetic circuit at very high frequencies (VHF) on the plasma dynamics. The model is used to assess the impact of azimuthal asymmetries in plasma reactor design (e.g., off-center pump, 3D magnetic field, slit valve, flow restrictor) on plasma characteristics at frequencies from 2 -- 180 MHz. With Jason Kenney, Ankur Agarwal, Ajit Balakrishna, Kallol Bera, and Ken Collins. [Preview Abstract] |
Friday, October 17, 2008 11:45AM - 12:00PM |
WF3.00006: Prediction of SiO$_{2}$ etching profile under the presence of RIE-lag effect Takashi Yagisawa, Toshiaki Makabe As the size of ULSI elements shrinks further, functional design for a top-down plasma processing will be strongly required in order to predict and overcome many types of damages induced by plasma etching. The reactive ion etching (RIE) of high-aspect contact hole (HARC) or inter-layer dielectric (ILD) has been traditionally performed by fluorocarbon chemistry under the presence of high-energy ion bombardment in a two-frequency capacitively coupled plasma (2f-CCP) reactor. It is experimentally known as RIE-lag effect that the etching rate at the bottom decreases with increasing the aspect ratio of the pattern. The dependence of etch rate on the aspect ratio will be a crucial issue to be addressed in a top-down plasma nano-processing. In the present study, a feature profile evolution of SiO$_{2}$ trench pattern is predicted under competition among etching and polymer deposition by the level-set method. When the etch depth is small, the incident ions are reflected at the sidewall and focused in the center of the trench, resulting in a slight enhancement of the etch rate at the bottom. On the other hand, the geometrical shadowing effect which reduces both ions and radicals striking the bottom surface will be dominant at high aspect ratio. Dependence of RIE-lag on a biasing voltage will also be discussed. [Preview Abstract] |
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