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Dispersive Transport Equations and Multiscale Models pp 51–76Cite as

Integrated Multiscale Process Simulation in Microelectronics

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Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 136))

Abstract

We discuss selected applications of integrated multiscale process simulation (IMPS) that are particularly relevant to integrated circuit fabrication. We first summarize approaches to IMPS for two processes for which the governing equations are well accepted. In these cases, models for equipment scale (meter), pattern scale (mm) and feature scale (micron) are solved simultaneously. The first approach uses regular grids, and is applied to low-pressure chemical vapor deposition (LPCVD) of silicon dioxide from tetraethoxysilane (TEOS). The second approach uses unstructured meshes, and is applied to electrochemical deposition (ECD) of copper. The goal is to develop approaches to estimate “loading” in these processes; i.e., the effects of pattern density and topography on local deposition rates. This is accomplished by resolving pattern (mesoscopic, mm) scales, which are between equipment (0.1-1 m) and feature scales (0.1-1 μm). In this work, we focus on steady state simulation results. We close the discussion of deposition processes with a few thoughts on extending IMPS to the grain scale, and the conversion of discrete atomistic representations to continuum representations of islands during deposition. We end by discussing progress made towards IMPS for chemical mechanical planarization (CMP). In this example, well-accepted models or relevant simulators do not exist for any scale of the process.

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Author information

Authors and Affiliations

  1. Focus Center-New York: Rensselaer, Rensselaer Polytechnic Institute, Troy, NY, 12180, USA

    Timothy S. Cale, Max O. Bloomfield, David F. Richards & Sofiane Soukane

  2. Scientific Computation Research Center, Rensselaer Polytechnic Institute, Troy, NY, 12180, USA

    Kenneth E. Jansent

  3. Mechanical Engineering, Aeronautical Engineering and Mechanics, Rensselaer Polytechnic Institute, Troy, NY, 12180, USA

    John A. Tichy

  4. Department of Mathematics and Statistics, University of Maryland, Baltimore County, Baltimore, MD, 21250, USA

    Matthias K. Gobbert

Authors
  1. Timothy S. Cale
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  2. Max O. Bloomfield
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  4. Sofiane Soukane
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  5. Kenneth E. Jansent
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  7. Matthias K. Gobbert
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Editor information

Editors and Affiliations

  1. Laboratoire MIP, Université Paul Sabatier, Toulouse Cedex 4, 31062, France

    Naoufel Ben Abdallah  & Pierre Degond  & 

  2. Angewandte Mathematik, Universität des Saarlandes, Saarbrucken, D-66041, Germany

    Anton Arnold

  3. Department of Mathematics, University of Texas at Austin, Austin, TX, 78712, USA

    Irene M. Gamba

  4. Department of Mathematics, Indiana University, Bloomington, IN, 47405-5701, USA

    Robert T. Glassey

  5. CSCAMM, University of Maryland, College Park, MD, 20742-4015, USA

    C. David Levermore

  6. Department of Mathematics, Arizona State University, Tempe, AZ, 85287, USA

    Christian Ringhofer

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Cale, T.S. et al. (2004). Integrated Multiscale Process Simulation in Microelectronics. In: Abdallah, N.B., et al. Dispersive Transport Equations and Multiscale Models. The IMA Volumes in Mathematics and its Applications, vol 136. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8935-2_4

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  • DOI: https://doi.org/10.1007/978-1-4419-8935-2_4

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-6473-6

  • Online ISBN: 978-1-4419-8935-2

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