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International Journal for Multiscale Computational Engineering
IF: 1.016 5-Year IF: 1.194 SJR: 0.554 SNIP: 0.68 CiteScore™: 1.18

ISSN Print: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.v4.i3.30
pages 319-335

Effect of the Knudsen Number on Transient Times During Chemical Vapor Deposition

Matthias K. Gobbert
Department of Mathematics and Statistics, University of Maryland, Baltimore County, 1000 Hilltop Circle, Baltimore, MD 21250, USA
Timothy S. Cale
Focus Center − New York, Rensselaer: Interconnections for Hyperintegration, Isermann Department of Chemical and Biological Engineering, Rensselaer Polytechnic Institute, СП 6015,110 8th Street, Troy, NY 12180-3590, USA

ABSTRACT

Models for the individual steps used to fabricate integrated circuits (ICs) are of interest in order to improve fabrication efficiency and process designs. Here we focus on deposition from the gas stream in which the dominant species is an inert carrier gas, as it flows across a wafer on which ICs are being fabricated. We model the transport of gaseous species to the surface and heterogeneous (surface) chemical reactions for chemical vapor deposition using a kinetic transport and reaction model (KTRM), which is represented by a system of linear Boltzmann equations. The model is valid for a range of pressures and for length scales from nanometers to decimeters, making it suitable for multiscale models. We present transient simulation results for transport of reactants into an inherently three-dimensional prototypical micron scale trench via structure for a wide range of Knudsen numbers. The results highlight the capabilities of the KTRM and its implementation, and demonstrate that the transients last longer for lower Knudsen numbers than for higher Knudsen numbers. We briefly discuss how the KTRM might be used in a multiscale computational model.


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