A multiscale domain decomposition approach for chemical vapor deposition

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:246

Article

Bogers, J.¹  Kumar, K.¹  Notten, P. H. L.²  Oudenhoven, J. F. M.³  Pop, I. S.^1,4 

[1] Tech Univ Eindhoven, Dept Math & Comp Sci, CASA, NL-5600 MB Eindhoven, Netherlands

[2] Tech Univ Eindhoven, Dept Chem Engn, EMD, NL-5600 MB Eindhoven, Netherlands

[3] Imec Holst Ctr, NL-5605 KN Eindhoven, Netherlands

[4] Univ Bergen, Inst Math, N-5020 Bergen, Norway

关键词: Domain decomposition;    Reactive flows;    Chemical vapor deposition;    Multiscale;   

DOI  :  10.1016/j.cam.2012.10.018

来源: Elsevier

【 摘 要 】

We consider the process of chemical vapor deposition on a trenched Si substrate. To understand the process (including e.g. the layer conformality) at the trench scale (microscale), we need solutions at both the trench and reactor scales (macroscale). Due to the huge difference in size of these scales, straightforward numerical computations are very challenging. To overcome this difficulty, we consider a multiscale approach by introducing an intermediate scale (the mesoscale). We start with a time-continuous model describing the transport processes and then perform time discretization. At each time step, using the ideas of domain decomposition inspired from Lions (1988) [4], we provide iterative coupling conditions for these three different scales. Using a weak formulation for the time-discrete equations, we prove the convergence of this iterative scheme at each time step. The approach also provides an alternative proof for the existence of the solutions for the time-discrete formulation. (C) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

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