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- W2014046198 abstract "Empirical models for chemical vapor deposition of SiO2 from tetraethylorthosilicate (TEOS) and O3 have been proposed using one- and two-precursor models of the surface rate limited reaction kinetics. In the one-precursor model, considered here, the wafer surface is described by a Robin boundary condition, Φ=Φsat−α̃(∂Φ/∂ñ), where Φ is the concentration of the gas phase generated reactant precursor, Φsat is its saturation concentration, ñ is a normal vector pointing outward from the diffusion region (into the wafer substrate), and α̃ is a surface reaction kinetics parameter. The validity of the diffusion model approximation for transport in the continuum and near continuum regimes dictates that Φ be a solution to the Laplace equation in the interior of a diffusion region “closed up” to form a polygon. The horizontal top side of the polygon represents the macroscopic free flow boundary layer. The Robin (wafer) boundary forms the base of a rectangle (flat Robin boundary) or five sides of an octagon (entrenched Robin boundary). Closure of the geometrical boundary (diffusion region) results from the abstract construction of outer vertical polygonal sides [homogeneous Neumann boundaries where (∂Φ/∂ñ)=0]. The closed-up polygon forms a rectangle in the case of a flat wafer surface and an octagon in the case of a wafer surface with a trench. For the rectangle, it suffices to model adsorption along the base (flat wafer substrate) with a constant α̃. For the entrenched wafer surface, a phenomenological curvature dependence in α̃ has been previously proposed to arise due to the introduction of corners and edges via the trench. We propose a spatial dependence in α̃ which unfolds from the transformation properties of the Robin boundary condition when an infinite rectangle (flat wafer geometry) is conformally mapped into an octagon (entrenched wafer geometry). The boundary conditions for the transformed wafer surface are then used in a Green’s function boundary integral equation formulation of the problem. Numerical solutions, presented for the diffusion current, the surface reaction kinetics parameter, α̃, and the deposition concentration, Φ, prove to be consistent with a conformal (uniform) film profile." @default.
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- W2014046198 date "1999-01-01" @default.
- W2014046198 modified "2023-09-24" @default.
- W2014046198 title "Vapor deposition modeling for an entrenched wafer geometry" @default.
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- W2014046198 doi "https://doi.org/10.1116/1.581575" @default.
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