Vapor deposition modeling for an entrenched wafer geometry

Empirical models for chemical vapor deposition of SiO2 from tetraethylortho silicate (TEOS) and O-3 have been proposed using one- and two-precursor mod els of the surface rate limited reaction kinetics. In the one-precursor mod el, considered here, the wafer surface is described by a Robin boundary con dition, Phi = Phi(sat) - <(alpha)over tilde>(partial derivative Phi/partial derivative (n) over tilde), where Phi is the concentration of the gas phas e generated reactant precursor, Phi(sat) is its saturation concentration, ( n) over tilde is a normal vector pointing outward from the diffusion region (into the wafer substrate), and d is a surface reaction kinetics parameter . The validity of the diffusion model approximation for transport in the co ntinuum and near continuum regimes dictates that Phi be a solution to the L aplace 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 r ectangle (flat Robin boundary) or five sides of an octagon (entrenched Robi n boundary). Closure of the geometrical boundary (diffusion region) results from the abstract construction of outer vertical polygonal sides [homogene ous Neumann boundaries where (partial derivative Phi/partial derivative (n) over tilde) = 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 tr ench. For the rectangle, it suffices to model adsorption along the base (fl at wafer substrate) with a constant <(alpha)over tilde>. For the entrenched wafer surface, a phenomenological curvature dependence in <(alpha)over til de> has been previously proposed to arise due to the introduction of corner s and edges via the trench. We propose a spatial dependence in <(alpha)over tilde> which unfolds from the transformation properties of the Robin bound ary condition when an infinite rectangle (flat wafer geometry) is conformal ly mapped into an octagon (entrenched wafer geometry). The boundary conditi ons for the transformed wafer surface are then used in a Green's function b oundary integral equation formulation of the problem. Numerical solutions, presented for the diffusion current, the surface reaction kinetics paramete r, <(alpha)over tilde>, and the deposition concentration, Phi, prove to be consistent with a conformal (uniform) film profile. (C) 1999 American Vacuu m Society. [S0734-2101(99)04801-0].