Theoretical analysis of a mass conservation equation for a surface reaction between two parallel plates of a chemical vapor deposition reactor

Abstract
A steady-state, two-dimensional mass conservation equation for a surface reaction is theoretically analyzed in order to investigate how the pressure, reactor size, and so on influence the chemical vapor deposition. A theoretical solution is obtained on the assumptions of an isothermal environment between the two parallel plates (distance h), a constant flow velocity (u), and a balanced surface reaction rate (rate constant k) and diffusion flux (diffusion coefficient D) on the plates. The concentration C(x, y) of the reactive species normalized by the inlet concentration C_o is expressed as [MATH] where θ_i tan θ_i = kh/2D which are key parameters. The deposition rate G(x) along the flow can be simplified to G(x)/G(0) = exp(-kx/2uh) when kh/2D << 1 and [MATH], which are often valid for low-pressure processes. We theoretically show that a higher rate results from a lower pressure when p > 100 Pa under kh/2D = 0.2, uh/2D = 1, and x/h = 10.