An Approximate Method for Solving Unsteady Transitional and Rarefied Flow Regimes in Pulsed Pressure Chemical Vapor Deposition Process using the Quiet Direct Simulation Method

Abstract

The Quiet Direct Simulation (QDS) method is a kinetic-based flux scheme that computes true-direction fluxes of mass, momentum and energy with high computational efficiency. In QDS, the molecular velocity is represented by the Maxwell-Boltzmann equilibrium distribution approximated by a Gauss-Hermite quadrature. The QDS algorithm is suitable for parallelization with its highly local nature. In this paper, the QDS method is used to simulate highly unsteady low pressure flows encountered in a Pulsed Pressure Chemical Vapor Deposition (PP-CVD) reactor. Two simulations were conducted to study the PP-CVD reactor flow field at 1Pa and 1 kPa reactor base pressures. The time required to establish the quasi-steady under-expanded jet is found to be similar to 5ms, and the jet dissipates within 1ms of the end of injection. Simulation results also show uniform molecular arrival at the depositing substrate surface to promote uniform deposition. This important information is important to set up PP-CVD operating conditions as well as the reactor design. The assumption of the local Maxwell-Boltzmann equilibrium distribution used in the QDS scheme is then verified by examining the gradient length local Knudsen number based on the density, and by estimating the average number of particles collisions within each computational cell in one computational time step. The validity of local equilibrium assumption is found satisfactory at I kPa reactor based pressure but not at 1Pa. However, the similarity of flow phenomena in both simulations suggests QDS to be a quick approximation method for low pressure flow simulations.