The direction decoupled Quiet Direct Simulation method for rapid simulation of axisymmetric inviscid unsteady flow in pulsed pressure chemical vapour deposition

Abstract

Pulsed Pressure–Chemical Vapour Deposition (PP–CVD) is a thin film deposition process which employs a highly unsteady flow with wide dynamic range of pressure. The large, time-varying density gradient during a PP–CVD process cycle produces a flow field in which the Knudsen number varies from the near-continuum to the rarefied regimes, making Direct Simulation Monte Carlo (DSMC) prohibitively expensive. The present directional decoupled Quiet Direct Simulation (DD-QDS) method is a novel kinetic-based flux scheme that computes fluxes of mass, momentum and energy at the interface of computational cells in a highly computationally efficient manner. The Maxwell–Boltzmann equilibrium distribution is enforced locally at each computational cell at each time step. In this paper, an axisymmetric second order directional decoupled QDS scheme is used to simulate highly unsteady flows encountered in PP–CVD reactor. Two simulations were conducted to investigate the PP–CVD reactor flow field at 1Pa and 1kPa reactor base pressures. The assumption of the local Maxwell–Boltzmann equilibrium distribution used in the QDS scheme is verified by examining the gradient length local Knudsen number based on the density, and by estimating the average number of molecular collisions within each computational cell in one computational time step. The validity of the local equilibrium assumption is found satisfactory at 1kPa reactor based pressure but not at 1Pa. The limitation of the QDS scheme in modelling PP–CVD flow was also investigated. The time required to establish the quasi-steady under-expanded jet is found to be ∼4ms, and the jet dissipates within 0.5ms of the end of injection. This important information is required to set up PP–CVD operating conditions which give uniform film deposition.