Mathematical model for simulating axisymmetric rod growth with kinetically limited and mass transport limited rates

摘要

Laser-induced Chemical Vapor Deposition (LCVD) is an emerging technique in freeform fabrication of high aspect ratio microstructures with many practical applications. The LCVD process is kinetically limited at low temperatures and pressure. The growth rate rises exponentially with temperature and becomes mass transport limited beyond a certain threshold. While the surface temperature drives the deposition rate of a heterogeneous pyrolytic reaction, the rate obtained depends on the reaction activation energy and the ability of the precursor reactants and by-products to transport to and from the surface. To achieve precise control of the thermal deposition near the focus of a laser beam, a mathematical model for 3-D LCVD is developed taking into account both kinetically limited and mass transport limited reactions. The model describes heat transport in the substrate and deposit as well as the gas-phase mass transport and temperature in the reaction zone in order to determine growth rate. A finite difference method is developed for solving the governing equations and an iterative algorithm is presented for simulating the process. The applicability of the model is demonstrated by growing a rod from silicon deposited on a graphite substrate.