Numerical modeling of diffusive-convective physical vapor transport in cylindrical vertical ampoules
Diffusive-convective physical vapor transport (PVT) in cylindrical, vertical ampoules of aspect ratio (length/radius) between 0.5 and 10 was modeled numerically. The transport of a crystal forming component through an inert component that undergoes zero net transport was considered. Systems were treated in which: (1) with unequal molecular weight of the components and with temperature gradients typically employed in PVT, convective flow arises dominantly from solutal density gradients; and (2) with equal molecular weight of the components, convective flow can arise only from thermal expansion. It was found that, due to the diffusion-induced horizontal density gradients, buoyancy-driven convective flows are superimposed on the diffusive-advective fluxes without threshold. Net recirculation sets in adjacent to the growing interface, in contrast to the corresponding monocomponent situation where marginally stable convective modes fill the whole fluid space. Depending on the orientation of the main transport direction with respect to gravity, convection can either reduce or enhance the diffusion-induced radial concentration gradients. Significant enhancement of the net transport rate was found to occur only when the whole vapor space between source and growing crystal is filled by a convective recirculation roll. Solutal and thermal convection results are similar; yet for quantitative discussions, thermal and solutal Rayleigh numbers are not interchangeable in contrast to convective situations that lack net mass transport across the fluid space.