For a proper description of growth by metal organic vapour phase epitaxy the three-dimensional Navier-Stokes partial differential equations need to be solved which govern the following series of processes: (i) transport by diffusion and flow through the gas phase, (ii) reactions which take place in this gas phase, (iii) reactions which take place at the surface. The authors are at first interested in the medium- and higher-temperature regions, which cover the growth determined by diffusion through the gas phase (medium temperature) and the growth that is determined by the desorption of growth species (higher temperature). Using a number of well justified assumptions one can reduce the problem to a two-dimensional one. For the diffusion-limited region (i.e. medium-temperature region) the effect of different flow profiles (plug flow, parabolic flow, linear increasing velocity and combination of plug and linear profile) on the growth rate has been studied under isothermal conditions. It was found that all profiles yield the same growth rate within a few per cent, so that it suffices to use the simple plug flow profile in growth rate calculations. It is also shown that axial diffusion is an important effect only at the end of long reactors. Finally a model is derived in which surface reaction kinetics is combined with the diffusion-limited model for the isothermal case.
Sark, van, W. G. J. H. M., Janssen, G. J. H. M., Croon, de, M. H. J. M., & Giling, L. J. (1990). Analytical models for growth by metal organic vapor phase epitaxy. I.Isothermal models. Semiconductor Science and Technology, 5(1), 16-35. https://doi.org/10.1088/0268-1242/5/1/003