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In some CVD processes the precursor is introduced into the reactor as vapor obtained by sublimation from particles of solid source forming packed bed in a column, where through a carrier gas passes. A typical example is the deposition of metal or metal oxide using its carbonyl compound. The study evaluates by mathematical modeling the effect of particle size reduction due to sublimation on the composition of the gas phase entering the reactor. A set of differential equations describing the convective solid to gas mass transfer process in the column is formulated. Equations for precursor equilibrium partial pressure, mass transfer coefficient, diffusivity and axial dispersion coefficient found from literature are added and the model is solved numerically by the method of finite differences. On the example of W(CO) 6 the influence of the carrier gas flow rate, temperature and CVD duration on the change of the precursor concentration is revealed. The calculated alterations are significant and may spoil the running experiments. As to prevent this problem three approaches are suggested allowing the maintenance of the reactor inlet precursor concentration in reasonable limits: (i) to use a sufficiently high initial bed for saturation of the carrier gas during the entire particular experiment; (ii) to increase step-by- step in time the bed temperature; (iii) to increase step-by-step in time the carrier gas velocity in the column on the account of its stream by-passing the column. In all three approaches the model allows to calculate the necessary factors, i.e. the sufficient bed height, the temperature and velocity increment in time. Some numerical experiments employing the suggested approaches with approximately constant precursor concentrations are illustrated. Approaches how to proceed when multicomponent coating is to be deposited are discussed. The main conclusion is that the CVD processes should be carefully prepared accounting for a possible unsteadiness and the concentration of the precursor at the reactor inlet should be monitored. |
