Dialytic regime

Figure 6.12. Arrhenius plot for silicon deposition from several precursors. The shaded area indicates a change from the catalytic to the dialytic regime on increasing temperature.

The pyrolytic regime is distinguished from the (diffusion-limited) dialytic regime by the effect of the input gas flow rate on the deposition rate. Both transport-controlled regimes occur at high temperatures, where the slopes of the Arrhenius plot decrease (Figure 6.12). In the case of small equilibrium constants, the slope of the Arrhenius plot in the pyrolytic regime equals the reaction heat, as will be shown below. 

The dialytic regime is characterized by high surface reaction rate coefficients and by rate-limiting diffusion. The Sherwood number (Sh) characterizes the regimes. Sh is defined as the ratio of the driving force for diffusion in the boundary layer to the driving force for surface reaction alternatively, it is the ratio of the resistivity for diffusion to the resistivity for chemical reaction (reciprocal reaction rate coefficient). Diffusion limitation is the regime at Sh 1 and reaction limitation means Sh 1. The Sherwood number is closely related to the Biot, Nusselt, and Damkohler II numbers and the Thiele modulus. Some call it the CVD number. In the boundary-layer model it is a simple function of the thickness of the boundary layer, the diffusion coefficient, and the reaction rate coefficient. For simplicity a first-order reaction will be considered in the derivation below. 

All this is valid only in the catalytic or reaction-limited regime (see Chapter 6). There is another effect of the fractal dimension of the surface on the growth rate and on the morphology of the resulting product. This is the ease of transport of the reactants to the surface before they adsorb and react. In the dialytic regime, e.g., in the case of an Eley-Rideal mechanism with slow diffusion, the reaction occurs mainly on the top of a fractal surface and less on the less accessible parts. The Eley-Rideal expression of the rate is then raised to a power dependent on the dimension of the surface.Higher surface dimensions mean relatively higher reaction rates because the reactants have better accessibility to the surface. 

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