Effects of Gas Phase Kinetics

To properly describe chemical vapor deposition, one must develop a system of equations that encompasses all phenomena involved. This includes a proper representation of reactions in the gas phase, a suitable description of the surface kinetics, and the gas dynamics of a reacting gas mixture. Because the full governing equations are extremely complex and difficult to solve, most authors have examined only limited regimes. For example, we can ignore the gas dynamics 

Unfortunately, chemical vapor deposition is a field which is, basically, interdisciplinary. Essential understanding can be gained by including all of the phenomena involved. To do this in full generality would require the solution of many coupled, nonlinear, partial differential equations. Such a formulation is clearly beyond the scope of this text. 

We will, therefore, choose to look at a particular simplified physical problem, but attempt to formulate the problem from first principles. This should lead to a problem, which although complex and involving nonlinear equations, can at least be described by ordinary differential equations. 

As in the classical Poisseulle flow, the channel is assumed to be two-dimensional (nothing varies in the z direction) and doubly infinite in the x direction. We will impose a constant temperature, T, on each wall and assume that T will not vary with x. An axial pressure gradient will have to exist in order for there to be an axial flow, and we recognize that it should be constant so that p will vary linearly with x. 

In a typical CVD reactor, mass flow is small so the pressure gradient will be small. Since p, T and density p are related by the equation of state, we can expect p = p(x). However, the variation in density with x will be small, and it will be reasonable to neglect it. 

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