Momentum and thermal boundary-layer thickness in a stagnation flow chemical vapor deposition reactor
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Momentum and thermal boundary-layer thickness in a stagnation flow chemical vapor deposition reactor David S. Dandy and Jungheum Yun Department of Chemical Engineering, Colorado State University, Fort Collins, Colorado 80523-1370 (Received 25 March 1996; accepted 21 October 1996)
Explicit expressions have been derived for momentum and thermal boundary-layer thickness of the laminar, uniform stagnation flows characteristic of highly convective chemical vapor deposition pedestal reactors. Expressions for the velocity and temperature profiles within the boundary layers have also been obtained. The results indicate that, to leading order, the momentum boundary-layer thickness is inversely proportional to the square root of the Reynolds number, while the thermal boundary-layer thickness is inversely proportional to the square root of the Peclet number. Values computed using the approximate expressions are compared directly with numerical solutions of the equations of motion and thermal energy equation, for a specific set of conditions typical of diamond chemical vapor deposition. Because values of the Lewis number do not vary significantly from unity for many different chemical vapor deposition systems, the expression derived here for thermal boundary-layer thickness may be used directly as an approximate concentration boundary-layer thickness.
I. INTRODUCTION
Chemical-vapor-deposited (CVD) diamond is grown in a variety of environments using many different techniques.1,2 Of the high growth rate deposition technologies for the synthesis of diamond via lowpressure chemical vapor deposition, direct current (dc) arcjet reactor systems3–8 have proven to be reliable for the production of high quality, relatively large area films.9–12 In this type of reactor, high growth rates result from very large fluxes of materials passing through the plasma gun and impinging upon the substrate, and a uniform gas-phase environment and deposition over a large surface area result from the stagnation flow occurring in this type of reactor.2 A number of specific models have been developed for idealized straining flow,4 stagnation flow,2 and one-dimensional boundary layers13 in dc arcjet reactors. These models are all based upon solution of the coupled momentum, energy, and species mass conservation equations, subject to the geometric constraints appropriate for each reactor type. While the theoretical treatment of transport and chemical kinetics in the dc arcjet reactors is rigorous,2,4,12–15 the models are generally very complex and computer intensive; further the ability to obtain a converged numerical solution is often sensitive to not only the operating conditions specified, but also to the initial condition used in the iterative solution technique. These models can require anywhere from tens of minutes to several hours to successfully execute, and consequently are difficult to incorporate directly into intelligent process control design algorithms.12 1112
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