A simplified analytical model of diamond growth in direct current arcjet reactors
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Michael E. Coltrin Chemical Processing Sciences Department, Sandia National Laboratories, Albuquerque, New Mexico 87185 (Received 9 February 1995; accepted 14 April 1995)
A simplified model of a direct current arcjet-assisted diamond chemical vapor deposition reactor is presented. The model is based upon detailed theoretical analysis of the transport and chemical processes occurring during diamond deposition, and is formulated to yield closed-form solutions for diamond growth rate, defect density, and heat flux to the substrate. In a direct current arcjet reactor there is a natural division of the physical system into four characteristic domains: plasma torch, free stream, boundary layer, and surface, leading to the development of simplified thermodynamic, transport, and chemical kinetic models for each of the four regions. The models for these four regions are linked to form a single unified model. For a relatively wide range of reactor operating conditions, this simplified model yields results that are in good quantitative agreement with stagnation flow models containing detailed multicomponent transport and chemical kinetics. However, in contrast to the detailed reactor models, the model presented here executes in near real-time on a computer of modest size, and can therefore be readily incorporated into process control models or global dynamic loop simulations. I. INTRODUCTION Of the high growth rate deposition technologies for the synthesis of diamond via low-pressure ( 2600 the model predicts subequilibrium concentrations of H in the free stream. This particular transition at 2600 K between sub- and superequilibrium H is a consequence of the torch power used in that calculation, 25 kW. This temperature would change for a different torch power. For a fixed torch power this transition must occur because as the desired exit temperature is increased more of the input energy goes into gas heating, and consequently less of this energy can go into H2 dissociation.
B. Free stream region The free stream region, the portion of the system between the plasma torch exit and the top of the boundary layer, is characterized by a high-velocity, moderately high Reynolds number (100 s£ Re =£ 300) flow. Although the jet issuing from the plasma torch has a high velocity, typically between 5 X 104 and 3 X 105 cm/s, the flow is laminar because of the moderate reactor pressures and high gas temperatures utilized in these systems. In this work, reactor pressures ranging from 5 to 60 Torr are considered; in this range the free stream flow is subsonic, with Mach numbers significantly below unity. At pressures lower than approximately 5 Torr, however, a significant portion of the flow region may be trans- or supersonic, with multiple transverse and oblique shocks present. While the model presented in this section for the free stream region does not capture the details of the hydrodynamics, it does rely on the assumption that the flow is incompressible, such that the speed of sound is infinite and the pressure is therefore uniform. Thu
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