Three-dimensional mathematical model for transport phenomena in horizontal chemical vapor deposition reactors
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INTRODUCTION
I N chemical vapor deposition (CVD) processes, the flow of gases plays an important role in controlling the rate and uniformity of deposition, because it governs the supply of reactants to the substrate for reactions that may be limited by mass transport. Eversteijn and co-workers tl,21 and Rundle t31 were among the first to study the flow characteristics and the rate of deposition in a horizontal CVD reactor. Their models assumed a stagnant fluid boundary layer with a uniform temperature profile adjacent to the substrate and provided an analytical expression for the deposition rate as a function of input flow velocity and position along the substrate. The stagnant layer concept originated from flow visualization experiments of TiO2 particles, in which a particle-free region seen close to the substrate was interpreted as a stagnant layer. However, later laser doppler velocimeter studies revealed that the seed particles were driven away from the substrate by thermophoretic forces, t41 Giling tSl used interference holography for measuring density gradients and, implicitly, temperature gradients. This eliminated the need for seed particles and showed that flow in horizontal reactors was strongly perturbed by the entrance and buoyancy effects. However, interference holography does not provide velocity data. More recently, flow phenomena in a horizontal CVD reactor with rectangular cross section were modeled by a three-dimensional (3-D) computer program by Moffat and Jensen. t61 They considered the deposition of GaAs from Ga(CH3)3 and ASH3, in hydrogen gas at one atmospheric pressure. The predicted flow patterns showed
DEWEI ZHU, Postdoctoral Fellow, and YOGESH SAHAI, ISS Professor, are with the Department of Materials Science and Engineering, The Ohio State University, Columbus, OH 43210. Manuscript submitted February 14, 1991. METALLURGICAL TRANSACTIONS B
the formation of eddys in the reactor enclosure. Their results showed that the thermal boundary conditions may have a significant effect on the rate of deposition profile. Rhee and co-workers i7] developed a 3-D representation for the velocity, temperature, and concentration fields in horizontal CVD reactors. Thermally driven eddy cells develop in such reactors and interfere with the uniformity of the deposition rate. However, operating at reduced pressure was found to alleviate the problem caused by this effect. Using a point source inlet gave a more uniform spatial deposition rate near the entrance. Continuing efforts t8,9] are being made to develop better mathematical models for CVD reactors. A recent 3-D study on deposition of silicon from silicon tetrachloride by Ilegbusi and Szekely t91 found that the roll cell formation may be eliminated by operating the reactor at a reduced pressure. However, their predicted deposition rates appear to be high in comparison to those found experimentally for similar systems. Experimental data for the silicon tetrachloride system in a horizontal CVD reactor could not be found. However, Eversteijn and co-worke
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