Three-dimensional transport phenomena in chemical vapor deposition equipment: A comparison of theoretical predictions wi
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I.
INTRODUCTION
THE rapidly
growing interest in chemical vapor deposition (CVD) processes has stimulated a great deal of useful research into the transport phenomena (heat flow, fluid flow, and mass transfer) that take place in CVD equipment, t1-14] An excellent review of such work has been recently reported by Jensen. t~SJ Virtually all of this earlier work, except References 13 and 14, has postulated two-dimensional (2-D) flow behavior; thus, it was possible to address longitudinal variations in the deposition rate (the majority of the papers have been addressing this problem), and attention has been drawn also to possible lateral variations due to the existence of roll cells at a fixed axial position. In a recent paper, El61 the present authors have addressed the full three-dimensional (3-D) problem in considering CVD in a rectangular reactor and have shown that the interaction of the lateral and longitudinal variations in flow and transport phenomena, in general, can have a marked effect in producing strong nonuniformities in the deposition rate. More specifically, it was shown that nonuniformities in the deposition rate may be produced by the combination of the entrance effects, that is, the initial development of the concentration boundary layer, by roll cells due to thermal natural convection and, to a lesser extent, by the "edge effects," that is, the proximity of the vertical wails. These computed results appear to be plausible and, in general, qualitative agreement with prior experience; however, a direct quantitative test of these 3-D predictions has not been possible up to the present time. In a recent paper, Park and Chun [171have reported on elegant experiments accompanied by a useful analysis of O.J. ILEGBUSI, Research Associate, and J. S Z E K E L Y , Professor of Materials Engineering, are with the Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, M A 02139. Manuscript submitted June 2, 1989. METALLURGICAL TRANSACTIONS B
the CVD of boron in a horizontally oriented reactor having the shape of a half-cylinder. Their interpretation of the measurements using a somewhat simplified, quasi 2-D (boundary layer-type) model was only partially successful. However, the data presented provide an excellent opportunity for testing predictions that may be derived on the basis of a more realistic 3-D representation of the system. The purpose of the present paper is twofold. One objective is to develop an improved interpretation of the experimental measurements reported by Park and C h u n . [171 The second objective is to provide a more detailed examination of the behavior of horizontal CVD equipment, exploring the effect of key process parameters on the uniformity of the deposition rate.
II.
FORMULATION
Let us consider a horizontal CVD reactor of arbitrary shape, such as that sketched in Figure 1. The specific cases to be examined in this instance are also sketched in this figure and are seen to include a rectangular box, a half-cylinder (corresponding to the
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