* Corresponding author. Tel.: # 31-15-2782835; fax: # 31- 15-2782838. E-mail address: crkleijn@klft.tn.tudelft.nl (C.R. Kleijn). 1 Current address: Philips Research Laboratories, Eindhoven, The Netherlands. Journal of Crystal Growth 212 (2000) 311}323 Symmetry breaking in a stagnation-#ow CVD reactor Helmar Van Santen1, Chris R. Kleijn*, Harry E.A. Van Den Akker Kramers Laboratorium voor Fysische Technologie, Delft University of Technology, Prins Bernhardlaan 6, 2628 BW Delft, The Netherlands Received 7 September 1999; accepted 10 January 2000 Communicated by J.J. Derby Abstract Flow-symmetry breaking owing to buoyancy e!ects in cold-wall stagnation #ow chemical vapor deposition reactors has been studied through numerical solution of the 3-D laminar Navier}Stokes equations. The mechanisms behind symmetry breaking have been outlined, and the process windows in which it may occur have been determined. For reactor height-to-diameter aspect ratios larger than one, and Rayleigh numbers (based on the reactor diameter) between Ra"2]103 and Ra"105, steady, non-axi-symmetric #ows may occur in axi-symmetric geometries. These non-axi- symmetric #ows coexist with a solution family of axi-symmetric #ows. Symmetry-breaking is found to be due to buoyancy e!ects alone, and does not result from an interaction between forced and free convection. On the other hand, symmetry-breaking can be suppressed through a relatively low inlet #ow and/or rotation rate of the wafer, corresponding to Ra/(Re2 Pr)~50. ( 2000 Elsevier Science B.V. All rights reserved. PACS: 02.30; 02.70.B; 47.11.#j; 47.15.Fe; 47.20.Bp; 52.75.R; 81.15.G Keywords: Chemical vapor deposition; Fluid dynamics; Modeling; Buoyancy; Mixed convection; Heat transfer; Symmetry; Stagnation #ow 1. Introduction In most chemical vapor deposition (CVD) ap- plications, it is essential that the deposited "lm is uniform across the susceptor surface. Hence, single-wafer CVD reactors often are designed to be axi-symmetric with a view to deposition being uni- form in the circumferential direction. Many of such CVD reactor designs are based on a stagnation type of #ow, impinging perpendicularly on to a horizontally placed susceptor [1}4]. In practise, however, an axi-symmetric design, resulting in axi- symmetric boundary and operating conditions, does not guarantee the #ow to be axi-symmetric. De Keijser and coworkers [5] were the "rst to show that the axi-symmetry may be broken in geometries of interest for CVD applications. The geometry they used was similar to that illustrated in Fig. 1 with H/D+3. In this geometry, they carried out smoke visualisation experiments on the mixed convection gas #ow, clearly exhibiting sym- metry breaking phenomena. Mixed-convection #ows, however, are very sensitive to boundary con- ditions [6] and with the experimental conditions 0022-0248/00/$ - see front matter ( 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 0 2 4 8 ( 0 0 ) 0 0 0 3 4 - 8