Effects of angular vibration on the flow, segregation, and interface morphology in vertical Bridgman crystal growth W.C. Yu a , Z.B. Chen a , W.T. Hsu b , B. Roux c , T.P. Lyubimova d , C.W. Lan b, * a Department of Molecular Science and Engineering, National Taipei University of Technology, Taiwan, ROC b Department of Chemical Engineering, National Taiwan University, Taipei 10617, Taiwan, ROC c Laboratoire Mode ´lisation et simulation nume ´rique en me ´canique, L3M: CNRS-Universite ´s d’Aix-Marseille, France d Institute of Continuous Media Mechanics UB RAS, Perm, Russia Received 18 May 2006 Available online 25 September 2006 Abstract The effect of angular vibration on the flow, segregation, and interface morphology during vertical Bridgman crystal growth was inves- tigated. Transparent experiments using SCN containing about 0.02 wt.% acetone were performed. To simulate the observed results, both direct numerical simulation (DNS) and Schlichting boundary layer approximation (SBLA) were considered in the computer model. The simulated morphological breakdown patterns, as a result of acetone accumulation (segregation), are consistent with the experimental observation. At high frequency with low amplitudes, both simulation approaches gave consistent results. However, care must be taken in using SBLA for low frequency vibration of several hertz. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: Angular vibration; Convection; Morphology; Segregation; Directional solidification 1. Introduction The vertical Bridgman or gradient freeze technique is a popular method for crystal growth. The simplicity in oper- ation and the low thermal gradients are particular suitable to the growth of compound semiconductor crystals [1,2]. The stabilized thermal configuration is also a great advan- tage offering weak convection and less growth striations due to flow stability. However, the lack of melt stirring could often cause large radial and axial non-uniformities due to the segregation of dopants. For the heavy-doping situation, the local accumulation of dopants can also accelerate constitutional supercooling, which leads to the morphological breakdown of the planar interface [3–6]. Therefore, an active control over the melt convection is extremely important for this growth process. Several control methods have been proposed for vertical Bridgman crystal growth, including using magnetic fields e.g., [7,8], centrifugal forces [9–11], and the accelerated crucible rota- tion technique (ACRT) [12]. Recently, a technique using angular vibration has been proposed and found effective in reversing the flow and seg- regation near the growth interface [13,14]. However, the detailed numerical analysis and parameter studies have not yet been carried out. In principle, the angular vibration technique (AVT) is very similar to ACRT, but ACRT uses a much lower frequency. In ACRT, in order to develop the Eckman boundary layer, the time for a spin-up or spin- down cycle is usually in the order of 2R c = ffiffiffiffiffiffiffiffiffiffiffi X R m m p , where R c is the crystal radius, X R the rotation speed, and m m the kinematic viscosity of the melt. This time constant is usu- ally several tens of seconds for most of the materials having the diameter of several centimeters. On the other hand, based on the same operation, AVT uses a much higher fre- quency. Such a vibration causes a streaming flow at the growth interface, and thus effective in the local flow and 0017-9310/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijheatmasstransfer.2006.06.040 * Corresponding author. Tel./fax: +886 2 2363 3917. E-mail address: cwlan@ntu.edu.tw (C.W. Lan). www.elsevier.com/locate/ijhmt International Journal of Heat and Mass Transfer 50 (2007) 58–66