Journal of Crystal Growth 193 (1998) 552—562 Theoretical analysis of the micro-pulling-down process for Ge  Si  fiber crystal growth C.W. Lan*, S. Uda, T. Fukuda  Department of Chemical Engineering, National Taiwan University, Taipei 10617, Taiwan, ROC  Central Research Institute, Mitsubish Materials Co. Ltd., 1-297 Kitabukuro-Cho, Omiya, Saitama 330, Japan  Institute of Materials Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-77, Japan Received 29 December 1997; accepted 2 June 1998 Abstract Theoretical analysis of the micro-pulling-down process for the growth of Ge  Si  single crystal fibers is conducted using a finite-volume/Newton’s method. Steady-state heat and nondilute solute transfer, melt flow, the melt/crystal interface, and the free surface as well as the grown fiber diameter are solved simultaneously. The effects of process parameters including the melt height, the die temperature, and the growth rate on the grown fiber diameter and solute distribution are investigated. Good agreement is found for the calculated meniscus shape and the grown fiber diameter with the observed ones. In the melt zone, due to the small physical dimension and the damping effect by Ge, buoyancy convection is negligible. However, Marangoni convection is dominant there and the solute segregation is thus affected. As the melt zone becomes shorter with the decreasing die temperature, a secondary flow is induced by the Marangoni convection leading to an inversion on radial segregation and a large depletion of Ge in the fiber core, which are consistent with the measurements.  1998 Published by Elsevier Science B.V. All rights reserved. PACS: 44.25. #f; 47.27.Te; 81.10.Fg; 02.60.Cb; 02.70.Fj Keywords: Micro-pulling-down; Fiber growth; Computer simulation; Convection; Segregation 1. Introduction The unique properties of near one-dimensional single crystal fibers have attracted some attention on the applications of optical and electronic devices * Corresponding author. Fax: #886 2 2363 3917; e-mail: lan@ruby.che.ntu.edu.tw. [1—3]. The device-size as-grown fibers also reduce processing cost (for size reduction) significantly for device fabrication. There are several methods for growing fiber crystals [4], such as the edge-defined film-fed growth (EDFG), floating zone (pedestal growth) methods, etc. Recently, the micro-pulling- down (-PD) process, a variant of the inverse EDFG, developed by Fukuda’s laboratory in Japan [5—9] has been shown promising in pro- ducing single crystal fibers with good diameter 0022-0248/98/$ — see front matter  1998 Published by Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 0 2 4 8 ( 9 8 ) 0 0 5 2 7 - 2