Journal of Crystal Growth 240 (2002) 305–312 Modelling of the temperature changes by adequate changes of the pulling rate in the case of sheets and filaments grown from the melt in a vacuum by EFG method L. Braescu a , A.M. Balint b, *, I. Jadaneantu b , St. Balint c a Department of Mathematics, University Politehnica Timisoara, Str: Regina Maria, Nr: 1, 1900 Timisoara, Romania b Department of Physics, University of the West Timisoara, Blv: V. Parvan, Nr: 4, 1900 Timisoara, Romania c Department of Mathematics, University of the West Timisoara, Blv: V. Parvan, Nr: 4, 1900 Timisoara, Romania Received 10 October 2001; accepted 22 January 2002 Communicated by D.T.J. Hurle Abstract The main purpose of this paper is to give a model-based proof of the fact that the effect of the variations of the melt temperature at the meniscus basis can be compensated by an adequate variation of the pulling rate in the case of sheets and filaments grown from the melt in a vacuum by EFG method. For that, we find the range of the pulling rate and the melt temperature couples for which the system of differential equations which governs the evolution of the sheet half- thickness (or filament radius) x ¼ xðtÞ and the meniscus height h ¼ hðtÞ has asymptotically stable steady states. Computation is made in a nonlinear model for silicon sheets and filaments for a die of half-thickness x 0s ¼ 0:03 cm and radius x 0f ¼ 0:2 cm, respectively. The asymptotically stable steady states are determined and the region of attraction of each steady state is estimated. Using these regions of attractions we show what happens if during the growth the pulling rate v or/and the melt temperature T m at the meniscus basis are changed. For a given variation of the melt temperature at the meniscus basis during the growth, we find an adequate variation of the pulling rate v in order to obtain a single crystal sheet or filament with constant half-thickness or radius, respectively. r 2002 Elsevier Science B.V. All rights reserved. PACS: 81.10 Keywords: A1. Computer simulation; A1. Directional solidification; A2. Edge defined film fad growth; A2. Growth from melt; A2. Microgravity conditions; A2. Single crystal growth 1. The mathematical model The system of differential equations which governs the evolution of the sheet half-thickness (or the filament radius) x ¼ xðtÞ and the meniscus height h ¼ hðtÞ is dx dt ¼v tg½aðx; hÞ a c ; dh dt ¼ v  1 Lr 2 ½l 1 G 1 ðx; hÞ l 2 G 2 ðx; hÞ: ð1Þ *Corresponding author. Tel./fax: +40-56-2011-05. E-mail address: balint@quasar.physics.uvt.ro (A.M. Balint). 0022-0248/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII:S0022-0248(02)00904-1