L. Braescu

The growth of a single crystal filament and of a sheet with pre-established piece-wise constant diameter cross-section and half-thickness, respectively, from the melt in a vacuum by EFG method

Abstract In this paper we give a model based proof of the fact that it is possible to grow from the melt in a vacuum by EFG method single crystal filament and sheet with pre-established piece-wise constant diameter cross-section and constant thicknesses d 1 , d 2 ,…, d n , respectively of lengths l 1 , l 2 ,…, l n , changing adequately during the growth, the melt temperature T m at the meniscus basis and the pulling rate v .

The effect of a periodic movement on the die of the bottom line of the melt/gas meniscus in the case of edge-defined film-fed growth system

Abstract In this paper the usual model which permits to describe the evolution of the radius r = r ( t ) and of the meniscus height h = h ( t ) in the case of filament growth from the melt by edge-defined film-fed growth method is considered. What is specific is that the bottom line of the melt/gas meniscus is movable on the die. The main objective is to show that a periodic movement of the bottom line leads to a periodic change of the crystal radius (as it was observed by practical crystal growers) and to show that this effect can be compensated for example by an adequate periodic change of the pulling rate.

Temperature control of filament growth

Abstract In this paper for a given pulling rate we find the range of the melt temperature at the meniscus basis for which the system of differential equations governing the evolution of the crystal radius r and the meniscus height h in the case of silicon filaments grown from the melt in a vacuum by edge-defined film-fed growth method (EFG method), has asymptotically stable steady states. Computation is made in a nonlinear model for a die of radius r 0 =20 ( cm ×10 −2 ) in the case when the meniscus weight is ignored. For the pulling rate v=4 (( cm ×10 −2 )/ s ) we find that the computed range of the melt temperature at the meniscus basis Tm is 1674–1752 (K). For the melt temperature Tm in this range the computed radius r of the filament is in the range 10.269–19.966 (cm×10−2) and the meniscus height h is in the range 0.245–11.235 (cm×10−2). For each asymptotically stable steady state we estimate the region of attraction and using these regions we give a model based numerical proof of the fact that it is possible to control the diameter of a single crystal filament by changing the melt temperature at the meniscus basis, i.e. it is possible to obtain a desired piece-wise constant output with an adequate piece-wise constant input.