St. Balint

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.

A modified Chang–Brown model for the determination of the dopant distribution in a Bridgman–Stockbarger semiconductor crystal growth system

Abstract In this paper, we start from the Chang–Brown model which allows computation of flow, temperature and dopant concentration in a vertical Bridgman–Stockbarger semiconductor growth system. The modifications made by us concern the melt/solid interface. Namely, we assume that the phase transition does not take place on a flat mathematical surface, but in a thin region (the so-called precrystallization-zone), masking the crystal, where both phases, liquid and solid, co-exist. We deduce for this zone new effective equations which govern flow, heat and dopant transport and make the coupling of these equations with those governing the same phenomena in the pure melt. We compute flow, temperature and dopant concentration for crystal and melt with thermophysical properties similar to gallium-doped germanium using the modified Chang–Brown model and compare the results to those obtained using the Chang–Brown model.

The effect of the initial dopant distribution in the melt on the axial compositional uniformity of a thin doped crystal grown in strictly zero-gravity environment by Bridgman–Stockbarger method

Abstract The objective of this paper is to show (numerically in the framework of a mathematical model) that using a nonuniform initial dopant repartition, given by an explicit formula, the prescribed constant axial dopant concentration c cr =1 can be achieved on the solidified fraction 0–0.7 in a thin doped crystal, grown in strictly zero-gravity by Bridgman–Stockbarger method. It is also shown that the magnitude of the axial compositional nonuniformities of the crystal is small on the solidified raction 0–0.7.

The dopant distribution computed in the modified Chang-Brown model using quasi-steady state approximation

Abstract In this paper we present computed flow, temperature and concentration fields in the case of Bridgman–Stockbarger semiconductor crystal growth system, using the modified Chang–Brown model. This model is an extension of the initial Chang–Brown model in the framework of the continuum mechanics. The effect of the precrystallization-zone is included by mean of a thin porous layer (of width 10−9 m; size of solid inclusions 10−10 m; porosity 0.9) which reduces the dopant diffusivity from D to Deff=0.917D, increases the heat conductivity from K to Keff=1.1K and does not influence the flow in the zone. In computing, the true unsteady process is replaced with a quasi-steady state process. The obtained results are compared to those obtained using the initial Chang–Brown model. Comparisons prove, that the influence of the precrystallization-zone is relevant.

Interface structure in the growth of semiconductor crystals using the Bridgman-Stockbarger method

Abstract In this paper we assume, like in Balint et al. [Mater. Sci. Semiconductor Process. V3/3 (2000) 115–121], that the melt/solid interface in the case of vertically stabilized Bridgman–Stockbarger semiconductor growth system is a thin layer, masking the crystal, where a weak form of the periodical structure of the crystal exists. In these conditions, using a new diffusion coefficient in the equation of the dopant transport in the interface region, we compute the axial and radial variation of the dopant field in this region for crystal and melt with thermophysical properties similar to the gallium-doped germanium. We compare the results to those obtained in Mater. Sci. Semiconductor Process. V3/3 (2000) 115–121 [1] , where we have changed the diffusion coefficient only in the boundary condition for the dopant concentration at the melt/solid interface.

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.