Thermal-capillary analysis of the horizontal ribbon growth of silicon crystals

Daggolu, Parthiv; Yeckel, Andrew; Bleil, C.E.; Derby, Jeffrey J.

doi:10.1016/j.jcrysgro.2012.06.055

Cited by 26 publications

(17 citation statements)

References 40 publications

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“…A substantial change in growth length at the solidification interface was found to significantly affect the growth process, because this large change means that an increased amount of latent heat is extracted, and there is a heat imbalance. The results obtained via the study described in this section do not agree with a finding presented by Dagglou [15], as the simulation performed in this study demonstrated that a long interface may facilitate heat dissipation while also disrupting growth stability as a result of the meniscus growing in size and consequently restricting the length of silicon growth. Although sufficient heat extraction is necessary because the thickness is dependent on the rate of heat extraction, the interface length must be controlled to ensure that changes to the shape of the interface will be minimized, as this would mandate a higher heat extraction rate on the surface or a smaller initial thickness.…”

Section: Diffuse Growth Lengthcontrasting

confidence: 95%

“…Past studies [11,12,15,17] have shown that, because of the viscosity, pulling rate, and heat extraction on the surface, an unstable meniscus forms on the underside of the silicon crystal at the edge of the crucible. Consequently, the unstable meniscus generates a heat imbalance in the growth process, which thus results in an irregular lower surface.…”

Section: Analytical Modelmentioning

confidence: 99%

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Modeling and Analysis of Novel Horizontal Ribbon Growth of Silicon Crystal

Shen

Sun

et al. 2018

Crystals

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Abstract:We present a novel horizontal ribbon growth (HRG) process and a theoretical analysis of this method. Assuming that the existence of the meniscus is defined by diffuse growth, we determine analytically the thickness and height of the meniscus and an explicit expression for the performance of meniscus under different conditions. We then calculate the thermal profile in melt part, as well as the conditions under which the undercooling is sufficient around the solidification point. We find that diffuse growth is more sensitive to small initial thickness, and find the minimum length of the melt part to obtain undercooling. Finally, we calculate the change rule of solidification position by a variational approach, as well as the stability of the process under different conditions. We also give an expression to the instability of past HRG methods.

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Section: Diffuse Growth Lengthcontrasting

confidence: 95%

Section: Analytical Modelmentioning

confidence: 99%

Modeling and Analysis of Novel Horizontal Ribbon Growth of Silicon Crystal

Shen

Sun

et al. 2018

Crystals

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“…8 Daggolu analyzed the thermal capillary action, stable growth state, and solute segregation of HRG via numerical analysis. [9][10][11] Weinstein simulated the evolution of the melt crystallization interface in a large melt growth system. 12 More recently, numerical simulations of the heat transfer, melt convection and capillary effects problems have been analysed during the HRG process.…”

Section: Introductionmentioning

confidence: 99%

Simulating the horizontal growth process of silicon ribbon

et al. 2018

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In this paper, we present a solidification growth model that primarily describes the principal components of horizontal ribbon growth process, but also discusses the interaction between fluid flow and heat transfer, crystallization dynamics, and the effects of oxygen impurity distribution in melts, particularly with respect to the morphology of the interface. The effects of the jet cooling rate, pulling speed, and transfer coefficient on solute transport were studied. The results showed that a higher jet velocity produces a sharper temperature gradient at the interface and a stronger Marangoni effect, facilitates solute transport in the silicon melt, and promotes higher oxygen concentration in crystal. The stronger Marangoni convection causes more rapid oxygen transfer in the silicon melt and a higher oxygen concentration. Solidification front increases the downward flow velocity of the eddy current as the pulling speed is increased; this leads to a decrease in solute concentration at the interface. An increase in the downward flow of the vortex confluence facilitates the reduction of solute concentration in the crystal. An increase in the upward flow of the vortex confluence will increase the concentration in the crystal. The oxygen concentration is concentrated at the top and bottom of the silicon ribbon.

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“…More recently, numerical simulations of the Stefan problem have been used to verify the conclusions of the wedge analysis [18][19][20]. In [18], it was shown that the growth wedge changes length as a function of pull speed, and it was also shown that, depending on the assumed boundary conditions, supercooling could appear in front of the solidification front.…”

Section: Introductionmentioning

confidence: 99%

Experimental and numerical investigation of the horizontal ribbon growth process

Helenbrook

Kellerman

Carlson

et al. 2016

Journal of Crystal Growth

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Experimental and numerical results are presented on the process of horizontal ribbon growth (HRG) of single-crystal silicon. Experimental data on the leading edge position of the growth front as a function of pull speed is compared to model predictions with and without solidification kinetic effects. Without kinetics, the numerical results predict leading edge positions which are completely different than that observed in the experiment. With kinetics, the leading edge position is predicted typically within 1 mm and the change in position with pull speed also is well predicted. Conclusions from the kinetic model are that the growth occurs through a faceted process where the leading edge is a {111} facet that requires significant supercooling to maintain the growth. An outcome of the model is that the leading edge position versus pull speed response shows a turning point beyond which there are no steady growth solutions. This is consistent with all previously reported experiments on this process, which have reported maximum attainable pull-speeds. These results

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Thermal-capillary analysis of the horizontal ribbon growth of silicon crystals

Cited by 26 publications

References 40 publications

Modeling and Analysis of Novel Horizontal Ribbon Growth of Silicon Crystal

Modeling and Analysis of Novel Horizontal Ribbon Growth of Silicon Crystal

Simulating the horizontal growth process of silicon ribbon

Experimental and numerical investigation of the horizontal ribbon growth process

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