Analysis of Ge distribution in Si1 − xGex single crystal fibers by the micro-pulling down method

Study of the mechanism of crystallization electromotive force during growth of congruent LiNbO3 using a micro-pulling-down method

“…Therefore, the solute flux is described basically in terms of the diffusion of the solute concentration and the growth velocity. A detail analysis of solute distribution in m-PD growth using a one-dimensional differential equation was reported by Uda et al [13,14]. The treatment of the electricfield-driven transport using effective velocity, V E:cry , is based on the method reported in Ref.…”

“…Fig. 8 shows a schematic diagram of the m-PD growth system that consists of the molten zone (zone 1) next to the interface and the capillary nozzle (zone 2) through which the solute transform from the bulk melt to the molten zone [13,14]. The coordinate system is tied to the moving interface.…”

“…Even though Marangoni flow is clearly observed in m-PD growth, the influence of Marangoni flow is negligible because it exists only at the free surface of the molten zone and it does not disturb the solute transport. Therefore, the diffusion layer is characterized mainly by diffusion in a direction perpendicular to the growth interface [13,14]. In a conventional growth method such as Czochralski growth, solute distribution near the liquid-solid interface is influenced not only by the vertical flow of the solute but also by radial flow, and hence one cannot simply apply a one-dimensional differential equation to the analysis of solute distribution [15,16].…”

The effect of the pressure difference across the free surface in case of a NdYAG micro fiber growth by the micro-pulling-down process

“…3b. c) The pressure limits (13) can be written as: (according to (13)). The stability of the meniscus can be obtained using (14).…”

“…According to [10], for this process some simple theoretical analyses for the operation limits [11] and solute distribution [12,13] have been performed and no detailed modeling has been conducted. In [14] the meniscus shape and size, appearing in μ-PD were evaluated in function of pressure difference, which incorporates the hydrostatic pressure of the melt column situated behind the meniscus and the gas pressure in front of the free surface of the meniscus.…”