A computer simulation of crystal growth by the traveling-solvent method (TSM): pseudo-steady-state calculations

Abstract

A computer rimulauoo is conducted to smdy single-crystal growth by the travelingsolvent method (TSM) using a pseudo-steady-state model. The model. which ts govemed by momentum, heat, and mass balances in the system. is solved by a Bnite-volume/Newton method.Flow patterns, temperature and solute distributions, and unknown melWsolid interfaces are calculated simultaneously. The model is mainly developed for binary compounds for which the solubility of solvent in solid materials is negtigible. In such a system an integrability condition, which results from an overall solvent balance, is required to ensure the unique solution of solute fields in the computation. Sample calculations are reponed for CdTe. a 11-VI-compound semicandudor. grown from Te solvent. Due to strong couplmg of solute and tempemme fields and Rurd Row, as well as phase equilibrium, the effect of convection on the interface morphology and zone positron IS significant in such a system. Through computer simulation, the effects of some process parmeters, including the growth speed. heater temperature, and initial solvent volume, on interface shapes, convective mass uansfer, and constitutional supercooling at different degrees of convection xe also demonstrated. C JV Lan and D T Yang hlodel descriptionThe steady-state TSM growth of a binary-compound crystal is simulated using a pseudosteady-state model (PSSM). The PSSM mainly neglects the evolution of the system caused by the displacement of the ampoule in the furnace. This approximation is usually valid for the TSM system, because of the sufficiently small growth rates used. So, when a steady State is reached the growth rate is equal to the ampoule pulling speed. If heating is axisymmetic, the physical domain for the feed, the solution zone, the crystal, and the ampoule can be taken as shown in figure 1. The RHS of figure 1 shows an effective ambient-temperature distribution for computation. As it is, it can be treated as a two-dimensional model. The flow, temperature, and solute fields, as well as the shapes of the feed front (the feedsolution interface, hf(r)) and the growth front (solutiodcrystal interface, hC(r)), are represented in the cylindrical coordinate system ( r , z).The solubility of the solvent in the feed and the crystal is neglected, while the feed and growth fronts are assumed to be in equilibrium. Since the density difference between

Analysis of the traveling heater method for the growth of cadmium telluride

“…At slightly higher growth rates (not shown), the increased tellurium segregation drives the dissolution interface further downward until it meets the growth interface, representing the maximum growth rate in zero gravity. Qualitatively, these results agree remarkably well with the prior computations by Lan and Yang [19], where a similar effect is seen for cases under microgravity with small solvent volumes.…”

“…With the exception of the model of Lan and Yang [19], we argue that all of the prior attempts to model this complicated system have been flawed by ignoring important transport phenomena or by inconsistent application of thermodynamic concepts. We address these shortcomings in the model presented here.…”

“…However, most prior THM models apply different conditions along the dissolution interface, which we assert is inappropriate. Only Apanovich and Ljumkis [18] and Lan and Yang [19] openly identify the use of this condition at the dissolution interface.…”

“…The quantity C V is known from the amount of excess tellurium originally added to the growth system to produce the liquid zone. The prior models of Chang et al [17], Lan and Yang [19], Martinez-Tomas et al [23], and Dost and Liu [26] explicitly identified the specification of such an integral constraint, while Ghaddar et al [22] and Stelian and Duffar [14] did not. These two models instead relied on the specification of composition at the dissolution interface to set the overall level of excess tellurium in the zone, an expedient that we believe is inappropriate (see also the discussion after eq.…”

Fluid dynamics in crystal growth: The good, the bad, and the ugly

“…Despite the strengths of the THM, it is currently hampered by growth rates that are more than one order of magnitude slower than those routinely employed in Bridgman methods [71,72,[85][86][87][88][89]. Prior models for this process have suggested that morphological instability could readily arise in THM [90,91]. However, these past works did not identify the mechanisms that are responsible for such instability.…”