Liquid Phase Diffusion Growth Research Articles

Conservative finite volume strategy for investigation of solution crystal growth techniques

The article presents a finite volume method for the numerical study of solution crystal growth. The mathematical model is based on the time-dependent Navier-Stokes equations in the stream function/vorticity form, energy and mass transfer equations in solid and liquid phases, and thermodynamics equilibrium conditions at the phase transition interface. The problem is axisymmetric and studied in a cylindrical body-fitted coordinate system. The equations for temperature and composition in the solid and liquid phases, and interface velocity are solved simultaneously. The approach ensures global conservation of kinetic and thermal energy and conservation of the solute. The proposed strategy allows performing a full-scale numerical simulation of a variety of technological regimes with a reversal in the crystal dissolution and growth. Sample calculations are reported for prototypes of liquid phase diffusion growth process and Bridgman-Stockbarger method.

Numerical Analysis of the Combined Influence of Accelerated Crucible Rotation and Dynamic Crucible Translation on Liquid Phase Diffusion Growth of SiGe

The effects of accelerated crucible rotation technique (ACRT) and dynamic translation on liquid phase diffusion (LPD) growth of SixGe1−x single crystals have been separately investigated numerically in earlier works and were found to have a very positive impact on the LPD growth process. Building upon these findings, in this paper, we study the consequences of imposing both ACRT and dynamic translation on this growth technique. Time-dependent, axisymmetric numerical simulations using moving grid approach have been carried out using finite volume code Ansys Fluent. Crucible translation effect is simulated using dynamic thermal boundary condition. Results are compared to the case in which this growth system is subjected to ACRT only. It is predicted that by combining ACRT with dynamic pulling, excellent axial compositional uniformity can be achieved and growth rate can be improved substantially without significantly compromising on the benefits of employing ACRT. The results show that it is advantageous to utilize the combination of ACRT and dynamic translation during LPD growth rather than using them independently for producing relatively uniform composition SixGe1−x single crystals in a shorter span of time.

Numerical study of liquid phase diffusion growth of SiGe subjected to accelerated crucible rotation

The effect of accelerated crucible rotation technique (ACRT) on liquid phase diffusion (LPD) growth of SixGe1−x crystal has been investigated numerically. Transient, axisymmetric simulations have been carried out for triangular and trapezoidal ACRT cycles. Natural convection driven flow in the early growth hours is found to be modified by the ACRT induced Ekman flow. Results also reveal that a substantial mixing in the solution can be induced by the application of ACRT in the later hours of growth which is otherwise a diffusion dominated growth period for LPD growth technique. A comparison is drawn to the cases of stationary crucible and crucible rotating at a constant speed examined previously for this growth system by Sekhon and Dost (J. Cryst. Growth 430 (2015) 63). It is found that a superior interface flattening effect and radial compositional uniformity along the growth interface can be accomplished by employing ACRT at 12rpm than that which could be achieved by using steady crucible rotation at 25rpm, owing to the higher time averaged growth velocity achieved in the former case. Furthermore, minor differences are also predicted in the results obtained for trapezoidal and triangular ACRT cycles.

Numerical examination of the effect of steady crucible rotation in the liquid phase diffusion growth of SiGe

A numerical simulation study has been carried out to investigate the influence of steady crucible rotation on the LPD growth of SixGe1−x. Results reveal the effectiveness of suppressing natural convection driven flows with the application of ampoule rotation. Improvement in the uniformity of radial composition of the growing crystal is predicted after two hours of growth for the remaining simulated growth period. Further, a marginal reduction in the growth interface curvature due to crucible rotation is also observed in the results. Numerical computation shows the potential of crucible rotation as a viable alternative to static magnetic field in inhibiting buoyancy induced flows in the LPD growth of SixGe1−x.

Numerical and experimental investigation of the effect of crucible translation in liquid phase diffusion growth of SiGe

We have studied the effect of crucible translation in liquid phase diffusion (LPD) growth of bulk SixGe1−x crystals numerically and experimentally. Two sets of translation experiments were performed at the stationary and translated (at constant rate) modes. Experiments showed the feasibility of growing SiGe crystals with uniform composition.In order to determine the optimum translation profile, the LPD system was numerically simulated. The impact of dynamic translation rate has also been examined numerically by prescribing dynamic thermal boundary conditions along the growth ampoule. The numerical and experimental findings reveal a significant reduction in the axial composition variation in the grown crystal, with an additional advantage of shorter growth period thereby justifying the use of crucible translation as a means to achieve higher compositional uniformity in the grown crystals.

The Effect of Applied Magnetic Fields on Silicon Transport in Liquid Phase Diffusion Growth of SiGe

The effect of applied rotating and static magnetic fields on silicon transport during the liquid phase diffusion growth of SiGe was experimentally studied. The fields were examined on their own and in combination. A 72-hour growth period was used to produce the concentration profiles. Single crystal growth was not of primary concern. The effect of the magnetic fields on the thermal field in the system was significant, often inhibiting good growth conditions. The static field had the effect of slowing transport when compared with a sample processed with no applied field. The application of rotating magnetic field leads to additional mixing and enhances transport in the melt compared with that with no field. The combined field exhibited a similar concentration profile to the rotating field alone.

Silicon transport under rotating and combined magnetic fields in liquid phase diffusion growth of SiGe

AbstractThe effect of applied rotating and combined (rotating and static) magnetic fields on silicon transport during the liquid phase diffusion growth of SiGe was experimentally studied. 72‐hour growth periods produced some single crystal sections. Single and polycrystalline sections of the processed samples were examined for silicon composition. Results show that the application of a rotating magnetic field enhances silicon transport in the melt. It also has a slight positive effect on flattening the initial growth interface. For comparison, growth experiments were also conducted under combined (rotating and static) magnetic fields. The processed samples revealed that the addition of static field altered the thermal characteristics of the system significantly and led to a complete melt back of the germanium seed. Silicon transport in the melt was also enhanced under combined fields compared with experiments with no magnetic field. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Effect of a static magnetic field on silicon transport in liquid phase diffusion growth of SiGe

AbstractLiquid phase diffusion experiments have been performed without and with the application of a 0.4 T static magnetic field using a three‐zone DC furnace system. SiGe crystals were grown from the germanium side for a period of 72 h. Experiments have led to the growth of single crystal sections varying from 0 to 10 mm thicknesses. Examination of the processed samples (single and polycrystalline sections) has shown that the effect of the applied static magnetic field is significant. It alters the temperature distribution in the system, reduces mass transport in the melt, and leads to a much lower growth rate. The initial curved growth interface was slightly flattened under the effect of magnetic field. There were no growth striations in the single crystal sections of the samples. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Effect of an applied static magnetic field on silicon dissolution into a germanium melt

An experimental investigation has been undertaken to explore the benefits of an applied static magnetic field on silicon transport into a germanium melt in a crucible configuration similar to that used in the liquid phase diffusion (LPD) and Czochralski growth systems. The measured concentration profiles with and without an applied magnetic field showed a very similar shape, while the amount of silicon transport into the melt was slightly higher in the samples processed under magnetic field. There was, however, a substantial difference in the dissolution interface shape. Without field, a flat stable interface is observed. In the presence of an applied field, the dissolution interface remains flat in the center but dramatically curves back into the source material near the wall. This indicates a far higher dissolution rate at the edges of the silicon source. It appears that the altered flow structure in the melt, due to the applied magnetic field, has increased transport at the dissolution interface near the crucible wall. In LPD growth the silicon transport is higher through the center of the melt and leads to a change in the interface shape from a concave interface towards the melt to a convex interface towards the melt at growth conclusion. The present experimental results indicate that an applied static field may be used to enhance silicon transport in LPD to obtain a more favorable (flatter) growth interface for less inclusions in the grown crystals.

A numerical simulation study for the combined effect of static and rotating magnetic fields in liquid phase diffusion growth of SiGe

The article presents the results of a numerical simulation study conducted to examine the combined effect of static and rotating magnetic fields on the liquid phase diffusion (LPD) growth process of SiGe single crystals. The simulation results indicate that the combined use of static and rotating magnetic fields is more effective than using either a static or rotating field alone. The application of a combined field does not only suppress natural convection but also leads to better mixing in the solution and flatter growth interfaces. For the system considered here, the application of a static field of 0.3 T and a rotating field of 4.0 or 5.0 mT makes the growth interface almost flat.

A numerical simulation study for the effect of magnetic fields in liquid phase diffusion growth of SiGe single crystals

The article presents the results of a numerical simulation study conducted to examine the effect of static and rotating magnetic fields on the growth process of SiGe single crystals by liquid phase diffusion (LPD). A three-dimensional transient numerical simulation model was developed to observe the heat, mass, and momentum transfer characteristics of the SiGe solution. Simulation results indicate that the use of a static, vertical magnetic field in this growth setup is effective in suppressing natural convection in the solution. A stationary field intensity of 0.3 T is sufficient to provide significant suppression, above which the flow becomes numerically unstable. However, the vertical magnetic field does not provide the expected flattening in the growth interface. In the case of a rotating magnetic field (RMF), results show that the use of RMF is effective in providing sufficient mixing in the melt leading to more homogeneous SiGe crystals. In addition, RMF is also very beneficial for flattening the growth interface. At the 3.0 mT a RMF intensity level, the growth interface becomes almost flat.

A continuum model for the Liquid Phase Diffusion growth of bulk SiGe single crystals

In this article, we present a computational model for the growth of Si x Ge 1− x single crystals by Liquid Phase Diffusion (LPD) from the germanium-rich side of the binary Si x Ge 1− x phase diagram. The model accounts for some important physical features of the LPD growth process of Si x Ge 1− x such as a growth-zone design on the thermal field, the buoyancy induced convective flow and its effect on the growth process, the evolution of growth interface, and the variation of growth velocity with time. Two- and three-dimensional numerical simulations were carried out. Simulation results show that the natural convection in the solution is very strong during the initial stages of the growth process, and gets weaker as the growth progresses. Diffusion becomes the dominant mass transport mechanism during the rest of the growth process. Computed growth interface shapes and growth velocities agree with experimental observations.