scholarly journals Three-Dimensional Modeling of the Rotation Effect on the Growth of Ge₁₋ˣSiˣ, by the Traveling Solvent Method

2021 ◽  
Author(s):  
Theodore Jason Makriyannis
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Axial Rotation ◽  
Considerable Effect ◽  
Navier Stokes ◽  
Computational Time ◽  
Solvent Method ◽  
Three Dimensional Modeling ◽  
Continuity Equations ◽  
Element Technique

The travelling solvent method known as TSM is a process used to produce pure and homogeneous crystals. The TSM process has been tested on many alloys producing uniform and uncontaminated crystal products. A three-dimensional numerical simulation for the growth of Ge1-xSix by the travelling solvent method under axial rotation has been modelled. In this model a mesh sensitivity analysis has been carried out to find an optimum mesh which provides accurate results while saving computational time, The full Navier-Stokes equations together with the energy, mass transport and continuity equations were solved numerically using the finite element technique. The application of crucible rotation to the travelling solvent method is an attempt to control the buoyancy induced convection throughout the melt and to suppress the three-dimensional characteristics of unsteady heat flow. The application of different rotational speeds on the solvent has also been investigated. These different speeds of rotation were shown to have a considerable effect on the buoyancy induced flow. The solute distribution throughout the melt was also affected substantially. Taking these two factors into account plays a crucial role in the crystal growth process. The speed of rotation was found to have a significant effect on the intensity of the convective flow in the melt and an optimal rotational speed was encountered.

scholarly journals Three-Dimensional Modeling of the Rotation Effect on the Growth of Ge₁₋ˣSiˣ, by the Traveling Solvent Method

2021 ◽  
Author(s):  
Theodore Jason Makriyannis
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Axial Rotation ◽  
Considerable Effect ◽  
Navier Stokes ◽  
Computational Time ◽  
Solvent Method ◽  
Three Dimensional Modeling ◽  
Continuity Equations ◽  
Element Technique

The travelling solvent method known as TSM is a process used to produce pure and homogeneous crystals. The TSM process has been tested on many alloys producing uniform and uncontaminated crystal products. A three-dimensional numerical simulation for the growth of Ge1-xSix by the travelling solvent method under axial rotation has been modelled. In this model a mesh sensitivity analysis has been carried out to find an optimum mesh which provides accurate results while saving computational time, The full Navier-Stokes equations together with the energy, mass transport and continuity equations were solved numerically using the finite element technique. The application of crucible rotation to the travelling solvent method is an attempt to control the buoyancy induced convection throughout the melt and to suppress the three-dimensional characteristics of unsteady heat flow. The application of different rotational speeds on the solvent has also been investigated. These different speeds of rotation were shown to have a considerable effect on the buoyancy induced flow. The solute distribution throughout the melt was also affected substantially. Taking these two factors into account plays a crucial role in the crystal growth process. The speed of rotation was found to have a significant effect on the intensity of the convective flow in the melt and an optimal rotational speed was encountered.

scholarly journals Three-dimensional modeling of Ge₁₋xSix by the traveling solvent method to study the effect of gravity orientations under different rotational speed

2021 ◽  
Author(s):  
Mahwish Sohail
Keyword(s):  
Crystal Growth ◽  
Rotational Speed ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Axial Rotation ◽  
Considerable Effect ◽  
Computational Time ◽  
Solvent Method ◽  
Continuity Equations ◽  
Element Technique

This thesis presents a 3-D numerical simulation study for the growth of germanium-silicon (Ge₁₋xSix) under different gravity orientation and axial rotation. The process use for crystal growth of Ge₁₋xSix is traveling solvent method known as TSM. The TSM process has been tested on many alloys producing uniform and uncontaminated crystal products. In this model a mesh sensitivity analysis his been carried out to find an optimum mesh which provides accurate results while saving computational time. The full Navier-Stokes equations together with the energy, mass transport and continuity equations were solved numerically using the finite element technique. The application of gravity orientation and crucible rotation to the traveling solvent method is an attempt to control the buoyancy induced convection throughout the melt and to suppress the three-dimensional characteristics of unsteady heat flow. These different speeds of rotation were shown to have a considerable effect on the buoyancy induced flow. The solute distribution throughout the melt was also affected substantially. Taking these two factors into account plays a crucial role in the crystal growth process. The speed of rotation showed to have a significant effect on the intensity of the convective flow in the melt and an optimal rotational speed was encountered.

scholarly journals Three-dimensional modeling of Ge₁₋xSix by the traveling solvent method to study the effect of gravity orientations under different rotational speed

2021 ◽  
Author(s):  
Mahwish Sohail
Keyword(s):  
Crystal Growth ◽  
Rotational Speed ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Axial Rotation ◽  
Considerable Effect ◽  
Computational Time ◽  
Solvent Method ◽  
Continuity Equations ◽  
Element Technique

This thesis presents a 3-D numerical simulation study for the growth of germanium-silicon (Ge₁₋xSix) under different gravity orientation and axial rotation. The process use for crystal growth of Ge₁₋xSix is traveling solvent method known as TSM. The TSM process has been tested on many alloys producing uniform and uncontaminated crystal products. In this model a mesh sensitivity analysis his been carried out to find an optimum mesh which provides accurate results while saving computational time. The full Navier-Stokes equations together with the energy, mass transport and continuity equations were solved numerically using the finite element technique. The application of gravity orientation and crucible rotation to the traveling solvent method is an attempt to control the buoyancy induced convection throughout the melt and to suppress the three-dimensional characteristics of unsteady heat flow. These different speeds of rotation were shown to have a considerable effect on the buoyancy induced flow. The solute distribution throughout the melt was also affected substantially. Taking these two factors into account plays a crucial role in the crystal growth process. The speed of rotation showed to have a significant effect on the intensity of the convective flow in the melt and an optimal rotational speed was encountered.

scholarly journals Three Dimensional Effect of Axial Magnetic Field to Suppress Convection in the Solvent of Ge0.98Si0.02 Grown By the Traveling Solvent Method

2021 ◽  
Author(s):  
Leily Abidi
Keyword(s):  
Magnetic Field ◽  
Stokes Equations ◽  
Axial Magnetic Field ◽  
Three Dimensional ◽  
Maximum Velocity ◽  
Navier Stokes ◽  
Growth Interface ◽  
Navier Stokes Equations ◽  
Solvent Method ◽  
Element Technique

A three dimensional numerical simulation of the effect of an axial magnetic field on the fluid flow, heat and mass transfer within the solvent of GE0.98Si0.02 grown by the travelling solvent method is presented. The full steady state Navier-Stokes equations, as well as the energy, continuity and the mass transport equations, were solved numerically using the finite element technique. It is found that a strong convective flow exists in the solvent, which is known to be undesirable to achieve a uniform crystal. An external axial magnetic field is applied to suppress this convection. By increasing the magnetic induction, it is observed that the intensity of the flow at the centre of the crucible reduces at a faster rate than near the wall. This phenomenon creates a stable and flat growth interface and the silicon distribution in the horizontal plane becomes relatively homocentric. The maximum velocity is found to obey a power law with respect to the Hartmann number Umax Ha⁻⁷/⁴

scholarly journals Three Dimensional Effect of Axial Magnetic Field to Suppress Convection in the Solvent of Ge0.98Si0.02 Grown By the Traveling Solvent Method

2021 ◽  
Author(s):  
Leily Abidi
Keyword(s):  
Magnetic Field ◽  
Stokes Equations ◽  
Axial Magnetic Field ◽  
Three Dimensional ◽  
Maximum Velocity ◽  
Navier Stokes ◽  
Growth Interface ◽  
Navier Stokes Equations ◽  
Solvent Method ◽  
Element Technique

A three dimensional numerical simulation of the effect of an axial magnetic field on the fluid flow, heat and mass transfer within the solvent of GE0.98Si0.02 grown by the travelling solvent method is presented. The full steady state Navier-Stokes equations, as well as the energy, continuity and the mass transport equations, were solved numerically using the finite element technique. It is found that a strong convective flow exists in the solvent, which is known to be undesirable to achieve a uniform crystal. An external axial magnetic field is applied to suppress this convection. By increasing the magnetic induction, it is observed that the intensity of the flow at the centre of the crucible reduces at a faster rate than near the wall. This phenomenon creates a stable and flat growth interface and the silicon distribution in the horizontal plane becomes relatively homocentric. The maximum velocity is found to obey a power law with respect to the Hartmann number Umax Ha⁻⁷/⁴

Numerical Modeling of Si0.15Ge0.85 by the Traveling Solvent Method

2002 ◽  
Author(s):  
T. J. Makriyannis ◽  
M. Z. Saghir ◽  
D. Labrie
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Promising Technique ◽  
High Quality ◽  
Growth Interface ◽  
Navier Stokes Equations ◽  
Solvent Method ◽  
Buoyancy Convection ◽  
Strong Convection ◽  
Element Technique

The traveling solvent method (TSM) is a relatively new and promising technique for the production of high quality semiconductors. TSM has been tested on many alloys producing pure and homogeneous crystals. In the present study the effect of buoyancy convection on the growth of the Si0.15Ge0.85 crystal grown by the traveling solvent method is investigated under different heating conditions. The full Navier-Stokes equations together with the energy and solutal equations were solved numerically using the finite element technique. The model take into consideration the losses of heat by radiation and the use of the phase diagram to determine the silicon concentration at the growth interface. Results revealed a strong convection in the solvent, which in turn is detrimental to the growth uniformity in the crystal rod. Additional numerical results showed that the convective heat transfer significantly influences the solute distribution in the liquid zone and the growth rate increases substantially.

A series-expansion study of the Navier–Stokes equations with applications to three-dimensional separation patterns

1986 ◽  
Vol 173 ◽  
pp. 207-223 ◽  
Author(s):  
A. E. Perry ◽  
M. S. Chong
Keyword(s):  
Series Expansion ◽  
Arbitrary Order ◽  
Stokes Equations ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Taylor Series Expansion ◽  
Navier Stokes ◽  
Three Dimensional Flow ◽  
Navier Stokes Equations ◽  
Continuity Equations

An algorithm has been developed which enables local Taylor-series-expansion solutions of the Navier-Stokes and continuity equations to be generated to arbitrary order. Much of the necessary algebra for generating these solutions can be done on a computer. Various properties of the algorithm are investigated and checked by making comparisons with known solutions of the equations of motion. A method of synthesizing nonlinear viscous-flow patterns with certain required properties is developed and applied to the construction of a number of two- and three-dimensional flow-separation patterns. These patterns are asymptotically exact solutions of the equations of motion close to the origin of the expansion. The region where the truncated series solution satisfies the full equations of motion to within a specified accuracy can be found.

scholarly journals THREE-DIMENSIONAL BIOMECHANICAL AND VISUALISATION MODEL OF VERTIGO DISEASE IN THE SEMI-CIRCULAR CANAL

2016 ◽  
Vol 7 (2) ◽  
Author(s):  
Žarko Milošević ◽  
Dalibor Nikolić ◽  
Igor Saveljić ◽  
Velibor Isailović ◽  
Thanos Bibas ◽  
...  
Keyword(s):  
Stokes Equations ◽  
Numerical Models ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Patient Specific ◽  
Arbitrary Lagrangian Eulerian ◽  
Navier Stokes Equations ◽  
Specific Patient ◽  
Continuity Equations ◽  
Ale Formulation

Benign paroxysmal positional vertigo (BPPV) is the most common type of vertigo. The symptoms of BPPV typically appear after angular movements of the head. BPPV leads to dizziness, nausea and imbalance. In this study, we examined a model of the semi-circular canal (SCC) with fully 3D three dimensional anatomical data from specific patient. A full Navier-Stokes equations and continuity equations are used for fluid domain with Arbitrary-Lagrangian Eulerian (ALE) formulation for mesh motion of finite element. Fluid-structure interaction for fluid coupling with cupula deformation is used. Particle tracking algorithm is implemented for particle motion. Motion of the otoconia particles which is main cause for BPPV is simulated. Velocity distribution, shear stress and force from endolymph side are presented for patient specific three SCC. We compared our numerical models with experiments with head moving and nystagmus eye tracking. Numerical simulation can give more details and understanding of the pathology of the specific patient in standard clinical diagnostic and therapy procedure for BPPV.

Buoyancy Convection During the Growth of SixGe1−x by the Traveling Solvent Method (TSM)

2004 ◽  
Vol 126 (2) ◽  
pp. 223-228 ◽  
Author(s):  
M. Z. Saghir ◽  
T. J. Makriyannis ◽  
D. Labrie
Keyword(s):  
Stokes Equations ◽  
Numerical Results ◽  
Silicon Concentration ◽  
Navier Stokes ◽  
Qualitative Comparison ◽  
Growth Interface ◽  
Navier Stokes Equations ◽  
Solvent Method ◽  
Buoyancy Convection ◽  
Element Technique

The traveling solvent method known as TSM is a process used to produce pure and homogeneous crystals structures. TSM has been tested on many alloys producing uniform and uncontaminated single crystals. In the present study the effect of buoyancy convection on the growth of the Si0.02Ge0.98 crystal grown by the traveling solvent method is investigated under different heating conditions. The full Navier-Stokes equations together with the energy and solutal equations are solved numerically using the finite element technique. The model takes into consideration the losses of heat by radiation and the use of the phase diagram to determine the silicon concentration at the growth interface. Results reveal a strong convection in the solvent, which in turn is detrimental to the growth uniformity in the crystal rod. Additional numerical results show that the convective heat transfer significantly influences the solute distribution in the liquid zone and affects the growth rate substantially. Qualitative comparison of the numerical results with the experiment conducted at Dalhousie University showed a good agreement for the silicon concentration at the growth interface.

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