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.

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.

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

Combined Marangoni and buoyancy convection in a porous annular cavity filled with Ag-MgO/water hybrid nanofluid

2021 ◽  
Vol 17 ◽  
Author(s):  
B. Kanimozhi ◽  
M. Muthtamilselvan ◽  
Qasem M. Al-Mdallal ◽  
Bahaaeldin Abdalla
Keyword(s):  
Magnetic Field ◽  
Stokes Equations ◽  
Volume Fraction ◽  
Axial Magnetic Field ◽  
Vertical Wall ◽  
Navier Stokes ◽  
Hybrid Nanofluid ◽  
Radial Magnetic Field ◽  
Navier Stokes Equations ◽  
Buoyancy Convection

Background: This article numerically examines the effect of buoyancy and Marangoni convection in a porous enclosure formed by two concentric cylinders filled with Ag-MgO water hybrid nanofluid. The inner wall of the cavity is maintained at a hot temperature and the outer vertical wall is considered to be cold. The adiabatic condition is assumed for other two boundaries. The effect of magnetic field is considered in radial and axial directions. The Brinkman-extended Darcy model has been adopted in the governing equations. Methods: The finite difference scheme is employed to work out the governing Navier-Stokes equations. The numerically simulated outputs are deliberated in terms of isotherms, streamlines, velocityand average Nusselt number profiles for numerous governing parameters. Results: Except for a greater magnitude of axial magnetic field, our results suggest that the rate of thermal transport accelerates as the nanoparticle volume fraction grows.Also, it is observed that there is an escalation in the profile of average Nusselt numberwith an enhancement in Marangoni number. Conclusion: Furthermore, the suppression of heat and fluid flow in the tall annulus is mainly due to the radial magnetic field whereas in shallow annulus, the axial magnetic field profoundly affects the flow field and thermal transfer.

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 Thermo-solutal convection with Soret effect

2021 ◽  
Author(s):  
Md. Abdur Rahman
Keyword(s):  
Porous Layer ◽  
Liquid Layer ◽  
Marangoni Convection ◽  
Stokes Equations ◽  
Soret Effect ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Solutal Convection ◽  
Buoyancy Convection

In the present study, the onset of thermal convection in a liquid layer overlying a porous layer where the whole system is being laterally heated is investigated. The non-linear two-dimensional Navier Stokes equations, the energy equation, the mass balance equation and the continuity equation are solved for the liquid layer. Instead of the Navier Stokes equations, the Brinkman model is used for the porous layer. The partial differential equations are solved numerically using the finite element technique. A two-dimensional geometrical model with lateral heating is considered. Two different cases are analyzed in this thesis. In the first case, the gravity driven buoyancy convection and the Marangoni convection are studied. For the Marangoni convection, the microgravity condition is considered and the surface tension is assumed to vary linearly with temperature. Different aspect ratios, as well as thickness ratios, are studies in detail for both the buoyancy and the Marangoni convection. Results revealed that for both the buoyancy and the Marangoni cases, flow penetrates into the porous layer, only when the thickness ratio is more than 0.90. In the case of thermo-solutal convection in the presence of Soret effect, it has been found that the isopropanol component goes either towards the hot or the cold walls depending on the fluid mixtures which has been used in the system.

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.

Thermodiffusion, Marangoni and Gravity Driven Convections in a Liquid Layer Overlying a Porous Layer: Lateral Heating Conditions

2008 ◽  
Author(s):  
M. A. Rahman ◽  
M. Z. Saghir
Keyword(s):  
Porous Layer ◽  
Liquid Layer ◽  
Marangoni Convection ◽  
Stokes Equations ◽  
Microgravity Condition ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Aspect Ratios ◽  
Buoyancy Convection ◽  
Gravity Driven

In this paper, we study the onset of thermal convection in a liquid layer overlying a porous layer, where the whole system being laterally heated. The non-linear two-dimensional Navier Stokes equations, the energy equation and the mass transfer equation are solved for the liquid layer. Instead of Navier Stokes equations, the Brinkman model is used for the porous layer. The partial differential equations are solved numerically using the finite element technique. Three cases are presented in this paper. In the first case, the gravity driven buoyancy convection is studied. In the second case, the surface tension is assumed to vary linearly with temperature, therefore the existence of Marangoni convection. To analyze the Marangoni convection, we consider microgravity condition. Different aspect ratios as well as the thickness ratios are studied in detail for both the first and second cases. In the third case, diffusion and the thermodiffusion between two binary fluids with two different compositions in liquid and porous layer is studied.

scholarly journals Thermo-solutal convection with Soret effect

2021 ◽  
Author(s):  
Md. Abdur Rahman
Keyword(s):  
Porous Layer ◽  
Liquid Layer ◽  
Marangoni Convection ◽  
Stokes Equations ◽  
Soret Effect ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Solutal Convection ◽  
Buoyancy Convection

In the present study, the onset of thermal convection in a liquid layer overlying a porous layer where the whole system is being laterally heated is investigated. The non-linear two-dimensional Navier Stokes equations, the energy equation, the mass balance equation and the continuity equation are solved for the liquid layer. Instead of the Navier Stokes equations, the Brinkman model is used for the porous layer. The partial differential equations are solved numerically using the finite element technique. A two-dimensional geometrical model with lateral heating is considered. Two different cases are analyzed in this thesis. In the first case, the gravity driven buoyancy convection and the Marangoni convection are studied. For the Marangoni convection, the microgravity condition is considered and the surface tension is assumed to vary linearly with temperature. Different aspect ratios, as well as thickness ratios, are studies in detail for both the buoyancy and the Marangoni convection. Results revealed that for both the buoyancy and the Marangoni cases, flow penetrates into the porous layer, only when the thickness ratio is more than 0.90. In the case of thermo-solutal convection in the presence of Soret effect, it has been found that the isopropanol component goes either towards the hot or the cold walls depending on the fluid mixtures which has been used in the system.

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