Numerical investigation of heat transport and fluid flow during the seeding process of oxide Czochralski crystal growth Part 1: non‐rotating seed

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For the seeding process of oxide Czochralski crystal growth, influence of the crucible bottom shape on the heat generation, temperature and flow field of the system and the seed-melt interface shape have been studied numerically using the finite element method. The configuration usually used in a real Czochralski crystal growth process consists of a crucible, active afterheater, induction coil with two parts, insulation, melt, gas and seed crystal. At first, the volumetric distribution of heat inside the metal crucible and afterheater inducted by the RF-coil was calculated. Using this heat generation in the crucible wall as a source the fluid flow and temperature field of the entire system as well as the seed-melt interface shape were determined. We have considered two cases, flat and rounded crucible bottom shape. It was observed that using a crucible with a rounded bottom has several advantages such as: (i) The position of the heat generation maximum at the crucible side wall moves upwards, compared to the flat bottom shape. (ii) The location of the temperature maximum at the crucible side wall rises and as a result the temperature gradient along the melt surface increases. (iii) The streamlines of the melt flow are parallel to the crucible bottom and have a curved shape which is similar to the rounded bottom shape. These important features lead to increasing thermal convection in the system and influence the velocity field in the melt and gas domain which help preventing some serious growth problems such as spiral growth.

“…(3) The displacement current is neglected. Under these assumptions, the governing equations in cylindrical coordinates are [1][2][3]:…”

Section: Induction Heatingmentioning

confidence: 99%

“…(12) and (16), T a,l and T a,c are the corresponding effective ambient temperature with respect to the melt surface and the afterheater internal surfaces, respectively. In our calculation, T a,l and T a,c are given by [3,6,11,12]:…”

Section: Temperature and Flow Fieldmentioning

confidence: 99%

Influence of the crucible bottom shape on the heat transport and fluid flow during the seeding process of oxide Czochralski crystal growth

Tavakoli¹,

Wilke²,

Crnogorac³

2007

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“…without and with a gap between crucible and afterheater. The calculation conditions have been described in part 1 [11]. The results based on these extended set of boundary conditions and parameters will be presented hereafter.…”

Section: Mathematical Modelmentioning

confidence: 99%

Numerical investigation of heat transport and fluid flow during the seeding process of oxide Czochralski crystal growth Part 2: rotating seed

Tavakoli

Wilke

2007

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In this paper, the role of seed rotation on the characteristics of the two-dimensional temperature and flow field in the oxide Czochralski crystal growth system has been studied numerically for the seeding process. Based on the finite element method, a set of two-dimensional quasi-steady state numerical simulations were carried out to analyze the seed-melt interface shape and heat transfer mechanism in a Czochralski furnace with different seed rotation rates: ω seed = 5-30 rpm. The results presented here demonstrate the important role played by the seed rotation for influencing the shape of the seed-melt interface during the seeding process. The seed-melt interface shape is quite sensitive to the convective heat transfer in the melt and gaseous domain. When the local flow close to the seed-melt interface is formed mainly due to the natural convection and the Marangoni effect, the interface becomes convex towards the melt. When the local flow under the seed-melt interface is of forced convection flow type (seed rotation), the interface becomes more concave towards the melt as the seed rotation rate (ω seed ) is increased. A linear variation of the interface deflection with respect to the seed rotation rate has been found, too.

“…The self-inductance effect in the RF-coil is taken into account. Under these assumptions, the governing equations in cylindrical coordinates ( , , ) r z ϕ are [2,3,5]: Numerical method The set of fundamental equations with boundary conditions have been solved using the finite element method (the FlexPDE package [6]). …”

Section: Introductionmentioning

confidence: 99%

Influence of active afterheater on the induction heating process in oxide Czochralski systems

Tavakoli¹,

Samavat

Babaiepour

2008

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Different shapes and orientations of an active afterheater for oxide Czochralski crystal growth systems are considered and corresponding results of electromagnetic field and volumetric heat generation have been computed using a finite element method (Flex-PDE package). For the calculations, the eddy current in the induction coil (i.e. the self-inductance effect) has been taken into account. The calculation results show the importance of an active afterheater, its shape as well as its geometry and position with respect to the crucible on the heat generation distribution in a CZ growth system.