晶体生长数值模拟

Quasi-steady
– thermal equilibrium – adapted heater power Inverse dynamic to get the prescribed – adapted heater power Quasi-dynamic crystal diameter to grow the prescribed frozen geometry – –heat source on the (except the crystal shape solid-liquid interface) solidification front in – effect of pull rate and to thepower pull to getsolid-liquid interface –proportion adapted heater rate the prescribed crystal diameter deformation on the – effect of pull rate and solid-solidification heat liquid interface deformation on the solidification heat
Numerical strategy (cont’d)
FEMAG-1 timedependent simulation of Czochralski Ge growth
Direct dynamic simulation (imposed stepwise decrease of heater power, calculated crystal shape): evolution of the temperature field
2
Introduction
How to improve the growth process in terms of:
- crystal quality ? - process yield ? - energy consumption ? - production rate ?
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• d) Geometrical modeling: to accurately handle strongly deforming bodies and interface and well-capture all the boundary layers
• e) Solution technique: coupled Newton-Raphson iterations by use of a highly effective linear solver
Analysis of conical growth and shouldering stages m = 8.225 10-4 kg/m.s Wc= 3.82 rpm (0.4 s-1) Ws= -3.82 rpm (-0.4 s-1) Vpul = 1.8 cm/h (5. 10-6 m/s)
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• Principal objective has been to complete the platform
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Introduction (cont’d)
FEMAG software development strategy
• a) Global modeling: subdivision of the furnace into “macro-elements” (solid or liquid constituents, radiation enclosures, “cement” elements...) • b) Time-dependent modeling: use of various simulation modes (ex: quasi-steady, quasi-dynamic, inverse or direct dynamic models in Cz growth) • c) FEM discretization: use of 2D, Spectral 3D, Cartesian 3D,… models (high geometrical flexibility, simple assembling technique)
Inverse dynamic simulation (imposed crystal shape, calculated heater power): power oscillations resulting from inverse modeling, and smoothed power
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晶体生长数值模拟
Franç ois Dupret1,2, Roman Rolinsky2, Brieuc Delsaute2, Rajesh Ramaya2, Nathalie Van den Bogaert2
1
Universitécatholique de Louvain, Louvain-la-Neuve, Belgium FEMAGSoft S.A. company, Louvain-la-Neuve, Belgium
Direct dynamic
– simulation of the system response to perturbations of the input parameters – very useful for controller design FEMAGSoft © 2013
Numerical strategy (cont’d)
Heat shield
Typical FEMAG-CZ global unstructured mesh
components
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Numerical strategy (cont’d)
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Numerical strategy (cont’d)
Different simulation techniques
Quasi-steady
Quasi-dynamic
– may capture the – frequently used detailed system – cheap, but not always valid dynamics at various stages – does not allow crystal quality prediction – very useful for Inverse dynamic controller design – often more reliable than quasi-steady model – highly attractive to predict crystal quality
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Introduction (cont’d)
Solving these problems requires …
• To develop a sound physical model for each separate effect
→ global and time-dependent modeling of heat transfer, turbulence modeling, defect modeling, …
Direct dynamic
– calculated crystal shape – precribed heater power history – effect of pull rate and solid-liquid interface deformation on the solidification heat
Numerical strategy (cont’d)
Stream function Temperature field
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Numerical strategy (cont’d)
FEMAG-1 timedependent simulation of Czochralski Ge growth
• To resort to appropriate and up-to-date numerical simulation techniques to couple and solve these models
→ quasi-steady and dynamic models
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Stream function
psi 7.4E-05 7.1E-05 6.8E-05 6.5E-05 6.2E-05 5.8E-05 5.5E-05 5.2E-05 4.9E-05 4.6E-05 4.3E-05 4.0E-05 3.6E-05 3.3E-05 3.0E-05 2.7E-05 2.4E-05 2.1E-05 1.7E-05 1.4E-05 1.1E-05 8.0E-06 4.8E-06 1.7E-06 -1.5E-06 -4.7E-06
Introduction (cont’d)
General objective of FEMAGSoft
• FEMAG-2 → FEMAG-3 software generation transition taking place from 2008-2009
→ strongly improved platform in terms of computation time, memory, etc.
Introduction (cont’d)
Main difficulties:
– Multi-physics: heat and mass transport in the melt and the gas, turbulence, radiation transfer, etc., all interact and strongly affect species incorporation and defect formation in the crystal – Multiple space scales: sharp diffusive, viscous, radiative and thermal boundary layers are present in the melt and the gas, together with complex defect boundary layers in the crystal – Multiple time scales: typically the growth process is very slow while the melt flow is governed by much shorter time constants
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1. Numerical strategy (cont’d)
Inverse QS and TD simulation of the Global temperature growth of a 300 field mm silicon crystal
t 1800 1740 1680 1620 1560 1500 1440 1380 1320 1260 1200 1140 1080 1020 960 900 840 780 720 660 600 540 480 420 360 300
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1. Numerical strawenku.baidu.comegy
Numerical strategy
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1. Numerical strategy (cont’d)
Different simulation modes
Quasi-steady Time dependent