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1、,FEMAG晶体生长模拟软件-建模策略,Franois Dupret1,2, Roman Rolinsky2, Brieuc Delsaute2, Rajesh Ramaya2, Nathalie Van den Bogaert2 1 Universit catholique de Louvain, Louvain-la-Neuve, Belgium 2 FEMAGSoft S.A. company, Louvain-la-Neuve, Belgium,FEMAGSoft 2013,How to improve the growth process in terms of: crystal q
2、uality ? process yield ? energy consumption ? production rate ?,Introduction,Main difficulties:,FEMAGSoft 2013,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 crys
3、tal,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
4、time constants,Introduction (contd),FEMAGSoft 2013,Solving these problems requires ,To resort to appropriate and up-to-date numerical simulation techniques to couple and solve these models quasi-steady and dynamic models,To develop a sound physical model for each separate effect global and time-depe
5、ndent modeling of heat transfer, turbulence modeling, defect modeling, ,Introduction (contd),FEMAGSoft 2013,Principal objective has been to complete the platform,FEMAG-2 FEMAG-3 software generation transition taking place from 2008-2009,General objective of FEMAGSoft, strongly improved platform in t
6、erms of computation time, memory, etc.,Introduction (contd),FEMAGSoft 2013,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 geometrica
7、l flexibility, simple assembling technique),a) Global modeling: subdivision of the furnace into “macro-elements” (solid or liquid constituents, radiation enclosures, “cement” elements.),d) Geometrical modeling: to accurately handle strongly deforming bodies and interface and well-capture all the bou
8、ndary layers,e) Solution technique: coupled Newton-Raphson iterations by use of a highly effective linear solver,Introduction (contd),FEMAG software development strategy,1. Numerical strategy,FEMAGSoft 2013,Numerical strategy,FEMAGSoft 2013,Quasi-steady thermal equilibrium adapted heater power to ge
9、t the prescribed crystal diameter heat source on the solidification front in proportion to the pull rate,Inverse dynamic adapted heater power to grow the prescribed crystal shape effect of pull rate and solid-liquid interface deformation on the solidification heat,Direct dynamic calculated crystal s
10、hape precribed heater power history effect of pull rate and solid-liquid interface deformation on the solidification heat,Time dependent,Quasi-steady,Quasi-dynamic frozen geometry (except the solid-liquid interface) adapted heater power to get the prescribed crystal diameter effect of pull rate and
11、solid-liquid interface deformation on the solidification heat,Different simulation modes,1. Numerical strategy (contd),Global temperaturefield,Streamfunction,FEMAGSoft 2013,Inverse QS and TD simulation of the growth of a 300 mm silicon crystal,Analysis of conical growth and shouldering stages m = 8.
12、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),1. Numerical strategy (contd),FEMAGSoft 2013,Temperaturefield,Streamfunction,Numerical strategy (contd),FEMAGSoft 2013,FEMAG-1 time-dependent simulation of Czochralski Ge growth,Inverse dynamic simulation (
13、imposed crystal shape, calculated heater power): power oscillations resulting from inverse modeling, and smoothed power,Numerical strategy (contd),FEMAGSoft 2013,Direct dynamic simulation (imposed stepwise decrease of heater power, calculated crystal shape): evolution of the temperature field,FEMAG-
14、1 time-dependent simulation of Czochralski Ge growth,Numerical strategy (contd),Inverse dynamic often more reliable than quasi-steady model highly attractive to predict crystal quality,Quasi-steady frequently used cheap, but not always valid does not allow crystal quality prediction,Direct dynamic s
15、imulation of the system response to perturbations of the input parameters very useful for controller design,Quasi-dynamic may capture the detailed system dynamics at various stages very useful for controller design,FEMAGSoft 2013,Different simulation techniques,Numerical strategy (contd),Typical FEM
16、AG-CZ global unstructured mesh,FEMAGSoft 2013,Heat shield,components,Numerical strategy (contd),FEMAG-CZ global unstructured mesh deformation,FEMAGSoft 2013,Numerical strategy (contd),Detail,FEMAGSoft 2013,Numerical strategy (contd),Use of special CAGD techniques for meniscus calculation during tail-end stage : Secondary mesh (constraining loci) and deformed melt- crystal and melt-gas interfaces (right) Generated 1D and 2D meshes (left),FEMAGSoft 2013,Numerical strate
