1、 全球半导体晶体生长建模著名商业软件FEMAG Numerical Simulation of Bulk Crystal Growth for Industrial Application 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, Belg
2、ium FEMAGSoft 2013 How to improve the growth process in terms of: - crystal quality ? - 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
3、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: typical
4、ly the growth process is very slow while the melt flow is governed by much shorter 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 mode
5、ls To develop a sound physical model for each separate effect global and time-dependent 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 pla
6、ce from 2008-2009 General objective of FEMAGSoft strongly improved platform in terms 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) F
7、EM discretization: use of 2D, Spectral 3D, Cartesian 3D, models (high geometrical 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 accura
8、tely 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 Introduction (contd) FEMAG software development strategy 1. Numerical strategy FEMAGSoft 2013 Numerical str
9、ategy FEMAGSoft 2013 Quasi-steady thermal equilibrium adapted heater power to get 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 inte
10、rface deformation on the solidification heat Direct dynamic calculated crystal shape 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) adap
11、ted heater power to get the prescribed crystal diameter effect of pull rate and solid-liquid interface deformation on the solidification heat Different simulation modes 1. Numerical strategy (contd) Global temperature field Stream function FEMAGSoft 2013 p s i7 . 4 E - 0 57 . 1 E - 0 56 . 8 E - 0 56
12、 . 5 E - 0 56 . 2 E - 0 55 . 8 E - 0 55 . 5 E - 0 55 . 2 E - 0 54 . 9 E - 0 54 . 6 E - 0 54 . 3 E - 0 54 . 0 E - 0 53 . 6 E - 0 53 . 3 E - 0 53 . 0 E - 0 52 . 7 E - 0 52 . 4 E - 0 52 . 1 E - 0 51 . 7 E - 0 51 . 4 E - 0 51 . 1 E - 0 58 . 0 E - 0 64 . 8 E - 0 61 . 7 E - 0 6- 1 . 5 E - 0 6- 4 . 7 E - 0
13、 6t1 8 0 01 7 4 01 6 8 01 6 2 01 5 6 01 5 0 01 4 4 01 3 8 01 3 2 01 2 6 01 2 0 01 1 4 01 0 8 01 0 2 09 6 09 0 08 4 07 8 07 2 06 6 06 0 05 4 04 8 04 2 03 6 03 0 0Inverse QS and TD simulation of the growth of a 300 mm silicon crystal 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) 1. Numerical strategy (contd) FEMAGSoft 2013 Temperature field Stream function 1. Numerical strategy (contd)
