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System of Mathematical Models for the Analysis of Industrial FZ‐Si‐Crystal Growth Processes
Author(s) -
Mühlbauer A.,
Muiznieks A.,
Raming G.
Publication year - 1999
Publication title -
crystal research and technology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.377
H-Index - 64
eISSN - 1521-4079
pISSN - 0232-1300
DOI - 10.1002/(sici)1521-4079(199902)34:2<217::aid-crat217>3.0.co;2-1
Subject(s) - dopant , materials science , silicon , electrical resistivity and conductivity , crystal (programming language) , crystal growth , melt flow index , temperature gradient , fluid dynamics , single crystal , semiconductor , heat transfer , transient (computer programming) , mechanics , mineralogy , doping , composite material , optoelectronics , chemistry , crystallography , electrical engineering , copolymer , quantum mechanics , computer science , programming language , engineering , polymer , physics , operating system
A system of coupled mathematical models and the corresponding program package is developed to study the interface shape, heat transfer, thermal stresses, fluid flow as well as the transient dopant segregation in the floating zone (FZ) growth of large silicon crystals (diameter more than 100mm) grown by the needle‐eye technique. The floating zone method with needle‐eye technique is used to produce high‐purity silicon single crystals for semiconductor devices to overcome the problems resulting from the use of crucibles. The high frequency electric current induced by the pancake induction coil, the temperature gradients and the feed/crystal rotation determine the free surface shape of the molten zone and cause the fluid motion. The quality of the growing crystal depends on the shape of the growth interface, the temperature gradients and corresponding thermal stresses in the single crystal, the fluid flow, and especially on the dopant segregation near the growth interface. From the calculated transient dopant concentration fields in the molten zone the macroscopic and microscopic resistivity distribution in the single crystal is derived. The numerical results of the resistivity distributions are compared with the resistivity distributions measured in the grown crystal.