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Transient and quasi‐stationary simulation of heat and mass transfer in Czochralski silicon crystal growth
Author(s) -
Voigt A.,
Weichmann C.,
Nitschkowski J.,
Dornberger E.,
Hölz R.
Publication year - 2003
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/crat.200310063
Subject(s) - steady state (chemistry) , transient (computer programming) , silicon , heat transfer , materials science , thermal , temperature gradient , crystal (programming language) , mechanics , mass transfer , crystallographic defect , thermodynamics , crystal growth , growth rate , constant (computer programming) , chemistry , crystallography , physics , geometry , optoelectronics , mathematics , quantum mechanics , computer science , programming language , operating system
The formation of grown‐in defects in silicon crystals is controlled by the concentration of intrinsic point defects. Under steady state conditions the type of the prevailing point defect species is linked to the ratio of pull rate and temperature gradient in the crystal at the solidification front. It has been shown that this ratio as well as computed point defect distributions are in good agreement with experimental data. In this paper we compare a coupled transient heat transfer and transient point defect transport model with quasi steady state simulations at various time steps. Both simulations show the same qualitative results, quantitative differences in temperature are less than 1 %. But already for constant pull rates the defect distributions show qualitative differences between transient and quasi steady state simulations. Therefore, for a detailed understanding how defects are related to growth conditions, the thermal history should not be neglected.