Computer Modelling of the Temperature Distribution in the Silicon Single Crystals During Growth and the Thermal History
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COMPUTER MODELLING OF THE TEMPERATURE DISTRIBUTION IN THE SILICON SINGLE CRYSTALS DURING GROWTH AND THE THERMAL HISTORY OF THE CRYSTAL O.J. ANTTILA*,
M.V.
TILLI** AND V.K.
* Helsinki University of Technology,
LINDROOS* Laboratory of Physical Metallurgy,
SF-02150 Espoo, Finland ** Okmetic Ltd., PB 44, SF-02631 Espoo,
Finland
ABSTRACT Computer modelling of the silicon single crystal grown by the Czochralski method has been carried out in order to calculate the temperature isotherms as well as to evaluate the thermal history of the crystal. The aim of the present work is to find out to which extent the thermal history of the crystal can be altered without structural modifications of the single crystal furnace. Furthermore, another aim is to study the influence of external heaters, reflectors and cooling elements to the temperature isotherms as well as to the form of the solid-melt interface. The model developed so far takes into account the crystal diameter and the pull rate as well as the radiation from the heater, the crucible and the melt. Furthermore, the inclusive study of the cooling effect of the inert gas flow is under progress.
INTRODUCTION Supersaturated oxygen in Czochralski-grown single crystal silicon tends to precipitate during the wafer processing causing precipitates, dislocation loops and stacking faults in the wafer [1,21. These lattice defects may have a remarkable effect on the yield of integrated circuits fabricated on the wafer [2,3]. Electrically active defects in the active surface region are deleterious for the components but, on the other hand, these defects may have a beneficial influence on device quality when situated deep in the wafer. The precipitation behavior of oxygen during the process is closely related to the thermal history of the crystal during growth (3,41. The shape of the freezing interface affects the quality of growing crystal. It has an effect on the radial distribution of dopants and impurities and on thermal stresses near the interface [5,61. A realistic solution for the combined problem of the melt and the crystal is inherently laborious to find, and normally the crystal temperature distribution simulations are based on considerably simplifying assumptions concerning the freezing interface [7,81. It is supposed in the present model that the heat flux per unit area in the melt just below the interface remains unchanged, and the shape of the interface results from the calculations. The heat transfer from other surfaces of the crystal is assumed to be governed by thermal radiation, but the developed program can easily be enlarged to take the argon flow into account. The structure of the simulating program is such that the growth of other semiconducting materials than silicon can be simulated as well, and the effects of modifications in the single crystal furnace can easily be accounted for.
Mat. Res. Soc. Symp. Proc. Vol. 59, ý1986 Materials Research Society
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