Thermal modeling of a double-neck large diameter crystal growth process

This paper describes a unique method to reduce temperature at the end of the Dash thin neck during the process of crystal growth. The thin neck from the conventional Czochralski process is subjected to larger tensile and torsional stresses in growing large diameter crystals (>200 mm) than with small diameter crystals. The challenge is how to reduce these combination stresses so that they won´t exceed the yield strength of the crystal at the end of the thin neck. In this paper, we propose that after growing the thin neck, to grow a second neck with a diameter between 10 and 50 mm and about 25 to 76 mm long. In this way, the temperature at the thin neck will be much lower than that without the second neck and the corresponding yield strength of the silicon will be increased. A two-dimensional, axisymmetric heat conduction model was developed to predict temperature field within a crystal and demonstrated the advantage of using the double-neck method. This simplified model includes both convective and radiative boundary conditions on the crystal surfaces and applies the concept of “effective ambient temperature” to calculate radiation heat transfer. This model was validated from the conventional Dash thin neck technique. By applying this model to the double-neck method, it concludes that the height of the second neck has a major impact in reducing the crystal temperature at the end of the first thin neck. By comparing with the Dash thin-neck technique, the double-neck method can reduce the temperature at the end of the thin neck by as much as 123°C or 12%. This dramatic temperature reduction accounts for ~2.5 times increase in the yield strength of the silicon