In situ determination of thermal profiles during Czochralski silicon crystal growth by an eddy current technique

An eddy current testing method was developed to continuously monitor crystal growth process and determine thermal profiles in situ during Czochralski silicon crystal growth. The work was motivated by the need to improve the quality of the crystal by controlling thermal gradients and annealing history over the growth cycle. The experimental concept is to monitor intrinsic electrical conductivities of the growing crystal and deduce temperature values from them. The experiments were performed in a resistance-heated Czochralski puller with a 203 mm (8 inch) diameter crucible containing 6.5 kg melt. The silicon crystals being grown were about 80 mm in diameter and monitored by an encircling sensor operating at three different test frequencies (86, 53 and 19 kHz). A one-dimensional analytical solution was employed to translate the detected signals into electrical conductivities. In terms of experiments, the effects of changes in growth condition, which is defined by crystal and crucible rotation rates, crucible position, pull rate, and hot-zone configuration, were investigated. Under a given steady-state condition, the thermal profile was usually stable over the entire length of crystal growth. The profile shifted significantly, however, when the crucible rotation rate was kept too high. As a direct evidence to the effects of melt flow on heat transfer process, a thermal gradient minimum was observed about the crystal/crucible rotation combination of 20/{dollar}-{dollar}10 rpm cw. The thermal gradient reduction was still most pronounced when the pull rate or the radiant heat loss to the environment was decreased: a nearly flat axial thermal gradient was achieved when either the pull rate was halved or the height of the exposed crucible wall was effectively doubled. Under these conditions, the average axial thermal gradient along the surface of the crystal was about 4-5 {dollar}sp{lcub}rm o{rcub}{dollar}C/mm. Regardless of growth condition, the three-frequency data revealed radial thermal gradients much larger than what were predicted by existing theoretical models. This discrepancy seems to indicate that optical effects, which are neglected in theoretical modeling, play a major role in the internal heat transfer of the crystal.