Oxygen precipitates in Czochralski silicon (CZ-Si) are still considered as the major process-induced defects found in semiconductor device fabrication process because the role of oxygen precipitates in device process such as gettering of metal impurity, prevention of undesired wafer deformation, and degradation of carrier lifetime is quite significant to manufacture high-performance devices. Until now, various theoretical models to predict the oxygen precipitation in CZ-Si with respect to the interstitial oxygen (Oi), vacancy (CV), and the process temperature T have been suggested. However, the complexity and calculation time of a model strongly depend on the accuracy of the model. Thus, it is difficult to apply them on the evaluation of oxygen precipitation regularly in conventional wafer production. Hence, a practical and simple method to evaluate oxygen precipitation should be proposed. In this work, we derived the parameters that indicate the thermal stability and formation rate of the precipitate nuclei by analyzing as-grown oxygen precipitates formed in a p-type CZ-Si. First, we calculated a cumulative distribution function (CDF) of as-grown precipitate density with respect to the thermal history of CZ-Si crystal from the theoretical nucleation rate J(Oi, CV, T) [1]. After that, we fitted the CDF mathematically into the temperature-dependent precipitate density measured after slow ramped anneals with 1 K/min [2] at various stability temperatures followed by a growth anneal at 1000°C for 16 hours. Moreover, the first derivative Je (T) of the CDF was also calculated which was associated with an effective nucleation rate. The extreme point (T C, Je (TC)) on the Je (T) was determined as a new parameter that represents the precipitate behavior at a measured point. Finally, we correlated the parameters to the experimental results measured in various crystals after the test heat cycle started at 800°C for 4 hours and followed by 1000°C for 16 hours. As shown in Fig. 1, we found that both T C and Je (TC) were strongly correlated to the precipitate density, which means that the parameters were possibly applied to evaluate the behavior of oxygen precipitation in a crystal after various thermal processes. Fig. 1 Correlation of the T C (a) and Je (T C) (b) to the precipitate density measured after 2-step annealing starts at 800°C for 4 hours and followed by 1000°C for 16 hours. [1] G. Kissinger, D. Gräf, U. Lambert, and H. Richter, J. Electrochem. Soc. 144, 1447 (1997).[2] G. Kissinger and J. Dabrowski, J. Electrochem. Soc. 155, H448 (2008). Figure 1
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