By measuring the minimum supply voltage for normal operation of test random access memories, we detected low-density extrinsic defects in silicon-oxynitride (SiON) gate insulators that were formed by state-of-the-art technologies. The density of the detected defects had a strong correlation with optical thickness dopt, which was ellipsometrically measured, regardless of the processing conditions of the SiON films. We propose to maintain the dopt above a threshold value of 1.7nm to suppress the problems caused by the defects. The optimization of post nitridation annealing (PNA) condition is promising for meeting the criterion without sacrificing device performance. By elaborate investigations based on the Clausius-Mosotti relation, we found that the optical thickness of SiON films is approximately proportional to the atomic area density in the films. On the basis of this finding, we developed a model, which is an extension of the conventional analytical cell-based model, to figure out the physical process of the extrinsic-defect formation. The results analyzed using the model revealed that the extrinsic defects are formed in the SiON films in the case when the number of normal cells in a vertical arrangement becomes equal to or smaller than the threshold value of 3 or 4.
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