Uncertainty in the mutual calibration method for the traceable thickness measurement of ultra-thin oxide films

摘要

Mutual calibration by a combination of a zero-offset method and a length-unit traceable method has been suggested as a promising approach to determine the traceable thickness of ultra-thin oxide films. However, the measurement uncertainty is somewhat complicated to calculate because the standard uncertainties from the two measurement methods and the linear regression process should be combined. In this study, the mutual calibration method to evaluate the film thickness and uncertainty of ultra-thin oxide films was investigated. The algorithm of the linear regression equation in the mutual calibration method was studied and the uncertainty calculation program for the thickness measurement by mutual calibration was developed. The result will provide an effective and useful guideline to certify the thickness of the ultra-thin oxide film on Si(100) substrate which is used as the gate oxide in the semiconductor devices. The magnitude of the relative expanded uncertainty in the thickness measurement by mutual calibration is in the range from 8.6% to 9.3%.