Comparison of methods to determine bandgaps of ultrathin HfO2 films using spectroscopic ellipsometry

Abstract

With the replacement of SiO2 by high-k Hf-based dielectrics in complementary metal–oxide–semiconductor technology, the measurement of the high-k oxide bandgap is a high priority. Spectroscopic ellipsometry (SE) is one of the methods to measure the bandgap, but it is prone to ambiguity because there are several methods that can be used to extract a bandgap value. This paper describes seven methods of determining the bandgap of HfO2 using SE. Five of these methods are based on direct data inversion (point-by-point fitting) combined with a linear extrapolation, while two of the methods involve a dispersion model-based bandgap extraction. The authors performed all of these methods on a single set of data from a 40 Å HfO2 film, as well as on data from 20 and 30 Å HfO2 films. It was observed that the bandgap values for the 40 Å film vary by 0.69 eV. In comparing these methods, the reasons for this variation are discussed. The authors also observed that, for each of these methods, there was a trend of increasing bandgap with decreasing film thickness, which is attributed to quantum confinement. Finally, the authors observed a greater variation in bandgap values among the methods for the 40 Å films than among the methods for the 30 and 20 Å films. This is attributed to the larger tail in the extinction coefficient k curve for the 40 Å film.