Tracking the Defects of Ultra-Thin HfO2 using a Cody-Lorentz Multiple Oscillator Model

Defects in ultra-thin films appear as small perturbations in the measured optical dispersion using spectroscopic ellipsometry (SE). A common approach for quantifying these defects is to fit each pixel in the dispersion to an index of refraction and extinction coefficient for a known material thickness (point-by-point method). However, this point-by-point method is not physical because it produces dispersions that are not Kramers-Kronig consistent and it is also subject to overfitting. In this work, we demonstrate that the Kramers-Kronig consistent Cody Lorentz Multiple-Oscillator model (CLM) can precisely quantify defects in HfO2 using the Lorentz peak amplitude dispersion parameter as one of the fitting parameters. Using a KLA-Tencor spectroscopic ellipsometer, we collected optical dispersions of ultra-thin HfO2 grown on SiO2 for a variety of growth parameters including HfO2 thickness, SiO2 thickness, and anneal time, and then have used CLM to quantify the defects. The HfO2 defect value was found to successfully track the different growth conditions, which is consistent with literature, and the defect values have little within-wafer variance. Quantifying defects in a material sub-bandgap successfully will provide information about leakage currents and device performance for gated semiconductor devices.