Tracking the Defects of Ultra-Thin HfO_2 using a Cody-Lorentz Multiple Oscillator Model

摘要

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 HfO_2 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 HfO_2 grown on SiO_2 for a variety of growth parameters including HfO_2 thickness, SiO_2 thickness, and anneal time, and then have used CLM to quantify the defects. The HfO_2 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.