Four-dimensional dielectric property image obtained from electron spectroscopic imaging series

We have demonstrated a new quantitative method to characterize two-dimensional distributions of energy-dependent dielectric function of materials from low loss electron spectroscopic image (ESI) series. Two problems associated with extracted image-spectrum from the low-loss image series, under-sampling and loss of energy resolution, were overcome by using fast Fourier transformation (FFT) interpolation and maximum entropy deconvolution method. In this study, Black Diamond™/Si₃N₄/SiO₂/Si-substrate dielectric layer designed for copper metallization was used as the sample. We show that the reconstructed (FFT interpolated and maximum entropy deconvoluted) image-spectrum obtained from ESI series images can be quantified with the same accuracy as conventional electron energy-loss spectroscopy spectra. Since the analysis of the dielectric function is sensitive to the local thickness of the specimen using Kramers-Kronig analysis, we also developed a new method to quantitatively determine the dielectric constant for low-k materials. We have determined the thickness of the Black Diamond using the extrapolated thickness method from the materials of known dielectric constants. Using Kramers-Kronig formula, the dielectric function map can be deduced from two-dimensional reconstructed single scattering spectra with providing the information of thickness. We proposed a four-dimensional data presentation for revealing the uniformity of the energy dependent property. The accuracy of our methods depends on the thickness determination and on the quality of the reconstructed spectra from the image series.