Momentum-dispersion calibration and measurement of a surface layer dielectric constant using momentum-resolved electron energy-loss spectroscopy in the optical region

Momentum-resolved electron energy loss spectroscopy ($q$EELS) in the low-loss (from 0 to $\approx$10 eV) region provides means for measurement of sample optical properties at the nanoscale. When both energy loss $\Delta E=ħ\omega$ and momentum transfer $q$ are measured, the dispersion relation of surface-plasmon polaritons (SPP) can be studied. However, the momentum ($q$) dispersion calibration is challenging due to the small scattering angles involved, and the consequent lack of suitable calibration samples and methods. Here, we discuss how by fitting the experimental data to a simplified SPP dispersion formula, the momentum dispersion can be calibrated and the dielectric constant ${ϵ}_r$ of a thin surface layer measured. The dielectric constant measured by SPP fitting is robust to small sample tilts and stays within $\pm$11% over a −6 ° to +13.3 ° sample tilt relative to the incident-beam direction. Methods such as electron diffraction and chemical mapping, can be applied to the same area as examined by $q$EELS, potentially providing insights in materials structure and composition with its optical properties.