Modeling of dimensions and sensing properties of gold gratings by spectroscopic ellipsometry and finite element method

¹ Hungarian Research Network, Centre for Energy Research, Institute of Technical Physics and Materials Science, Budapest, Hungary
² Doctoral School of Materials Sciences and Technologies, Óbuda University, Budapest, Hungary
³ Zuse Institute Berlin, Takustraße 7, 14195 Berlin, Germany
⁴ JCMwave GmbH, Bolivarallee 22, 14050 Berlin, Germany
⁵ Institute of Applied Physics, Friedrich Schiller University, Jena, Germany
⁶ Physikalisch-Technische Bundesanstalt, Bundesallee 100 38116, Braunschweig, Germany
⁷ Department of Electrical and Electronic Engineering, Institute of Physics, Faculty of Science and Technology, University of Debrecen, Hungary

^* e-mail: petrik.peter@ek.hun-ren.hu

Published online: 31 October 2024

Abstract

Gold gratings were measured by spectroscopic ellipsometry and modeled by the finite element method to investigate the capabilities of optical dimensional metrology for plasmonic diffractive structures. The gratings were prepared by electron beam lithography using parameters determined by finite element simulations for significant variations of the amplitude ratio and phase shift of the polarized reflection coefficients to achieve high sensitivity for both the measurement of the grating dimensions and the sensing capabilities. Sub-nanometer sensitivity was shown to determine the grating dimensions and the thickness of an adsorbed layer to be detected in both traditional reflection and Kretschmann-Raether (KR) configurations. The sensitivity for the refractive index of the ambient was calculated to be 10⁻⁵ at best, which is not significantly better than the sensitivities for plane gold layers in KR configurations. However, in diffraction-based resonant setups, the high sensitivity dips can be shifted to a larger spectral range, which is highly significant in many applications. It was also revealed that 2D models assuming a perfect geometry fit the measured ellipsometry spectra only qualitatively, leaving room for model development in the future.