Quantitative investigation on the critical thickness of the dielectric shell for metallic nanoparticles determined by the plasmon decay length.

Inert dielectric shells coating the surface of metallic nanoparticles (NPs) are important for enhancing the NPs' stability, biocompatibility, and realizing targeting detection, but they impair NPs' sensing ability due to the electric fields damping. The dielectric shell not only determines the distance of the analyte from the NP surface, but also affects the field decay. From a practical point of view, it is extremely important to investigate the critical thickness of the shell, beyond which the NPs are no longer able to effectively detect the analytes. The plasmon decay length of the shell-coated NPs determines the critical thickness of the coating layer. Extracting from the exponential fitting results, we quantitatively demonstrate that the critical thickness of the shell exhibits a linear dependence on the NP volume and the dielectric constants of the shell and the surrounding medium, but only with a small variation influenced by the NP shape where the dipole resonance is dominated. We show the critical thickness increases with enlarging the NP sizes, or increasing the dielectric constant differences between the shell and surrounding medium. The findings are essential for applications of shell-coated NPs in plasmonic sensing.