Periodic metallic nanoparticle arrays have a wide range of applications in sensors due to the generation of the plasmonic lattice resonance (PLR). To increase the figure of merit (FOM) of periodic metallic nanoparticle arrays, schemes to reduce full-width at half maximum (FWHM) are necessary. Introducing silicon and dielectric nanopillars under metallic nanoparticles has been suggested as a feasible route to reducing FWHM and thus enhancing FOM. However, many factors may lead to a reduction in FOM. Thus, different factors, such as the diameter and height of metallic nanoparticles, the diameter and height of silicon nanopillars, the height of dielectric nanopillars, and the period of the arrays, should be explored to improve FOM of this structure. We investigate the influences of different structural parameters on FOM of Ag  /  Si  /  SiO₂ nanopillar array sensors. Results show that a larger diameter of the Ag nanopillars widens the FWHM and weakens the FOM. The optimal diameter of Si nanopillars and the optimal height of Ag nanopillars to obtain a high FOM are all 100 nm. The period of larger arrays corresponds to a narrower FWHM and higher FOM. A larger height of Si nanopillars or a larger height of SiO₂ nanopillars decreases the FWHM and increases the FOM. These results are relatively instructive and meaningful for the design of PLR sensors with a high FOM.