Plasmonic nanoparticles of noble metals, mostly gold (Au), show surface plasmon resonance features within the vicinities of visible and near-infrared spectrum, and its plasmonic techniques emerge from the cooperative oscillations of free electrons controlled by the electromagnetic field influence of the incident light within the region. This work aims at producing reduced cost surface-enhanced Raman spectroscopy (SERS) enhancement factor of gold nanoparticle (AuNP) using the finite-difference time-domain method. The result shows that for the selected three types of substrates of SiO2, Ge, and Al2O3, the SERS effects of Ag on SiO2 > Ge > Al2O3 agree with the enhancement order (i.e., SiO2 > Ge > Al2O3) from the previous experiment of Yang et al. (Appl Surf Sci 436:367-372, 2018). Due to the limitation of the semiconductor's substrates, in subsequence simulations, Al substrate was used instead. Further simulations reveal that the intensity of Ag on Al substrate is greater than that of SiO2, Ge, and Al2O3 semiconductor substrates. In like manner, the simulation also gave a greater enhancement with AuNP/Al substrate. (The localized electric field enhancement effect of AuNP/Al substrate has more signal than the previous.) The results obtained from the consideration of different diameters of the Au sphere and the interparticle spacing for some specified range of numbers under consideration have enlarged the comprehension of SERS substrates. The operation (mechanism) of the wavelength's arousal is a function of the particle's structure, miniaturization, and substrate type for the SERS effect.