The improvement in the sensitivity performance of conventional surface plasmon resonance (SPR) based sensors with the addition of thin layers of various high index dielectrics (e.g. 5 nm–10 nm of Silicon) is well established. This improvement in sensitivity comes at a price of reduced detection accuracy, deteriorated signal-to-noise ratio (SNR) and small value of Figure of Merit (FOM). Sensors with high detection accuracy and SNR find applications in the direct detection of small molecular (few hundreds of Daltons) interactions or low molecular concentrations (physiological concentration) on the surface of the sensor. The current paper presents design methodology and theoretical analysis of the performance of SPR based refractive index sensor with enhanced SNR, detection accuracy, and FOM attained when a thicker layer of Silicon (60 nm–400 nm thickness) is introduced in the conventional Kretschmann configuration employing angular interrogation technique. The analysis is valid for any high index dielectric layer that is used to enhance the electromagnetic field associated with the surface plasmon (SP) mode excited at the metal-dielectric interface. In the present paper, we show that the SP mode which participates in the sensing applications can be excited at the metal-dielectric interface for multiple thicknesses of Silicon. Analytical expressions are derived to compute the multiple thicknesses of Silicon using a modal analysis as well as the transfer matrix method (TMM) by considering the SPR sensor as a multi-layered optical waveguide structure. The refractive index SPR sensor with thicker silicon layer is shown to exhibit a long propagation length and large penetration depth in the analyte region, resulting in a higher depth-to-width ratio (defined as the SNR) and detection accuracy in its SPR reflectivity spectrum, hence enhancing the measurement precision of the sensor.