Silicon-Thickness-Dependent Optimization of Ultra-Thin SOI Graphene–Plasmonic Slot Electro–Optic Modulators

Graphene–plasmonic electro–optic (EO) modulators have attracted significant interest for compact and energy-efficient integrated photonic systems due to their electrically tunable optical response and strong light–matter interaction. In this work, an ultra-thin silicon-on-insulator (SOI) graphene–plasmonic slot modulator (G-PSM) is investigated using a combined semi-analytical and numerical framework. The analysis integrates finite-temperature Kubo conductivity modeling, perturbation-based effective-index analysis, overlap-factor evaluation, eigenmode analysis, and full-wave simulations to study the influence of silicon thickness on the EO performance of the proposed structure. The obtained results demonstrate that geometry engineering strongly affects modal confinement, overlap enhancement, effective-index perturbation, transmission characteristics, extinction ratio (ER), insertion loss (IL), energy-per-bit consumption, and EO bandwidth. Under optimized operating conditions, the proposed G-PSM achieves an effective refractive-index variation of approximately 3.1×10−3, an ER of approximately 3.5 dB, an IL of 1.5–2 dB, an energy-per-bit consumption of approximately 7.5 fJ/bit, and a 3 dB EO bandwidth approaching 200 GHz. Strong electromagnetic confinement is achieved inside the plasmonic slot region near the graphene-active layer, enabling efficient electro–absorptive and electro–refractive modulation. Excellent agreement between the semi-analytical calculations and numerical simulations validates the developed framework and confirms the suitability of the proposed ultra-thin SOI G-PSM for compact broadband EO modulation in future integrated photonic systems.