Recently High Electron Mobility Transistor (HEMT) inspired III-V electro-optic modulator topologies were proposed for realizing high speed electro-optic modulators leveraging plasma dispersion effect due to the 2D Electron Gas (2DEG) present at the III-V heterostructure interface. The 2DEG is highly confined at the interface, extending to very low depths in the bulk (≈10 nm) and therefore has limited spatial overlap with the optical mode. In this paper, we propose a novel modulator design to boost the 2DEG-light interaction, wherein the HEMT is embedded within a high contrast grating (HCG) mirror. We present an analytical model extending the conventional HCG model to multi-layer structures and observe good agreement with rigorous coupled-wave analysis (RCWA). We explore the design space for identifying optimal device topology and present geometries that produce a change in reflectivity as large as 70 % for C-and L-band wavelengths. We also present results of sensitivity analysis and observe low variation in device performance due to geometry variation arising from device fabrication imperfections. The device platforms presented here are suitable for designing high efficiency electro-optic modulators by incorporating the HEMT HCG into a Fabry-Perot cavity.