An analytical model of nanogap embedded Gallium Nitride Gate- Material and Dielectric Engineered- Schottky Nano-Wire Field Effect Transistor (GaN-GME-DE-SNW-FET) for implementation as a label-free biosensor is introduced. An expression for the surface potential is attained by resolving the 1-D Poisson equation and 2-D Laplace equation utilizing a superposition method. A Model for the threshold voltage is also developed to analyze the sensitivity of the biosensor. The projected model also contains the repercussion of barrier height dropping at the metal-semiconductor intersection along with Dielectric Engineering (DE) using high-k (HfO2) material and Gate Material Engineering (GME) using metal m1with workfunctionφm1and m2with workfunctionφm2. The sensitivity of biosensor's has been studied for diverse dielectric constant and charge densities immobilized within the nanogap cavity. A comparative study has also been done between Gallium nitride-based (GaN- GME-DE-SNW-FET) and Silicon-based (Si-GME-DE-SNW-FET) Label-free biosensors. The developed analytical model is verified and validated using ATLAS- TCAD device simulations.