By means of a dielectric modulation method, this research offers the first ever 2D analytical model for the surface potential of a dual material gate Ferroelectric-tunnel-field effect transistor (DMG-Fe-TFET) device used in an enzyme-free biosensor. Compared to a device with a single material gate, the sensitivity of a device with a gate made of two distinct metals (M1-M2) is improved by an increase in tunnelling width at the secondary tunnelling junction. This model accounts for the change in surface potential caused by varying the value, position, and fill factor of the target biomolecules. Several distinct device architectures are used to enhance the efficiency of the envisaged Fe-TFET in the nanoscale range. The DMG-Fe-TFET is one of many cutting-edge FET topologies that can reduce the impact of short-channel effects because of its adaptability. The surface potential can be expressed by computing the two-dimensional Poisson's equation using the parabolic-potential approach. The critical voltage is determined by using the minimal surface potential model. The percent change in the threshold voltage is used to determine the sensitivity of the model. Researchers have investigated how the dimensions of the Nano cavity and other parts of the device affect its sensitivity.