Among the members of tin-chalcogenides family, the narrow-band semiconductor SnTe has recently emerged as a 3D crystalline topological insulator (TCI) exhibiting band inversion at the L point where certain crystalline symmetries allow the protection of robust topological states at the surface. We investigated the electronic band structures of pristine P-doped SnTe doped using density functional theory (DFT) calculations followed by synthesis. The substitution of a Sn vacancy by P maintained the intrinsic band inversion at the L point but the direct band gap reduced to 30 meV upon the incorporation of spin orbit coupling (SOC), which is relatively smaller than the experimentally observed band gap of pristine SnTe. The experimental methods for P-doped SnTe synthesis was based on the vapor-liquid-solid technique. The morphology of the synthesized crystals was exotic in the form of micro-needles, as a consequence, it led to the amplification of signal arising from the topological surface states due to the reduction of surface area to volume ratio. Moreover, the modified effective mass, lattice imperfection and related charge carrier conductivity acted as our motivation to implement them in Ferro-electric Field Effect Transistor (FeFET). The application of a cyclic potential resulted in an exceptionally large memory window of 3.1 V accompanied by a drastic current change within a certain potential range.