The present research aims to implement a hafnium oxide (HfO2) based plasma-assisted gate all around carbon nanotube field effect transistor (GAA-CNTFET) and use it for a better understanding of plasma parameters and their effect on the device. With a more streamlined focus on plasma synthesized (plasma-enhanced chemical vapor deposition technique) CNT for channel material, the intention is to understand how the incorporation of high-k dielectrics leads to enhanced device performance. HfO2 is used as a high-k dielectric to overcome the limitations of conventional silicon dioxide (SiO2) gate dielectric. A comparative analysis has been performed, based on which it can be concluded that using HfO2 leads to improvement in all observed performance metrics; higher drain current, transconductance, output conductance, early voltage, and gate capacitance. Furthermore, by implementing a cavity in the oxide layer and utilizing the concept of dielectric modulation, it can be observed that tailoring the dielectric permittivity of the cavity affects and alters the device's performance characteristics. Better performance and high sensitivity are tilted towards a higher dielectric constant value. This analysis's results help quantify the practical usage of the device for sensing applications in biology, environment and other prominent industries.