ANALYTICAL MODELING OF PLASMA EFFECTS ON PECVD-GROWN GRAPHENE-HYBRID SUPERCAPACITOR PERFORMANCE

Abstract

We develop an analytical framework to examine how plasma parameters influence electrode formation and, consequently, device performance. Although plasma-enhanced chemical vapor deposition (PECVD) technique is widely used for graphene electrode synthesis, quantitative relations between plasma parameters and supercapacitor performance remain limited. In this work, fundamental of plasma parameters, including electron density, electron temperature, Debye screening length, and sheath-related ion dynamics are incorporated into an analytical model that describes plasma-surface interactions during electrode formation. A roughness factor driven by ion bombardment is derived to correlate the plasma conditions with the electrochemical surface accessibility. The resulting increase in effective surface area directly influences both the double layer and pseudo-capacitance charge storage mechanisms, which describe the key device performance parameters such as specific capacitance, energy density, and power density. These calculations are performed using a Python-based simulation under varying plasma conditions. The electron density is varied over the range of 1015-1017 m-3, while the electron temperature is limited to 1-5 eV to reflect typical PECVD conditions. The results show that increasing the plasma density enhances the ion flux to the electrode surface, which enhances surface roughness and increases the effective electrode area, leading to improved energy storage capability. However, electron temperature influences capacitance through competing mechanisms. While increased Debye length weakens electrostatic coupling, the simultaneous increase in ion velocity enhances ion-flux and surface roughness, resulting in a non-monotonic dependence. These trends align with previously reported energy storage improvements in graphene-based hybrid supercapacitors, showing that plasma conditions can control energy storage performance, thereby providing a physically grounded model for predicting energy storage trends under varying plasma conditions.