An approach for quantum capacitance of graphene, carbon nanotube, silicene and hexagonal boron nitride nanoscale supercapacitors by non-equilibrium Green’s function method

We introduce a comprehensive approach to calculate quantum capacitance of nanoscale capacitors as a function of applied potential difference to have resemblance to actual device operating conditions. Ab initio analysis based on the non-equilibrium Green’s functions combined with density functional theory was applied for different elementary materials and geometries for the soundness of the approach. The results of planar single layer graphene, silicene, and hexagonal boron nitride and for tubular carbon nanotube supercapacitor symmetric model systems on the quantum capacitance are presented together with widely utilized fixed band approximation at planar systems for comparison purposes. The proposed procedure not only successfully reproduced the results for planar systems in a qualitative manner but is also consistently applicable for non-planar (tubular) systems by remarking the robustness of the procedure. Our work highlights the importance of the separation spacing (such as contact distance) search in obtaining quantum capacitance for electric double layer supercapacitors. In that search procedure, it is basically aimed to minimize the charge on the leads/plates for eliminating quantum effects. Induced charge sites under the applied bias could be indicative in some degree for the possible ion adsorption/desorption from the electrolyte or redox reactions at electrode/electrolyte interface to create a double layer. So that the proposed approach on the presented study could also be treated as a qualitative measure on the quantum capacitance for realistic systems with dopants, defects, and functional groups for supercapacitor understanding.