Nanoscale capacitance: A quantum tight-binding model

Landauer–Buttiker formalism with the assumption of semi-infinite electrodes as reservoirs has been the standard approach in modeling steady electron transport through nanoscale devices. However, modeling dynamic electron transport properties, especially nanoscale capacitance, is a challenging problem because of dynamic contributions from electrodes, which is neglectable in modeling macroscopic capacitance and mesoscopic conductance. We implement a self-consistent quantum tight-binding model to calculate capacitance of a nano-gap system consisting of an electrode capacitance $C^{\prime }$ and an effective capacitance $C_d$ of the middle device. From the calculations on a nano-gap made of carbon nanotube with a buckyball therein, we show that when the electrode length increases, the electrode capacitance $C^{\prime }$ moves up while the effective capacitance $C_d$ converges to a value which is much smaller than the electrode capacitance $C^{\prime }$. Our results reveal the importance of electrodes in modeling nanoscale ac circuits, and indicate that the concepts of semi-infinite electrodes and reservoirs well-accepted in the steady electron transport theory may be not applicable in modeling dynamic transport properties.