▎ 摘　　要

To overcome the scaling problem in the semiconductor technology a nano scale Metal/Insulator/Metal structure is employed to adopt the minimization challenges in the ultra-high density architecture application. The graphene and its family due to unique properties (which one of the most important of them is its application in the atomically dimensions) are as a top candidate in the (Metal/Insulator/Metal) devices as memristor and new generation memory. Intense interesting to graphene and graphene oxide caused to used them in the high speed electronic devices; therefore, the investigation of electrostatic properties such as quantum capacitance in the nano-scale (Metal/Insulator/Metal) structure device is remarkable. In the present work the quantum capacitance of the memristor in the resistance switching process and in the both switching states (High Resistance Switching or Off state to Low Resistance Switching or On state) are explored. The switching mechanism of the graphene oxide based memristor is happened by formation/disruption of a conductive route by applying voltage. The quantum capacitance of the On memristor (Pt/Graphene Oxide/Pt) is investigated in the degeneracy limits at along a nano ribbon path of graphene. The quantum capacitance of this graphene nano ribbon-like path in comparison with the quantum capacitance model of the graphene is gained. The quantum capacitance of graphene nano ribbon like path in the On state (conductive path) is proportional of the quantum capacitance of graphene, when the Fermi level is shifted by applied voltage. Finally, the density of state model of conductive path formalism approves the results in comparison with measurement outcomes and an acceptable export is obtained.