  We study theoretically an influence of the near-interfacial insulator traps and electron-hole puddles on the small-signal capacitance and conductance characteristics of the gated graphene structures. Based on the self-consistent electrostatic consideration and taking into account the interface trap capacitance the explicit analytic expressions for charge carrier density and the quantum capacitance as functions of the gate voltage were obtained. This allows to extract the interface trap capacitance and density of interface states from the gate capacitance measurements. It has shown that self-consistent account of the interface trap capacitance enables to reconcile discrepancies in universal quantum capacitance vs the Fermi energy extracted for different samples. The electron-hole puddles and the interface traps impact on transfer I-V characteristics and conductivity has been investigated. It has been shown that variety of widths of resistivity peaks in various samples could be explained by different interface trap capacitance values. 
Influence of Interface Traps and Electron-Hole Puddles on Quantum   Capacitance and Conductivity in Graphene Field-Effect Transistors