Screening length and quantum capacitance in graphene by scanning probe microscopy.

A nanoscale investigation on the capacitive behavior of graphene deposited on a SiO2/n(+) Si substrate (with SiO2 thickness of 300 or 100 nm) was carried out by scanning capacitance spectroscopy (SCS). A bias V(g) composed by an AC signal and a slow DC voltage ramp was applied to the macroscopic n(+) Si backgate of the graphene/SiO(2)/Si capacitor, while a nanoscale contact was obtained on graphene by the atomic force microscope tip. This study revealed that the capacitor effective area (A(eff)) responding to the AC bias is much smaller than the geometrical area of the graphene sheet. This area is related to the length scale on which the externally applied potential decays in graphene, that is, the screening length of the graphene 2DEG. The nonstationary charges (electrons/holes) induced by the AC potential spread within this area around the contact. A(eff) increases linearly with the bias and in a symmetric way for bias inversion. For each bias V(g), the value of A(eff) is related to the minimum area necessary to accommodate the not stationary charges, according to the graphene density of states (DOS) at V(g). Interestingly, by decreasing the SiO(2) thickness from 300 to 100 nm, the slope of the A(eff) versus bias curve strongly increases (by a factor of approximately 50). The local quantum capacitance C(q) in the contacted graphene region was calculated starting from the screening length, and the distribution of the values of C(q) for different tip positions was obtained. Finally the lateral variations of the DOS in graphene was determined.