We demonstrate a considerable suppression of the low-field leakage through a Y2O3 topgate insulator on graphene by applying high-pressure O2 at 100 atm during post-deposition annealing (HP-PDA). Consequently, the quantum capacitance measurement for the monolayer graphene reveals the largest Fermi energy modulation (EF = 0.52 eV, i.e., the carrier density of 2×10 13 cm -2 ) in the solid-state topgate insulators reported so far. HP-PDA is the robust method to improve the electrical quality of high-k insulators on graphene.The deposition of ultrathin and reliable high-k dielectrics on graphene is required to realize the high transconductance in graphene field-effect transistors (FETs). Generally, two kinds of deposition methods are used: one is physical vapor deposition 1-4 (PVD) with low particle energies to avoid the defect introduction in graphene, 5 the other is atomic layer deposition (ALD) with buffer layers 6-8 to overcome the chemically inert surface of graphene. Recently, graphene FETs have been reported with ALD Al2O3 topgate insulators as thin as 2.6 nm. 9 Insulators fabricated by PVD and ALD, however, suffer from the dielectric breakdown at the voltage much lower than the complete breakdown voltage due to the fragility of dielectrics accumulated by the low-field leakage during the iterative measurements. Typical electrical field for this low-field dielectric breakdown is ~0.2 V/nm. This is a critical issue for the reliability of the topgate insulators. A common limitation for the insulators on graphene fabricated by both PVD and ALD is the lack of a robust methodology for post-deposition annealing (PDA) in an O2 atmosphere. Although PDA at a high temperature (e.g., ~500 C) is known to improve the electrical quality of the insulator considerably, 10 it introduces many defects in graphene by oxidation. 11 Here, from a thermodynamic viewpoint, 12 let's consider the Gibbs free energy change (G = G -RTlnPO2) for the oxidation reaction of M + O2 = MO2, where G is the standard Gibbs free energy change for the oxidation reaction, R is gas constant, PO2 is the oxygen partial pressure and M is the metal. G should be negative to facilitate the oxidation. The first term for G can be used for material selection. An appropriate rare-earth element for use in high-k insulators should be highly susceptible to oxidation. Figure 1(a) shows G of rare-earth, transition and representative elements at 300 C calculated using a thermodynamic database. 13 The G for yttrium is negatively largest among all of the metal oxides, even smaller than that of carbon. Therefore, Y2O3 can be obtained at relatively low oxidation temperatures and is thermodynamically stable on graphene. The band gap for Y2O3 is ~5.5 eV, which is almost identical to that of h-BN. 14 The dielectric constant of Y2O3 is ~12, 15 while it is ~3-4 for h-BN. 16 The second term for G is the process condition, which is derived from the oxygen potential. G should be further decreased to reduce the defects in the insulator such as oxygen vacancy. This c...