We investigate the dielectric screening across the Si-SiO2 interface using a first-principle approach. By determining the profile of the microscopic polarization and the effective polarizabilities of SiOn (n = 0,..4) structural units, we show that the variation of the local screening across the interface relates to the chemical grading. The oxide region near the Si substrate shows the same dielectric permittivity as bulk SiO2 as long as the oxide is locally stoichiometric. The suboxide region carries an enhanced permittivity, with a value intermediate between those corresponding to bulk Si mid SiO2. The implications of these findings for the scalability of the equivalent oxide thickness in high-kappa gate stacks are discussed.