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It has been reported that mobility in high-κ gate dielectric metal-insulator semiconductor field-effect transistors is lower than that in conventional metal-oxide semiconductor field-effect transistors and the reason for this degradation has been considered to be the fixed charge in dielectric films as well as remote phonon scattering. We investigated the influence of dielectric constant distribution in gate dielectrics on electron mobility determined by remote Coulomb scattering (μRCS) using numerical simulations and a physical model. It is shown that electron mobility in the inversion layer is strongly affected by the dielectric constant distribution in gate dielectrics. In the case of stacked-gate dielectrics of a high-κ film and an interfacial layer, mobility has a minimum as the dielectric constant of the interfacial layer increases while it increases virtually monotonically with dielectric constant of the high-κ film. These phenomena are explained, considering the electrical potential in the substrate induced by fixed charges in gate dielectrics using the Born approximation. Preferable dielectric constant distribution is presented in terms of the suppression of the remote Coulomb scattering.