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A combination of density functional theory and non-equilibrium Green's function formalism has been applied to the atomic scale calculation of the leakage current through the strained SiO2 dielectric layer of MOSFETs. This first-principles approach accounts for intrinsic strain at the Si/SiO2 interface as well as its influence on the leakage current. Furthermore, the impact of external mechanical stress on the leakage current was investigated. It is shown that compression of atomic layers along the direction perpendicular to the interface results in a lower tunneling probability and leakage current while the tensile strain in that direction leads to higher tunneling probability and consequently higher leakage current. Based on this behavior we give an explanation for the increase of the tunneling effective mass of electrons as the thickness of the dielectric layer decreases in terms of intrinsic strain at the Si/SiO2 interface.