Enhancement of the effective tunnel mass in ultrathin silicon dioxide layers

Abstract

Based on the results of three-dimensional atomistic tight-binding calculations, we argue that the effective tunnel mass of SiO2 employed as a fitting parameter in standard transfer-matrix multiple-scattering theory calculations increases strongly as the oxide thickness is decreased (we find more than 50% mass enhancement upon reduction of the oxide thickness from 4 to 1 nm). At least five factors, usually neglected in effective-mass-based calculations can contribute to this effect: the nonparabolicity of the complex bands in the gap of SiO2, the gradual (rather than abrupt) change of the electrostatic potential across the Si/SiO2 interface, a possible image force correction, the presence of native defects in the oxide, and the effective-mass approximation itself. Very good quantitative agreement between the theoretical predictions for the thickness dependence of the mass enhancement and corresponding results from transfer matrix fits to experimental currents is obtained if defect densities smaller than 1010 cm−2 and a small image force correction are assumed. Since the present findings imply significant errors (1–2 orders of magnitude) in tunnel currents through ultrathin oxides calculated with a single thickness-independent tunnel mass, an explicit parametrization of the thickness dependence for use in multiple-scattering calculations is suggested. For 4 nm thin oxides, we obtain a tunnel mass of 0.35 m0 (0.48 m0), if a parabolic (nonparabolic) dispersion of the complex bands in the band gap of the oxide is adopted. Furthermore, the mass at the conduction band bottom of SiO2 is found to be different from the tunnel mass and estimated to be 0.39 m0, in good agreement with previous measurements. The calculations also yield an estimate of the errors in oxide thicknesses obtained from current–voltage fitting, which are found to agree well with available experimental data.