The band-gap width of the nanometer-thick silicon dioxide

The band gap dependence on thickness $d_S$ of ultrathin silicon dioxide films has been studied using the Projection Augmented Wave method within the Density Functional Theory. It is shown that the value of $E_{gS}$ for ultrathin silicon dioxide films is less than its values for bulk crystals and increases with increasing thickness. For this, parameters of the band structure of the silicon dioxide tetragonal modification (stishovite) were calculated for the film thicknesses ranging from the thinnest-oxide thickness of 0.3 nm to 3.68 nm. It was found that the condition for minimizing leakage currents requires additional analysis since it is not satisfied for all thicknesses of oxide dielectrics.