First Principle Calculation of the Leakage Current Through $\hbox{SiO}_{2}$ and $\hbox{SiO}_{x}\hbox{N}_{y}$ Gate Dielectrics in MOSFETs

A combination of density functional theory and nonequilibrium Green's function formalism has been applied to the atomic scale calculation of the leakage current through SiO
₂
and SiO
_x
N
_y
dielectrics of MOSFETs. Samples with different dielectric thicknesses and nitrogen concentrations have been taken into account in order to study the dependence of the leakage current on these two parameters. It has been shown that the incorporation of nitrogen atoms into SiO
₂
increases the density of gap states, which leads to barrier lowering for both electrons and holes. The calculated leakage currents through different SiO
₂
polymorphs (e.g., ß-cristobalite, ¿-quartz, and ß-quartz) show thickness dependences, which are in very good agreement with measured values for amorphous SiO
₂
. The dependence of the leakage current on the concentration of nitrogen atom in oxynitride gate dielectrics has also been calculated and shown to be in good agreement with the values extracted from measured data.