On the Potential Profile of Ultrathin (Tunneling Transparent) Insulating Layers

Interface layers at insulator contacts with a semiconductor and metallic electrode produce inhomogeneous potential and external voltage distributions in the gap between a substrate and a gate regardless of a material used (a silicon oxide, high-k dielectrics, or ferroelectrics). Considering the resulting inhomogeneity of the permittivity distribution across a thin insulating layer, mathematical apparatus for restoring the actual potential profile in the gap between a substrate and a gate from experimental tunneling I–V characteristics of metal-insulator–semiconductor (MIS) structures was developed. Depending on the proximity of maximum field voltages used in the experiment to the potential barrier elimination voltage, the criteria for constructing the actual potential versus coordinate dependence along the normal to the film plane were formulated. Approaches for the computation of model potential profiles and permittivity distributions parameters in insulating layers providing for the best fit between theoretically calculated tunneling conductivity results and experimental data were proposed.