Laplace transform method of measuring the distribution of Si–SiO2 barrier heights: Basic principles

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Abstract
The electronegativity difference between silicon and SiO2 produces a dipole layer at the Si–SiO2 interface which determines the barrier height between the silicon and SiO2 conduction bands. Because thermally grown SiO2 is amorphous, the alignment of these dipoles with respect to each other fluctuates resulting in a barrier height distribution. Photon-assisted injection of electrons into the thermally grown gate oxide of a metal-oxide-semiconductor field-effect transistor is used to extract this distribution by experiment. The ratio of the injected gate current to the short-circuit source–drain photocurrent collected under the gate is shown to be the Laplace transform of the barrier height distribution. By inverting the Laplace transform, measured under the specific experimental conditions described, the barrier height distribution is found to be Gaussian. The average zero-field barrier height is found to be 3.5 eV with a standard deviation of 0.64 eV measured in the oxide over a plane parallel to the Si–SiO2 interface. The relation is given between the average barrier height and the high-field extrapolated barrier height of 3.1 eV, and it is argued that the standard deviation is a measure of the degree of disorder in the SiO2.