Abstract
Abstract A compact Fowler-Nordheim (FN) tunneling current model is derived to describe the non-ideal, surface roughness-related relationship between current and voltage in a metal-oxide-semiconductor (MOS). This relationship is achieved by applying a fractal continuum Laplacian operator in the 1D Schrödinger equation, resulting in a model that extends the standard FN to account for surface inhomogeneities through a fractional power α. Our error analysis predicts significant inaccuracies in the extracted FN parameters when using the standard FN model to interpret rough surface data.
A methodology for extracting FN fractal parameters and the flat band voltage via a fractal FN plot is proposed. Simulated datasets and real measurements of Al/SiO₂/4H-SiC capacitors are used to validate the model. Comparison of the parameters extracted using the fractal FN model and the standard FN model confirms the predictions from the error analysis and the suitability of the fractal FN model. The fractal FN model offers a potential explanation for the large discrepancies observed in FN parameters reported in the literature.
Published Version
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