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Field enhancement optimization of growing curved structures using the Loewner equation

The local electrostatic field enhancement factor (FEF) is analytically evaluated close to the tip of growing protrusions with quasi-one-dimensional curved geometries. This evaluation is done by using conformal transformations obtained as solutions to the Loewner equation under appropriate boundary conditions. This work allows us to detect the maximal FEF achieved during the growth of curved structures, providing theoretical support for its optimization, which is useful for the understanding of electrostatic interactions of complex free-form microstructured curved shapes.