3D electrostatic charge distribution on finitely thick busbars in micro-acoustic devices: combined regularization in the near- and far-field

The original work for 3-D charge distributions in micro-acoustic devices has been manifestly extended to account for finitely thick busbars. The work has been initiated to create a platform for simulating the electric charge localization and field enhancement at the electrode/busbar gaps depending on the thickness of the metalization in submicrometer geometries. A recipe for the construction of relevant Green´s functions has been provided. A universal function (UF) for setting up system matrices in the method-of-moments´ implementations has been constructed. Universal functions (moments of Green´s functions) are by construction highly smooth and easy to compute. This work also presents a comprehensive completion of earlier work. For the first time, the calculation of the UF for a 3-D problem has been presented in great detail, highlighting the underlying regularization techniques. It is shown that the singular Fourier-type integrals involved can be regularized simultaneously in the near- and far-field. The pinnacle of the work is the detailed demonstration of the property that Hadamard´s finite part regularization naturally arises in the construction of UFs. Three lemmata facilitate the understanding of the underlying concepts.