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

Abstract

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.