Three-dimensional electric charge distribution on finitely-thick bus-bars in micro-acoustic devices

The author´s original work for three dimensional charge distributions in micro-acoustic devices - dating back to 1986 - has been manifestly extended to include finitely-thick bus-bars. The work has been initiated to investigate the electric charge localization and field enhancement at the electrode/bus-bar junctions depending on the thickness of the metallization in submicron geometries. An easy-to-follow recipe for the construction of relevant Greens functions has been provided. Universal Functions for setting up system matrices in the Method-of-Moments implementations have been constructed. Universal functions (moments of Greens functions) turn out to be extraordinarily smooth and thus easy to compute. Four additional features stand out in the paper: (i) The Greens function for finite-size substrates has also been constructed. (ii) Furthermore, Greens functions for including the metallic package have been derived. (iii) In addition Greens functions for electrodes imbedded in dielectrics have been constructed. (iv) Finally, the Multi-level Multi-pole Method has been introduced, for the first time, in the micro-acoustic device modelling literature, to significantly accelerate computations and ensure O(N) or O(NlogN) computational complexity. The developed package promises to set a new standard for three dimensional accelerated computing of electric field distributions in micro-acoustics. The paper concludes with a brief discussion of universal functions and multipole expansions.