A SIMPLE FORMULA FOR THE CONCENTRATION OF CHARGE ON A 3-DIMENSIONAL CORNER OF A CONDUCTOR

A major problem in the computation of capacitance coefficients for mic rowave transmission and VLSI interconnection systems is caused by the singularities in the electric field at the corners and edges of conduc tors. For edges, a solution is given by the Duncan correction, which i s based on a two-dimensional (2-D) polar expansion of the field. No su ch exact expansion exists for corners. Recent research by Beagles and Whiteman has yielded an asymptotic expansion for the electric field In the vicinity of a rectangular three-dimensional conductive corner, an d this is used to derive a simple formula for the charge Q (in coulomb s) concentrated at any such corner. The formula is Q = 1.307 epsilon d (V-c - V-s), where epsilon is the dielectric permittivity (in farads p er meter) of the medium surrounding the conductive corner, d is the le ngth (in meters) of one Side of a cubic region situated on the conduct or adjacent to the corner, V-c is the electric potential (in volts) of the conductor, and V-s is the electric potential at a point in the me dium displaced from the corner's apex along a line through the cube's diagonal and at a distance equal to that diagonal. Q is the charge on the cube's three surfaces lying along the conductor's surfaces. Such a configuration is convenient for a finite-difference computation of ca pacitance.