Constriction Resistance and Current Crowding in Vertical Thin Film Contact

The constriction resistance and the current flow pattern are calculated analytically in a vertical thin film contact in which the thin film base is an equipotential surface. Both Cartesian and cylindrical thin film contacts are studied. The resistivities and the geometric dimensions in the individual contact members may assume arbitrary values. General scaling laws are constructed for the constriction resistance for arbitrary resistivity ratios and geometric aspect ratios. The analytic solutions are validated using a simulation code. Current crowding at the edges is displayed. In the limit of small film thickness, we show that current crowding in the vertical contact is far less serious than the current crowding in the horizontal contact. The data show that the normalized constriction resistance depends predominantly on the geometry of the thin film, but is relatively insensitive to the height and to the resistivity of the member with which the thin film is in contact.