Compact Models of Spreading Resistances for Electrical/Thermal Design of Devices and ICs

Building upon our recent work (IEEE Electron Device Lett., vol. 26, pp. 909-912, Dec, 2005), we present simple and continuous closed-form models for several rectangular and circular spreading resistance geometries encountered in electrical/thermal design of devices and integrated circuits. The resistance geometries considered involve current/heat flow between parallel contacts of rectangular or circular shape and concentric or eccentric nature, between a horizontal and a vertical stripe, and between a horizontal circular contact and a surrounding vertical cylindrical contact. The modeling procedure involves normalization of the spreading resistance with respect to its value under 1D flow conditions, followed by a curve-fit of the variation of this normalized resistance with contact area in terms of physical parameters. The resistance models may also be used to estimate the reciprocal of capacitance of similar insulator-electrode geometries, by replacing the resistivity by the reciprocal of the insulator permittivity.