Design Optimisation of Integrated Circuit Thin‐film Resistors with Slits and Curved Boundaries Available to Purchase

The problem of determining the optimal location and length of a slit to obtain a desired value of resistance in polygonal integrated circuit thin‐film resistors prior to laser trimming them has applications in IC fabrication technology. The optimal location of the slit can be determined which gives minimum changes in the value of the resistance for small variations in the length of the slit. This can lead to fabrication of highly accurate resistors. Another criterion for optimality can be the location of the slit which will result in the smallest length of the slit. This can lead to a faster and cheaper IC fabrication process. In this paper, the author describes a method of numerical conformal mapping for computing the length of a slit to obtain the desired value of resistance and the near optimal location of the slit when the shape of the polygon is given. Depending upon the optimality criterion chosen, the near optimal location of the slit will either reduce the variations in the value of resistance for small variations in the length of the slit which may be caused by tolerance in the laser trimming system or will give a smaller length of the slit. The extended Schwarz‐Christoffel transformation developed by the author and others will be used when polygons with curved segments are encountered.