A Conformal Mapping Analysis of Polygonal Planar Resistors with Curved Boundaries Available to Purchase

Introduction of curved boundaries in polygonally shaped integrated circuit planar resistors causes a crease in maximum electric field intensities and current densities present in them, and consequently decreases the likelihood of their failure. The presence of curved boundaries can also decrease the area occupied by the resistor. Therefore, polygonal resistors with curved boundaries can be highly desirable in integrated circuits. Resistances of conductors with curved boundaries are readily computed using conformal mapping, particularly the numerically, extended Schwarz‐Christoffel transformation developed by the authors. The resulting algorithm is applicable to polygonal resistors of arbitrary shape and is easily programmable. Several examples are presented. Rapid convergence and accurate results are obtained.