A statistical model for determining the minimum size in integrated circuits

A physical-statistical model for determining the minimum linewidth in integrated circuits of any kind is described. The minimum linewidth in integrated circuits is determined on the basis of a physical-statistical model for layout of the circuit pattern. First, the minimum spot size, 2.5 nm, of photon, electron, or ion beams, is determined, based on the Heisenberg uncertainty principle, minimum molecule size of resist, or particle scattering. In a second step, the minimum resolvable distance in the pattern is determined. It is based on two independent measurements of the end points of the distance. Also proximity effects are considered. The resultant minimum distance is about 10 nm. In a third step, the statistics of all the required measurements to define a complex circuit pattern is considered in two extreme cases. In the first case, all measurements are assumed independent. In the second case, complete dependence is assumed corresponding to a repetitive circuit pattern. This procedure determines a minimum linewidth of 70 nm and 30 nm, respectively, assuming 10⁵measurements and tolerances of ±100 percent in linewidth and yield of 37 percent. For integrated semiconductor circuits additional factors enter. Thus for silicon transistor circuits doping fluctuations and bombardment by cosmic rays and natural radioactivity set a minimum linewidth around 100 nm.