Design for Manufacturability a

Progress in microelectronics over the last several decades has been inTImatelylinked to our ability to accurately measure, model, and predict the physicalproperTIes of solid-state electronic devices. This ability is currently endangeredby the manufacturing and fundamental limitaTIons of nanometer scaletechnology, that result in increasing unpredictability in the physical properTIesof semiconductor devices. Recent years have seen an explosion of interestin Design for Manufacturability (DFM) and in statistical design techniques.This interest is directly attributed to the difficulties of manufacturing of integrated circuits in nanometer scale CMOS technologies with high functionaland parametric yield.The scaling of CMOS technologies brought about the increasing magnitudeof variability of key parameters affecting the performance of integratedcircuits. The large variation can be attributed to several factors. The first isthe rise of multiple systematic sources of parameter variability caused by theinteraction between the manufacturing process and the design attributes. Forexample, optical proximity effects cause polysilicon feature sizes to vary depending on the local layout surroundings, while copper wire thickness stronglydepends on the local wire density because of chemical-mechanical polishing.The second is that while technology scaling reduces the nominal values ofkey process parameters, such as effective channel length, our ability to correspondingly improve manufacturing tolerances, such as mask fabrication errorsand mask overlay control, is limited. This results in an increase in the relativeamount of variations observed. The third, and most profound, reason forthe future increase in parametric variability is that technology is approachingthe regime of fundamental randomness in the behavior of silicon structures.For example, the shrinking volume of silicon that forms the channel of theMOS transistor will soon contain a small countable number of dopant atoms.Because the placement of these dopant atoms is random, the final number ofatoms that end up in the channel of each transistor is a random variable. Thus,the threshold voltage of the transistor, which is determined by the numberof dopant atoms, will also exhibit significant variation, eventually leading tovariation in circuit-level performances, such as delay and power.