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Exposure latitude requirements for high yield with photon flux-limited laser sources

This paper presents an analysis of quantum statistical limits on photolithographic imaging of very large arrays of semiconductor features. In flux limited imaging systems the photon counting statistics contribute to the overall process variation. There is a direct relationship between exposure latitude and sensitivity to photon counting statistics. For example, in an array of 1 million 90 nm contact holes imaged with 20 mJ/cm2 of 157 nm light 1350 of these holes will receive a total dose less than 98% of the mean dose. If the exposure latitude is 4% then these 1350 contacts will print out-of-spec as a result of the Poisson statistical distribution of photon-limited light sources (sometimes called shot-noise). High yield for volume semiconductor manufacturing requires failure rates well below this level. Each new device generation requires more functional transistors than the previous one, increasing approximately linearly. As the imaging wavelength decreases the net number of photons available decreases linearly (assuming constant laser power). The area of a contact hole decreases as the square of the critical dimension. Thus the fraction of chips with at least one contact hole receiving inadequate dose increases approximately as the fourth power of the wavelength. This presents serious implications for 157nm lithography semiconductor yield. Electron imaging systems are not immune to this either, Poisson limited intensity uniformity is nearly identical with that of optical imaging. 157 nm lithography is marginal to photon-statistics limited yield, and 13 nm EUV lithography yield is almost certainly photon limited. In addition, as transistor array size increases the 0.987 ppb failure rate of a 6-sigma process will not be sufficient for high yield. Thus 8 or 9-sigma processing will be needed along with significant improvement in exposure latitude and optimized resist sensitivity will be necessary.