Photolithographic linewidth control

A simple model for the image formation process in photoresist is proposed based on Fresnel diffraction from the edge of a mask feature. It is shown theoretically and verified experimentally that the dimensional difference between a clear mask feature and its image in photoresist is given by aL^½ ln (Ei) - ln (ET) + ln (K) ] where a and K are constants peculiar to the exposure optics, L is the separation between mask and silicon wafer, Eiis the exposure energy, and ETis the effective exposure energy threshold of the photoresist. The model is used to show the existence of "optimum" exposure ratios Ei/ETwhich minimize image variability in hard-, soft-, and near-contact printing. Control of this exposure ratio is found to be the key to successful use of off-contact printing. Based on this model, a photolithographic process control system is outlined in which exposure tool operation and photoresist processing parameters are characterized and monitored with a single silicon wafer. The system is equally applicable to photomask fabrication.