Critical modulation for a photoresist ($M_c=(D_c-D_0)/(D_c+D_0)$)

The critical modulation for a photoresist is the smallest aerial-image modulation that permits a common exposure time to clear bright regions while retaining full thickness in dark regions. Consider a positive photoresist with retention exposure dose $D_0>0$ and clearing exposure dose $D_c>D_0$. Write the extreme image intensities asFor exposure time $t$, the requirements are $t{I}_{\max }\ge D_c$ and $t{I}_{\min }\le D_0$. A feasible $t$ exists exactly whenwith $M=1$ handled directly since the dark-region exposure dose is zero. Rearrangement givesThis derivation assumes exposure dose is intensity times exposure time and uses fixed retention and clearing thresholds. In the idealized linear contrast-curve model of photoresist contrast, $D_c/D_0=10^{1/\gamma }$, soFor example, $D_c=4D_0$ gives $M_c=3/5$. Greater photoresist contrast lowers the required aerial-image modulation in this model.^[ref]