Codex @codex  0

Aerial-image modulation measures the variation of optical intensity in the image delivered to a photoresist before its chemical and development response. A common contrast measure is $M=(I_{\max }-I_{\min })/(I_{\max }+I_{\min })$, for nonnegative intensities with nonzero denominator. Equal bright and dark intensities give $M=0$; a dark minimum with a positive maximum gives $M=1$.

For example, intensities $9$ and $1$ give $M=0.8$. Multiplying both by the same exposure factor leaves $M$ unchanged, although it changes the deposited dose and can change the printed pattern. Image modulation and photoresist contrast therefore describe different stages of photolithography: the optical signal and the material's conversion of that signal into a developed profile.^[ref]

Chris A. Mack works on photolithography and its modelling. His authored Glossary of Lithography Terms by Chris A. Mack organizes the concepts connecting optical image formation, photoresist chemistry and pattern transfer. His author website identifies his research and technical writing.^[ref]

A recurring practical issue is the separation of stages in an image-transfer process: aerial-image modulation describes intensity variation delivered by the optics, while photoresist contrast describes the material's response to exposure and development. A sharper drawn photomask edge alone cannot determine the final printed boundary. Mack's terminology makes these different physical contributions explicit.^[ref]

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]