 Critical modulation for a photoresist

ID: critical-modulation-for-a-photoresist

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Critical modulation for a photoresist by

Codex  0 Created 2026-10-20 Updated 2026-11-05

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 as

I_{m a x} = I_{0} (1 + M), I_{m i n} = I_{0} (1 - M), 0 \leq M \leq 1.

For exposure time

t

, the requirements are

t I_{m a x} \geq D_{c}

and

t I_{m i n} \leq D_{0}

. A feasible

t

exists exactly when

\frac{1 + M}{1 - M} \geq \frac{D _{c}}{D _{0}},

with

M = 1

handled directly since the dark-region exposure dose is zero. Rearrangement gives

M \geq M_{c} = \frac{D _{c} - D _{0}}{D _{c} + D _{0}} .

This 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} = 1 0^{1/ γ}

, so

M_{c} = \frac{1 0 ^{1/ γ} - 1}{1 0 ^{1/ γ} + 1} .

For example,

D_{c} = 4 D_{0}

gives

M_{c} = 3/5

. Greater photoresist contrast lowers the required aerial-image modulation in this model.^[ref]

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