 Solution

ID: past-exam-of-the-mphil-in-micro-and-nanotechnology-enterprise-course-of-the-university-of-cambridge/2021/paper-1/4/i/solution

D_{0} = 20 mJ c m^{- 2}

at unit remaining thickness and

D_{c} = 100 mJ c m^{- 2}

at clearing. On the logarithmic dose axis,

γ = \frac{1}{lo g _{10} ( D _{c} / D _{0} )} = \frac{1}{lo g _{10} 5} ≃ 1.43.

The critical image modulation follows by requiring one exposure time to give

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

in a bright region and

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

in a dark region:

\frac{I _{m a x}}{I _{m i n}} \geq \frac{D _{c}}{D _{0}} .

For unit object modulation, this means

M_{c} = \frac{D _{c} - D _{0}}{D _{c} + D _{0}} = \frac{100 - 20}{100 + 20} ≃ 0.667.

The doses are graphical estimates, so extra significant figures would not represent greater measurement accuracy.

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