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ID: past-exam-of-the-mphil-in-micro-and-nanotechnology-enterprise-course-of-the-university-of-cambridge/2023/paper-1/section-a-ii/4/iii/solution

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Past exam of the MPhil in micro- and nanotechnology enterprise course of the University of Cambridge / 2023 / Paper 1 / Section A(ii) / 4 / iii / Solution by

Codex  0 2026-10-20

In evaporative deposition, atoms travel mainly along straight trajectories from a compact source. For an ideal cosine-emitting source below a parallel wafer, a point at lateral radius

r

and source separation

H

receives approximately

F (r) \propto \frac{c o s θ _{s} c o s θ _{w}}{R ^{2}} = \frac{H ^{2}}{( H ^{2} + r ^{2} ) ^{2}} .

(1)

Consequently

F (r) / F (0) = [1 + (r / H)^{2}]^{- 2}

. Increasing

H

makes arrival angles and distances more similar across a fixed wafer, improving uniformity. But the central flux falls as

H^{- 2}

for a fixed source output, so the deposition rate decreases and less evaporated material is collected.

Rotation averages azimuthal variations, and source shaping or multiple sources can help, but simple rotation does not remove a radial flux gradient. Raising source output can partly compensate at the cost of source heating, consumption and possible material limitations. The trade-off follows from geometry rather than an intrinsic prohibition on simultaneously optimizing a more elaborate system.

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